%PDF-1.4
3 0 obj <<
/Length 1499
>>
stream
1 0 0 1 46.771 548.934 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
1 0 0 1 -280.63 -19.8 cm
0 g 0 G
1 0 0 1 -46.771 -529.134 cm
BT
/F16 10.909 Tf 46.771 518.175 Td[(The)-508(Project)-507(Gutenberg)-508(EBook)-508(of)-508(An)-507(Elementary)-508(Course)-508(in)]TJ 0 -13.549 Td[(Synthetic)-250(Projective)-250(Geometry)-250(by)-250(Lehmer,)-250(Derrick)-250(Norman)]TJ 0 -29.913 Td[(This)-546(eBook)-546(is)-546(for)-546(the)-546(use)-546(of)-546(anyone)-546(anywhere)-547(at)-546(no)-546(cost)]TJ 0 -13.549 Td[(and)-470(with)-470(almost)-470(no)-470(restrictions)-470(whatsoever.)-910(You)-470(may)-470(copy)]TJ 0 -13.549 Td[(it,)-565(give)-503(it)-502(away)-502(or)-502(re-use)-502(it)-503(under)-502(the)-502(terms)-502(of)-502(the)-503(Project)]TJ 0 -13.549 Td[(Gutenberg)-633(License)-632(included)-633(with)-632(this)-633(eBook)-632(or)-633(online)-633(at)]TJ 0 -13.55 Td[(http://www.gutenberg.org/license)]TJ 0 -29.913 Td[(Title:)-500(An)-500(Elementary)-500(Course)-500(in)-500(Synthetic)-500(Projective)]TJ 0 -13.549 Td[(Geometry)]TJ 0 -27.098 Td[(Author:)-500(Lehmer,)-500(Derrick)-500(Norman)]TJ 0 -27.098 Td[(Release)-500(Date:)-500(November)-500(4,)-500(2005)-500([Ebook)-500(17001])]TJ 0 -27.099 Td[(Language:)-500(English)]TJ 0 -40.647 Td[(***START)-500(OF)-500(THE)-500(PROJECT)-500(GUTENBERG)-500(EBOOK)]TJ 0 -13.55 Td[(AN)-500(ELEMENTARY)-500(COURSE)-500(IN)-500(SYNTHETIC)]TJ 0 -13.549 Td[(PROJECTIVE)-500(GEOMETRY***)]TJ
ET
1 0 0 1 46.771 38.782 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
2 0 obj <<
/Type /Page
/Contents 3 0 R
/Resources 1 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 9 0 R
/Annots [ 7 0 R 8 0 R ]
>> endobj
7 0 obj <<
/Type /Annot
/BS << /Type /Border /S /U >> /H /I /C [0 1 1]
/Rect [140.547 431.687 262.463 441.407]
/Subtype /Link
/A << /S /GoTo /D (pglicense) >>
>> endobj
8 0 obj <<
/Type /Annot
/BS << /Type /Border /S /U >> /H /I /C [1 0.5 0.5]
/Rect [46.771 418.138 193.422 427.858]
/Subtype /Link /A << /Type /Action /S /URI /URI (http://www.gutenberg.org/license) >>
>> endobj
4 0 obj <<
/D [2 0 R /XYZ 46.771 529.134 null]
>> endobj
1 0 obj <<
/Font << /F16 6 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
13 0 obj <<
/Length 126
>>
stream
1 0 0 1 93.543 548.934 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
1 0 0 1 -280.63 -510.152 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
12 0 obj <<
/Type /Page
/Contents 13 0 R
/Resources 11 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 9 0 R
>> endobj
11 0 obj <<
/ProcSet [ /PDF ]
>> endobj
16 0 obj <<
/Length 440
>>
stream
1 0 0 1 46.771 548.934 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
1 0 0 1 -327.401 -548.934 cm
BT
/F16 18.959 Tf 46.771 516.375 Td[(An)-253(Elementary)-253(Course)-254(in)-253(Synthetic)]TJ 0 -24.647 Td[(Projective)-250(Geometry)]TJ 0 -43.519 Td[(by)-250(Lehmer,)-250(Derrick)-250(Norman)]TJ/F16 15.781 Tf 0 -51.933 Td[(Edition)-250(1,)-250(\050November)-250(4,)-250(2005\051)]TJ
ET
1 0 0 1 46.771 38.782 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
15 0 obj <<
/Type /Page
/Contents 16 0 R
/Resources 14 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 9 0 R
>> endobj
14 0 obj <<
/Font << /F16 6 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
19 0 obj <<
/Length 126
>>
stream
1 0 0 1 93.543 548.934 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
1 0 0 1 -280.63 -510.152 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
18 0 obj <<
/Type /Page
/Contents 19 0 R
/Resources 17 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 9 0 R
>> endobj
17 0 obj <<
/ProcSet [ /PDF ]
>> endobj
20 0 obj
<< /S /GoTo /D (index1) >>
endobj
23 0 obj
(Preface)
endobj
26 0 obj <<
/Length 4046
>>
stream
1 0 0 1 46.771 548.934 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
1 0 0 1 -327.401 -548.934 cm
BT
/F16 7.97 Tf 337.795 512.811 Td[([iii])]TJ/F16 18.959 Tf -291.024 -68.984 Td[(Preface)]TJ/F16 10.909 Tf 0 -37.089 Td[(The)-298(following)-298(course)-298(is)-298(intended)-298(to)-298(give,)-310(in)-298(as)-298(simple)-299(a)-298(way)-298(as)]TJ 0 -13.549 Td[(possible,)-281(the)-274(essentials)-275(of)-275(synthetic)-274(projective)-275(geometry.)-324(While,)]TJ 0 -13.549 Td[(in)-281(the)-280(main,)-288(the)-281(theory)-280(is)-281(developed)-280(along)-281(the)-280(well-beaten)-281(track)]TJ 0 -13.549 Td[(laid)-366(out)-366(by)-366(the)-366(great)-366(masters)-366(of)-366(the)-366(subject,)-395(it)-366(is)-367(believed)-366(that)]TJ 0 -13.549 Td[(there)-377(has)-377(been)-376(a)-377(slight)-377(smoothing)-377(of)-376(the)-377(road)-377(in)-377(some)-377(places.)]TJ 0 -13.55 Td[(Especially)-405(will)-405(this)-405(be)-404(observed)-405(in)-405(the)-405(chapter)-405(on)-405(Involution.)]TJ 0 -13.549 Td[(The)-367(author)-368(has)-367(never)-367(felt)-368(satisfied)-367(with)-368(the)-367(usual)-367(treatment)-368(of)]TJ 0 -13.549 Td[(that)-248(subject)-248(by)-247(means)-248(of)-248(circles)-248(and)-248(anharmonic)-248(ratios.)-249(A)-248(purely)]TJ 0 -13.549 Td[(projective)-263(notion)-263(ought)-263(not)-262(to)-263(be)-263(based)-263(on)-263(metrical)-263(foundations.)]TJ 0 -13.549 Td[(Metrical)-213(developments)-213(should)-213(be)-213(made)-213(there,)-221(as)-213(elsewhere)-213(in)-213(the)]TJ 0 -13.549 Td[(theory,)-250(by)-250(the)-250(introduction)-250(of)-250(infinitely)-250(distant)-250(elements.)]TJ 11.956 -14.483 Td[(The)-531(author)-530(has)-531(departed)-530(from)-531(the)-530(century-old)-531(custom)-531(of)]TJ -11.956 -13.549 Td[(writing)-218(in)-219(parallel)-218(columns)-218(each)-219(theorem)-218(and)-218(its)-219(dual.)-239(He)-218(has)-219(not)]TJ 0 -13.549 Td[(found)-306(that)-306(it)-306(conduces)-306(to)-305(sharpness)-306(of)-306(vision)-306(to)-306(try)-306(to)-306(focus)-306(his)]TJ 0 -13.55 Td[(eyes)-289(on)-289(two)-289(things)-289(at)-289(once.)-367(Those)-289(who)-289(prefer)-289(the)-289(usual)-289(method)]TJ 0 -13.549 Td[(of)-362(procedure)-362(can,)-390(of)-362(course,)-390(develop)-362(the)-362(two)-362(sets)-362(of)-362(theorems)]TJ 0 -13.549 Td[(side)-204(by)-205(side;)-219(the)-205(author)-204(has)-204(not)-205(found)-204(this)-204(the)-205(better)-204(plan)-204(in)-205(actual)]TJ 0 -13.549 Td[(teaching.)]TJ 11.956 -14.483 Td[(As)-277(regards)-276(nomenclature,)-283(the)-277(author)-276(has)-277(followed)-277(the)-276(lead)-277(of)]TJ -11.956 -13.549 Td[(the)-290(earlier)-290(writers)-290(in)-290(English,)-300(and)-290(has)-290(called)-290(the)-290(system)-291(of)-290(lines)]TJ 0 -13.549 Td[(in)-257(a)-257(plane)-256(which)-257(all)-257(pass)-257(through)-257(a)-257(point)-256(a)]TJ/F20 10.909 Tf 187.386 0 Td[(pencil)-257(of)-257(rays)]TJ/F16 10.909 Tf 62.339 0 Td[(instead)]TJ -249.725 -13.549 Td[(of)-329(a)]TJ/F20 10.909 Tf 21.103 0 Td[(bundle)-329(of)-328(rays)]TJ/F16 10.909 Tf 64.139 0 Td[(,)-348(as)-329(later)-329(writers)-329(seem)-328(inclined)-329(to)-329(do.)-486(For)-329(a)]TJ -85.242 -13.549 Td[(point)-210(considered)-419(as)-210(made)-210(up)-210(of)-210(all)-210(the)-209(lines)-210(and)-210(planes)-210(through)-210(it)]TJ/F16 7.97 Tf 291.024 0 Td[([iv])]TJ/F16 10.909 Tf -291.024 -13.55 Td[(he)-229(has)-230(ventured)-229(to)-230(use)-229(the)-229(term)]TJ/F20 10.909 Tf 136.882 0 Td[(point)-229(system)]TJ/F16 10.909 Tf 54.015 0 Td[(,)-233(as)-230(being)-229(the)-230(natural)]TJ -190.897 -13.549 Td[(dualization)-281(of)-280(the)-281(usual)-281(term)]TJ/F20 10.909 Tf 129.235 0 Td[(plane)-281(system)]TJ/F16 10.909 Tf 56.386 0 Td[(.)-342(He)-281(has)-281(also)-280(rejected)]TJ -185.621 -13.549 Td[(the)-344(term)]TJ/F20 10.909 Tf 40.837 0 Td[(foci)-344(of)-344(an)-345(involution)]TJ/F16 10.909 Tf 91.271 0 Td[(,)-368(and)-344(has)-344(not)-344(used)-344(the)-345(customary)]TJ
ET
1 0 0 1 46.771 38.782 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
25 0 obj <<
/Type /Page
/Contents 26 0 R
/Resources 24 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 9 0 R
>> endobj
21 0 obj <<
/D [25 0 R /XYZ 46.771 529.134 null]
>> endobj
27 0 obj <<
/D [25 0 R /XYZ 46.771 518.175 null]
>> endobj
30 0 obj <<
/D [25 0 R /XYZ 121.036 106.79 null]
>> endobj
24 0 obj <<
/Font << /F16 6 0 R /F20 29 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
33 0 obj <<
/Length 5117
>>
stream
1 0 0 1 93.543 548.934 cm
0 g 0 G
1 0 0 1 -93.543 -548.934 cm
BT
/F16 10.909 Tf 93.543 548.934 Td[(vi)-2171(An)-250(E)-1(lementary)-250(Course)-250(in)-250(Synthetic)-250(Projective)-250(Geometry)]TJ
ET
1 0 0 1 374.173 548.934 cm
0 g 0 G
1 0 0 1 -374.173 -548.934 cm
BT
/F16 10.909 Tf 93.543 518.175 Td[(terms)-227(for)-228(classifying)-227(involutions)]TJ/F21 10.909 Tf 140.773 0 Td[(\024)]TJ/F20 10.909 Tf 10.909 0 Td[(hyperbolic)-227(involution)]TJ/F16 10.909 Tf 93.386 0 Td[(,)]TJ/F20 10.909 Tf 5.257 0 Td[(elliptic)]TJ -250.325 -13.549 Td[(involution)]TJ/F16 10.909 Tf 47.364 0 Td[(and)]TJ/F20 10.909 Tf 18.869 0 Td[(parabolic)-286(involution)]TJ/F16 10.909 Tf 89.789 0 Td[(.)-357(He)-286(has)-285(found)-286(that)-286(all)-285(these)]TJ -156.022 -13.549 Td[(terms)-318(are)-319(very)-318(confusing)-318(to)-318(the)-319(student,)-335(who)-318(inevitably)-318(tries)-319(to)]TJ 0 -13.549 Td[(connect)-250(them)-250(in)-250(some)-250(way)-250(with)-250(the)-250(conic)-250(sections.)]TJ 11.956 -15.186 Td[(Enough)-373(examples)-372(have)-373(been)-373(provided)-373(to)-372(give)-373(the)-373(student)-373(a)]TJ -11.956 -13.549 Td[(clear)-463(grasp)-463(of)-463(the)-463(theory.)-889(Many)-463(are)-463(of)-463(sufficient)-463(generality)]TJ 0 -13.55 Td[(to)-415(serve)-414(as)-415(a)-414(basis)-415(for)-415(individual)-414(investigation)-415(on)-414(the)-415(part)-415(of)]TJ 0 -13.549 Td[(the)-462(student.)-886(Th)-1(us,)-515(the)-462(third)-462(example)-462(at)-462(the)-462(end)-462(of)-462(the)-463(first)]TJ 0 -13.549 Td[(chapter)-376(will)-375(be)-376(found)-375(to)-376(be)-375(very)-376(fruitful)-375(in)-376(interesting)-376(results.)]TJ 0 -13.549 Td[(A)-303(correspo)-1(ndence)-303(is)-304(there)-303(indicated)-304(between)-303(lines)-304(in)-303(space)-304(and)]TJ 0 -13.549 Td[(circles)-284(through)-285(a)-284(fixed)-284(point)-284(in)-285(space.)-352(If)-285(the)-284(student)-284(will)-284(trace)-285(a)]TJ 0 -13.55 Td[(few)-295(of)-295(the)-295(consequences)-295(of)-295(that)-295(correspondence,)-307(and)-295(determine)]TJ 0 -13.549 Td[(what)-362(configurations)-362(of)-362(circles)-362(correspond)-362(to)-362(inte)-1(rsecting)-362(lines,)]TJ 0 -13.549 Td[(to)-392(lines)-393(in)-392(a)-392(plane,)-428(to)-392(lines)-392(of)-393(a)-392(plane)-392(pencil,)-428(to)-392(lines)-393(cutting)]TJ 0 -13.549 Td[(three)-294(skew)-294(lines,)-305(etc.,)-306(he)-294(will)-294(have)-294(acquired)-294(no)-294(little)-294(practice)-295(in)]TJ 0 -13.549 Td[(picturing)-250(to)-250(himself)-250(figures)-250(in)-250(space.)]TJ 11.956 -15.186 Td[(The)-410(writer)-410(has)-410(not)-409(followed)-410(the)-410(usual)-410(practice)-410(of)-410(inserting)]TJ -11.956 -13.549 Td[(historical)-304(notes)-304(at)-303(the)-304(foot)-304(of)-304(the)-304(page,)-317(and)-304(has)-304(tried)-303(instead,)-318(in)]TJ 0 -13.549 Td[(the)-315(last)-315(chapter,)-331(to)-315(give)-314(a)-315(consecutive)-315(account)-315(of)-315(the)-315(history)-315(of)]TJ 0 -13.55 Td[(pure)-323(geometry,)-342(or,)-341(at)-323(least,)-342(of)-323(as)-323(much)-323(of)-323(it)-323(as)-323(the)-323(student)-324(will)]TJ 0 -13.549 Td[(be)-354(able)-355(to)-354(appreciate)-354(who)-355(has)-354(mastered)-354(the)-355(course)-354(as)-354(given)-355(in)]TJ 0 -13.549 Td[(the)-324(preceding)-324(chapters.)-472(One)-324(is)-324(not)-324(apt)-324(to)-324(get)-324(a)-324(very)-324(wide)-324(view)]TJ 0 -13.549 Td[(of)-369(the)-370(history)-369(of)-369(a)-370(subject)-369(by)-369(reading)-370(a)-369(hundred)-739(biographical)]TJ/F16 7.97 Tf -72.755 0 Td[([v])]TJ/F16 10.909 Tf 72.755 -13.549 Td[(footnotes,)-220(arranged)-213(in)-212(no)-213(sort)-213(of)-212(sequence.)-238(The)-212(writer,)-221(moreover,)]TJ 0 -13.55 Td[(feels)-257(that)-257(the)-257(proper)-257(time)-257(to)-257(learn)-257(the)-257(history)-257(of)-257(a)-257(subject)-257(is)-257(after)]TJ 0 -13.549 Td[(the)-250(student)-250(has)-250(some)-250(general)-250(ideas)-250(of)-250(the)-250(subject)-250(itself.)]TJ 11.956 -15.186 Td[(The)-290(course)-289(is)-290(not)-290(intended)-289(to)-290(furnish)-290(an)-290(illustration)-289(of)-290(how)-290(a)]TJ -11.956 -13.549 Td[(subject)-251(may)-250(be)-251(developed,)-251(from)-250(the)-251(smallest)-250(possible)-251(number)-251(of)]TJ 0 -13.549 Td[(fundamental)-224(assumptio)-1(ns.)-241(The)-224(author)-225(is)-224(aware)-225(of)-224(the)-225(importance)]TJ 0 -13.549 Td[(of)-410(work)-409(of)-410(this)-409(sort,)-450(but)-409(he)-410(does)-410(not)-409(believe)-410(it)-409(is)-410(possible)-410(at)]TJ 0 -13.549 Td[(the)-278(present)-278(time)-279(to)-278(write)-278(a)-278(book)-279(along)-278(such)-278(lines)-278(which)-278(shall)-279(be)]TJ 0 -13.549 Td[(of)-355(much)-354(use)-355(for)-355(elementary)-354(students.)-564(For)-355(the)-354(purposes)-355(of)-355(this)]TJ 0 -13.55 Td[(course)-235(the)-235(student)-236(should)-235(have)-235(a)-235(thorough)-235(grounding)-235(in)-236(ordinary)]TJ 0 -13.549 Td[(elementary)-299(geometry)-298(so)-299(far)-299(as)-298(to)-299(include)-299(the)-299(study)-298(of)-299(the)-299(circle)]TJ
ET
1 0 0 1 93.543 38.782 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
32 0 obj <<
/Type /Page
/Contents 33 0 R
/Resources 31 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 9 0 R
>> endobj
36 0 obj <<
/D [32 0 R /XYZ 315.61 216.82 null]
>> endobj
31 0 obj <<
/Font << /F16 6 0 R /F21 35 0 R /F20 29 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
39 0 obj <<
/Length 3708
>>
stream
1 0 0 1 46.771 548.934 cm
0 g 0 G
1 0 0 1 -46.771 -548.934 cm
BT
/F16 10.909 Tf 46.771 548.934 Td[(Preface)-21671(vii)]TJ
ET
1 0 0 1 327.401 548.934 cm
0 g 0 G
1 0 0 1 -327.401 -548.934 cm
BT
/F16 10.909 Tf 46.771 518.175 Td[(and)-236(of)-235(similar)-236(triangles.)-245(No)-236(solid)-236(geometry)-235(is)-236(needed)-236(beyond)-236(the)]TJ 0 -13.549 Td[(little)-221(used)-220(in)-221(the)-221(proof)-220(of)-221(Desargues')-220(theorem)-221(\05025\051,)-226(and,)-227(except)-221(in)]TJ 0 -13.549 Td[(certain)-207(metrical)-207(developments)-206(of)-207(the)-207(general)-207(theory,)-215(there)-207(will)-207(be)]TJ 0 -13.549 Td[(no)-276(call)-275(for)-276(a)-275(knowledge)-276(of)-275(trigonometry)-276(or)-275(analytical)-276(geometry.)]TJ 0 -13.55 Td[(Naturally)-217(the)-217(student)-218(who)-217(is)-217(equipped)-217(with)-217(these)-217(subjects)-217(as)-218(well)]TJ 0 -13.549 Td[(as)-384(with)-385(the)-384(calculus)-384(will)-384(be)-385(a)-384(little)-384(more)-384(mature,)-418(and)-384(may)-385(be)]TJ 0 -13.549 Td[(expected)-373(to)-374(follow)-373(the)-373(course)-374(all)-373(the)-373(more)-373(easily.)-620(The)-374(author)]TJ 0 -13.549 Td[(has)-248(had)-248(no)-247(difficulty,)-249(however,)-248(in)-248(presenting)-247(it)-248(to)-248(students)-248(in)-248(the)]TJ 0 -13.549 Td[(freshman)-250(class)-250(at)-250(the)-250(University)-250(of)-250(California.)]TJ 11.956 -13.55 Td[(The)-227(subject)-227(of)-227(synthetic)-227(projective)-227(geometry)-227(is,)-232(in)-227(the)-227(opinion)]TJ -11.956 -13.549 Td[(of)-404(the)-403(writer,)-442(destined)-404(shortly)-403(to)-404(force)-403(its)-404(way)-403(down)-404(into)-404(the)]TJ 0 -13.549 Td[(secondary)-293(schools;)-314(and)-293(if)-293(this)-293(little)-293(book)-293(helps)-293(to)-293(accelerate)-293(the)]TJ 0 -13.549 Td[(movement,)-263(he)-261(will)-260(feel)-260(amply)-261(repaid)-260(for)-261(the)-260(task)-261(of)-260(working)-261(the)]TJ 0 -13.549 Td[(materials)-228(into)-227(a)-227(form)-228(available)-227(for)-228(such)-227(schools)-228(as)-227(well)-228(as)-227(for)-228(the)]TJ 0 -13.55 Td[(lower)-250(classes)-250(in)-250(the)-250(university.)]TJ/F16 7.97 Tf 291.024 0 Td[([vi])]TJ/F16 10.909 Tf -279.068 -13.549 Td[(The)-166(material)-167(for)-166(the)-166(course)-167(has)-166(been)-167(drawn)-166(from)-166(many)-167(sources.)]TJ -11.956 -13.549 Td[(The)-376(author)-375(is)-376(chiefly)-376(indebted)-375(to)-376(the)-376(classical)-375(works)-376(of)-376(Reye,)]TJ 0 -13.549 Td[(Cremona,)-259(Steiner,)-258(Poncelet,)-259(and)-257(Von)-257(Staudt.)-271(Acknowledgments)]TJ 0 -13.549 Td[(and)-260(thanks)-259(are)-260(also)-259(due)-260(to)-260(Professor)-259(Walter)-260(C.)-259(Eells,)-262(of)-260(the)-260(U.S.)]TJ 0 -13.55 Td[(Naval)-466(Academy)-465(at)-466(Annapolis,)-519(for)-466(his)-465(searching)-466(examination)]TJ 0 -13.549 Td[(and)-318(keen)-318(criticism)-318(of)-318(the)-318(manuscript;)-352(also)-318(to)-318(Professor)-318(Herbert)]TJ 0 -13.549 Td[(Ellsworth)-324(Slaught,)-341(o)-1(f)-323(The)-324(University)-323(of)-324(Chicago,)-342(for)-323(his)-324(many)]TJ 0 -13.549 Td[(valuable)-275(suggestions,)-282(and)-275(to)-276(Professor)-275(B.)-276(M.)-275(Woods)-275(and)-276(Dr.)-326(H.)]TJ 0 -13.549 Td[(N.)-348(Wright,)-374(of)-348(the)-348(University)-349(of)-348(California,)-373(who)-349(have)-348(tried)-349(out)]TJ 0 -13.55 Td[(the)-250(methods)-250(of)-250(presentation,)-250(in)-250(their)-250(own)-250(classes.)]TJ 207.834 -13.549 Td[(D.)-309(N.)-309(LEHMER)]TJ -195.878 -13.549 Td[(B)]TJ/F16 7.97 Tf 7.276 0 Td[(ERKELEY)]TJ/F16 10.909 Tf 36.304 0 Td[(,)-250(C)]TJ/F16 7.97 Tf 12.731 0 Td[(ALIFORNIA)]TJ
ET
1 0 0 1 46.771 38.782 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
38 0 obj <<
/Type /Page
/Contents 39 0 R
/Resources 37 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 41 0 R
>> endobj
40 0 obj <<
/D [38 0 R /XYZ 46.771 326.108 null]
>> endobj
37 0 obj <<
/Font << /F16 6 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
44 0 obj <<
/Length 126
>>
stream
1 0 0 1 93.543 548.934 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
1 0 0 1 -280.63 -510.152 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
43 0 obj <<
/Type /Page
/Contents 44 0 R
/Resources 42 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 41 0 R
>> endobj
42 0 obj <<
/ProcSet [ /PDF ]
>> endobj
45 0 obj
<< /S /GoTo /D (index2) >>
endobj
48 0 obj
(Contents)
endobj
51 0 obj <<
/Length 10136
>>
stream
1 0 0 1 46.771 548.934 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
1 0 0 1 -327.401 -548.934 cm
BT
/F16 18.959 Tf 46.771 479.321 Td[(Contents)]TJ/F16 10.909 Tf 0 -32.635 Td[(Preface)-252(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 446.686 cm
0 g 0 G
1 0 0 1 -321.947 -446.686 cm
BT
/F16 10.909 Tf 321.947 446.686 Td[(v)]TJ
ET
1 0 0 1 327.401 446.686 cm
0 g 0 G
1 0 0 1 -327.401 -446.686 cm
BT
/F16 10.909 Tf 46.771 433.092 Td[(Contents)-444(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 318.914 433.092 cm
0 g 0 G
1 0 0 1 -318.914 -433.092 cm
BT
/F16 10.909 Tf 318.914 433.092 Td[(ix)]TJ
ET
1 0 0 1 327.401 433.092 cm
0 g 0 G
1 0 0 1 -327.401 -433.092 cm
BT
/F16 10.909 Tf 46.771 419.498 Td[(CHAPTER)-250(I)-250(-)-250(ONE-TO-ONE)-250(CORRESPONDENCE)-446(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 419.498 cm
0 g 0 G
1 0 0 1 -321.947 -419.498 cm
BT
/F16 10.909 Tf 321.947 419.498 Td[(1)]TJ
ET
1 0 0 1 327.401 419.498 cm
0 g 0 G
1 0 0 1 -327.401 -419.498 cm
BT
/F16 10.909 Tf 63.135 405.904 Td[(1.)-250(Definition)-250(of)-250(one-to-one)-250(correspondence)-949(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 405.904 cm
0 g 0 G
1 0 0 1 -321.947 -405.904 cm
BT
/F16 10.909 Tf 321.947 405.904 Td[(1)]TJ
ET
1 0 0 1 327.401 405.904 cm
0 g 0 G
1 0 0 1 -327.401 -405.904 cm
BT
/F16 10.909 Tf 63.135 392.31 Td[(2.)-250(Consequences)-250(of)-250(one-to-one)-250(correspondence)-839(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 392.31 cm
0 g 0 G
1 0 0 1 -321.947 -392.31 cm
BT
/F16 10.909 Tf 321.947 392.31 Td[(1)]TJ
ET
1 0 0 1 327.401 392.31 cm
0 g 0 G
1 0 0 1 -327.401 -392.31 cm
BT
/F16 10.909 Tf 63.135 378.716 Td[(3.)-250(Applications)-250(in)-250(mathematics)-556(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 378.716 cm
0 g 0 G
1 0 0 1 -321.947 -378.716 cm
BT
/F16 10.909 Tf 321.947 378.716 Td[(2)]TJ
ET
1 0 0 1 327.401 378.716 cm
0 g 0 G
1 0 0 1 -327.401 -378.716 cm
BT
/F16 10.909 Tf 63.135 365.122 Td[(4.)-250(One-to-one)-250(correspondence)-250(and)-250(enumeration)-728(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 365.122 cm
0 g 0 G
1 0 0 1 -321.947 -365.122 cm
BT
/F16 10.909 Tf 321.947 365.122 Td[(2)]TJ
ET
1 0 0 1 327.401 365.122 cm
0 g 0 G
1 0 0 1 -327.401 -365.122 cm
BT
/F16 10.909 Tf 63.135 351.528 Td[(5.)-250(Correspondence)-250(between)-250(a)-250(part)-250(and)-250(the)-250(whole)-311(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 351.528 cm
0 g 0 G
1 0 0 1 -321.947 -351.528 cm
BT
/F16 10.909 Tf 321.947 351.528 Td[(4)]TJ
ET
1 0 0 1 327.401 351.528 cm
0 g 0 G
1 0 0 1 -327.401 -351.528 cm
BT
/F16 10.909 Tf 63.135 337.934 Td[(6.)-250(Infinitely)-250(distant)-250(point)-805(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 337.934 cm
0 g 0 G
1 0 0 1 -321.947 -337.934 cm
BT
/F16 10.909 Tf 321.947 337.934 Td[(5)]TJ
ET
1 0 0 1 327.401 337.934 cm
0 g 0 G
1 0 0 1 -327.401 -337.934 cm
BT
/F16 10.909 Tf 63.135 324.339 Td[(7.)-250(Axial)-250(pencil;)-250(fundamental)-250(forms)-474(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 324.339 cm
0 g 0 G
1 0 0 1 -321.947 -324.339 cm
BT
/F16 10.909 Tf 321.947 324.339 Td[(5)]TJ
ET
1 0 0 1 327.401 324.339 cm
0 g 0 G
1 0 0 1 -327.401 -324.339 cm
BT
/F16 10.909 Tf 63.135 310.745 Td[(8.)-250(Perspective)-250(position)-917(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 310.745 cm
0 g 0 G
1 0 0 1 -321.947 -310.745 cm
BT
/F16 10.909 Tf 321.947 310.745 Td[(6)]TJ
ET
1 0 0 1 327.401 310.745 cm
0 g 0 G
1 0 0 1 -327.401 -310.745 cm
BT
/F16 10.909 Tf 63.135 297.151 Td[(9.)-250(Projective)-250(relation)-890(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 297.151 cm
0 g 0 G
1 0 0 1 -321.947 -297.151 cm
BT
/F16 10.909 Tf 321.947 297.151 Td[(6)]TJ
ET
1 0 0 1 327.401 297.151 cm
0 g 0 G
1 0 0 1 -327.401 -297.151 cm
BT
/F16 10.909 Tf 63.135 283.557 Td[(10.)-250(Infinity-to-one)-250(correspondence)-587(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 283.557 cm
0 g 0 G
1 0 0 1 -321.947 -283.557 cm
BT
/F16 10.909 Tf 321.947 283.557 Td[(7)]TJ
ET
1 0 0 1 327.401 283.557 cm
0 g 0 G
1 0 0 1 -327.401 -283.557 cm
BT
/F16 10.909 Tf 63.135 269.963 Td[(11.)-250(Infinitudes)-250(of)-250(different)-250(orders)-392(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 269.963 cm
0 g 0 G
1 0 0 1 -321.947 -269.963 cm
BT
/F16 10.909 Tf 321.947 269.963 Td[(7)]TJ
ET
1 0 0 1 327.401 269.963 cm
0 g 0 G
1 0 0 1 -327.401 -269.963 cm
BT
/F16 10.909 Tf 63.135 256.369 Td[(12.)-250(Points)-250(in)-250(a)-250(plane)-361(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 256.369 cm
0 g 0 G
1 0 0 1 -321.947 -256.369 cm
BT
/F16 10.909 Tf 321.947 256.369 Td[(8)]TJ
ET
1 0 0 1 327.401 256.369 cm
0 g 0 G
1 0 0 1 -327.401 -256.369 cm
BT
/F16 10.909 Tf 63.135 242.775 Td[(13.)-250(Lines)-250(through)-250(a)-250(point)-667(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 242.775 cm
0 g 0 G
1 0 0 1 -321.947 -242.775 cm
BT
/F16 10.909 Tf 321.947 242.775 Td[(8)]TJ
ET
1 0 0 1 327.401 242.775 cm
0 g 0 G
1 0 0 1 -327.401 -242.775 cm
BT
/F16 10.909 Tf 63.135 229.181 Td[(14.)-250(Planes)-250(through)-250(a)-250(point)-278(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 229.181 cm
0 g 0 G
1 0 0 1 -321.947 -229.181 cm
BT
/F16 10.909 Tf 321.947 229.181 Td[(8)]TJ
ET
1 0 0 1 327.401 229.181 cm
0 g 0 G
1 0 0 1 -327.401 -229.181 cm
BT
/F16 10.909 Tf 63.135 215.587 Td[(15.)-250(Lines)-250(in)-250(a)-250(plane)-640(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 215.587 cm
0 g 0 G
1 0 0 1 -321.947 -215.587 cm
BT
/F16 10.909 Tf 321.947 215.587 Td[(8)]TJ
ET
1 0 0 1 327.401 215.587 cm
0 g 0 G
1 0 0 1 -327.401 -215.587 cm
BT
/F16 10.909 Tf 63.135 201.993 Td[(16.)-250(Plane)-250(system)-250(and)-250(point)-250(system)-722(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 201.993 cm
0 g 0 G
1 0 0 1 -321.947 -201.993 cm
BT
/F16 10.909 Tf 321.947 201.993 Td[(9)]TJ
ET
1 0 0 1 327.401 201.993 cm
0 g 0 G
1 0 0 1 -327.401 -201.993 cm
BT
/F16 10.909 Tf 63.135 188.399 Td[(17.)-250(Planes)-250(in)-250(space)-890(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 188.399 cm
0 g 0 G
1 0 0 1 -321.947 -188.399 cm
BT
/F16 10.909 Tf 321.947 188.399 Td[(9)]TJ
ET
1 0 0 1 327.401 188.399 cm
0 g 0 G
1 0 0 1 -327.401 -188.399 cm
BT
/F16 10.909 Tf 63.135 174.805 Td[(18.)-250(Points)-250(of)-250(space)-945(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 321.947 174.805 cm
0 g 0 G
1 0 0 1 -321.947 -174.805 cm
BT
/F16 10.909 Tf 321.947 174.805 Td[(9)]TJ
ET
1 0 0 1 327.401 174.805 cm
0 g 0 G
1 0 0 1 -327.401 -174.805 cm
BT
/F16 10.909 Tf 63.135 161.211 Td[(19.)-250(Space)-250(system)-834(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 161.211 cm
0 g 0 G
1 0 0 1 -316.492 -161.211 cm
BT
/F16 10.909 Tf 316.492 161.211 Td[(10)]TJ
ET
1 0 0 1 327.401 161.211 cm
0 g 0 G
1 0 0 1 -327.401 -161.211 cm
BT
/F16 10.909 Tf 63.135 147.617 Td[(20.)-250(Lines)-250(in)-250(space)-529(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 147.617 cm
0 g 0 G
1 0 0 1 -316.492 -147.617 cm
BT
/F16 10.909 Tf 316.492 147.617 Td[(10)]TJ
ET
1 0 0 1 327.401 147.617 cm
0 g 0 G
1 0 0 1 -327.401 -147.617 cm
BT
/F16 10.909 Tf 63.135 134.023 Td[(21.)-250(Correspondence)-250(between)-250(points)-250(and)-250(numbers)-837(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 134.023 cm
0 g 0 G
1 0 0 1 -316.492 -134.023 cm
BT
/F16 10.909 Tf 316.492 134.023 Td[(10)]TJ
ET
1 0 0 1 327.401 134.023 cm
0 g 0 G
1 0 0 1 -327.401 -134.023 cm
BT
/F16 10.909 Tf 63.135 120.429 Td[(22.)-250(Elements)-250(at)-250(infinity)-611(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 120.429 cm
0 g 0 G
1 0 0 1 -316.492 -120.429 cm
BT
/F16 10.909 Tf 316.492 120.429 Td[(11)]TJ
ET
1 0 0 1 327.401 120.429 cm
0 g 0 G
1 0 0 1 -327.401 -120.429 cm
BT
/F16 10.909 Tf 63.135 106.835 Td[(PROBLEMS)-971(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 106.835 cm
0 g 0 G
1 0 0 1 -316.492 -106.835 cm
BT
/F16 10.909 Tf 316.492 106.835 Td[(12)]TJ
ET
1 0 0 1 327.401 106.835 cm
0 g 0 G
1 0 0 1 -327.401 -106.835 cm
BT
/F16 10.909 Tf 46.771 93.241 Td[(CHAPTER)-702(II)-702(-)-703(RELATIONS)-702(BETWEEN)-702(FUNDA-)]TJ 15.273 -13.549 Td[(MENTAL)-208(FORMS)-208(IN)-208(ONE-TO-ONE)-208(CORRESPON-)]TJ 0 -13.55 Td[(DENCE)-250(WITH)-250(EACH)-250(OTHER)-352(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 66.142 cm
0 g 0 G
1 0 0 1 -316.492 -66.142 cm
BT
/F16 10.909 Tf 316.492 66.142 Td[(14)]TJ
ET
1 0 0 1 327.401 66.142 cm
0 g 0 G
1 0 0 1 -280.63 -27.36 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
50 0 obj <<
/Type /Page
/Contents 51 0 R
/Resources 49 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 41 0 R
>> endobj
46 0 obj <<
/D [50 0 R /XYZ 46.771 529.134 null]
>> endobj
49 0 obj <<
/Font << /F16 6 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
54 0 obj <<
/Length 11292
>>
stream
1 0 0 1 93.543 548.934 cm
0 g 0 G
1 0 0 1 -93.543 -548.934 cm
BT
/F16 10.909 Tf 93.543 548.934 Td[(x)-2449(An)-250(E)-1(lementary)-250(Course)-250(in)-250(Synthetic)-250(Projective)-250(Geometry)]TJ
ET
1 0 0 1 374.173 548.934 cm
0 g 0 G
1 0 0 1 -374.173 -548.934 cm
BT
/F16 10.909 Tf 109.907 518.175 Td[(23.)-250(Seven)-250(fundamental)-250(forms)-474(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 518.175 cm
0 g 0 G
1 0 0 1 -363.264 -518.175 cm
BT
/F16 10.909 Tf 363.264 518.175 Td[(14)]TJ
ET
1 0 0 1 374.173 518.175 cm
0 g 0 G
1 0 0 1 -374.173 -518.175 cm
BT
/F16 10.909 Tf 109.907 504.457 Td[(24.)-250(Projective)-250(properties)-946(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 504.457 cm
0 g 0 G
1 0 0 1 -363.264 -504.457 cm
BT
/F16 10.909 Tf 363.264 504.457 Td[(14)]TJ
ET
1 0 0 1 374.173 504.457 cm
0 g 0 G
1 0 0 1 -374.173 -504.457 cm
BT
/F16 10.909 Tf 109.907 490.738 Td[(25.)-250(Desargues's)-250(theorem)-989(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 490.738 cm
0 g 0 G
1 0 0 1 -363.264 -490.738 cm
BT
/F16 10.909 Tf 363.264 490.738 Td[(15)]TJ
ET
1 0 0 1 374.173 490.738 cm
0 g 0 G
1 0 0 1 -374.173 -490.738 cm
BT
/F16 10.909 Tf 109.907 477.02 Td[(26.)-707(Fundamental)-402(theorem)-403(concerning)-402(two)-403(complete)]TJ 25.091 -13.55 Td[(quadrangles)-618(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 463.47 cm
0 g 0 G
1 0 0 1 -363.264 -463.47 cm
BT
/F16 10.909 Tf 363.264 463.47 Td[(16)]TJ
ET
1 0 0 1 374.173 463.47 cm
0 g 0 G
1 0 0 1 -374.173 -463.47 cm
BT
/F16 10.909 Tf 109.907 449.752 Td[(27.)-250(Importance)-250(of)-250(the)-250(theorem)-864(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 449.752 cm
0 g 0 G
1 0 0 1 -363.264 -449.752 cm
BT
/F16 10.909 Tf 363.264 449.752 Td[(18)]TJ
ET
1 0 0 1 374.173 449.752 cm
0 g 0 G
1 0 0 1 -374.173 -449.752 cm
BT
/F16 10.909 Tf 109.907 436.033 Td[(28.)-250(Restatement)-250(of)-250(the)-250(theorem)-474(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 436.033 cm
0 g 0 G
1 0 0 1 -363.264 -436.033 cm
BT
/F16 10.909 Tf 363.264 436.033 Td[(18)]TJ
ET
1 0 0 1 374.173 436.033 cm
0 g 0 G
1 0 0 1 -374.173 -436.033 cm
BT
/F16 10.909 Tf 109.907 422.315 Td[(29.)-250(Four)-250(harmonic)-250(points)-639(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 422.315 cm
0 g 0 G
1 0 0 1 -363.264 -422.315 cm
BT
/F16 10.909 Tf 363.264 422.315 Td[(18)]TJ
ET
1 0 0 1 374.173 422.315 cm
0 g 0 G
1 0 0 1 -374.173 -422.315 cm
BT
/F16 10.909 Tf 109.907 408.596 Td[(30.)-250(Harmonic)-250(conjugates)-724(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 408.596 cm
0 g 0 G
1 0 0 1 -363.264 -408.596 cm
BT
/F16 10.909 Tf 363.264 408.596 Td[(20)]TJ
ET
1 0 0 1 374.173 408.596 cm
0 g 0 G
1 0 0 1 -374.173 -408.596 cm
BT
/F16 10.909 Tf 109.907 394.878 Td[(31.)-250(Importance)-250(of)-250(the)-250(notion)-250(of)-250(four)-250(harmonic)-250(points)-864(.)]TJ
ET
1 0 0 1 363.264 394.878 cm
0 g 0 G
1 0 0 1 -363.264 -394.878 cm
BT
/F16 10.909 Tf 363.264 394.878 Td[(20)]TJ
ET
1 0 0 1 374.173 394.878 cm
0 g 0 G
1 0 0 1 -374.173 -394.878 cm
BT
/F16 10.909 Tf 109.907 381.159 Td[(32.)-250(Projective)-250(invariance)-250(of)-250(four)-250(harmonic)-250(points)-809(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 381.159 cm
0 g 0 G
1 0 0 1 -363.264 -381.159 cm
BT
/F16 10.909 Tf 363.264 381.159 Td[(20)]TJ
ET
1 0 0 1 374.173 381.159 cm
0 g 0 G
1 0 0 1 -374.173 -381.159 cm
BT
/F16 10.909 Tf 109.907 367.441 Td[(33.)-250(Four)-250(harmonic)-250(lines)-445(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 367.441 cm
0 g 0 G
1 0 0 1 -363.264 -367.441 cm
BT
/F16 10.909 Tf 363.264 367.441 Td[(21)]TJ
ET
1 0 0 1 374.173 367.441 cm
0 g 0 G
1 0 0 1 -374.173 -367.441 cm
BT
/F16 10.909 Tf 109.907 353.722 Td[(34.)-250(Four)-250(harmonic)-250(planes)-529(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 353.722 cm
0 g 0 G
1 0 0 1 -363.264 -353.722 cm
BT
/F16 10.909 Tf 363.264 353.722 Td[(21)]TJ
ET
1 0 0 1 374.173 353.722 cm
0 g 0 G
1 0 0 1 -374.173 -353.722 cm
BT
/F16 10.909 Tf 109.907 340.004 Td[(35.)-250(Summary)-250(of)-250(results)-667(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 340.004 cm
0 g 0 G
1 0 0 1 -363.264 -340.004 cm
BT
/F16 10.909 Tf 363.264 340.004 Td[(21)]TJ
ET
1 0 0 1 374.173 340.004 cm
0 g 0 G
1 0 0 1 -374.173 -340.004 cm
BT
/F16 10.909 Tf 109.907 326.285 Td[(36.)-250(Definition)-250(of)-250(projectivity)-695(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 326.285 cm
0 g 0 G
1 0 0 1 -363.264 -326.285 cm
BT
/F16 10.909 Tf 363.264 326.285 Td[(22)]TJ
ET
1 0 0 1 374.173 326.285 cm
0 g 0 G
1 0 0 1 -374.173 -326.285 cm
BT
/F16 10.909 Tf 109.907 312.567 Td[(37.)-250(Correspondence)-250(between)-250(harmonic)-250(conjugates)-366(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 312.567 cm
0 g 0 G
1 0 0 1 -363.264 -312.567 cm
BT
/F16 10.909 Tf 363.264 312.567 Td[(22)]TJ
ET
1 0 0 1 374.173 312.567 cm
0 g 0 G
1 0 0 1 -374.173 -312.567 cm
BT
/F16 10.909 Tf 109.907 298.848 Td[(38.)-250(Separation)-250(of)-250(harmonic)-250(conjugates)-586(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 298.848 cm
0 g 0 G
1 0 0 1 -363.264 -298.848 cm
BT
/F16 10.909 Tf 363.264 298.848 Td[(23)]TJ
ET
1 0 0 1 374.173 298.848 cm
0 g 0 G
1 0 0 1 -374.173 -298.848 cm
BT
/F16 10.909 Tf 109.907 285.13 Td[(39.)-250(Harmonic)-250(conjugate)-250(of)-250(the)-250(point)-250(at)-250(infinity)-335(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 285.13 cm
0 g 0 G
1 0 0 1 -363.264 -285.13 cm
BT
/F16 10.909 Tf 363.264 285.13 Td[(23)]TJ
ET
1 0 0 1 374.173 285.13 cm
0 g 0 G
1 0 0 1 -374.173 -285.13 cm
BT
/F16 10.909 Tf 109.907 271.411 Td[(40.)-247(Projective)-241(theorems)-240(and)-241(metrical)-241(theorems.)-247(Linear)]TJ 25.091 -13.549 Td[(construction)-506(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 257.862 cm
0 g 0 G
1 0 0 1 -363.264 -257.862 cm
BT
/F16 10.909 Tf 363.264 257.862 Td[(24)]TJ
ET
1 0 0 1 374.173 257.862 cm
0 g 0 G
1 0 0 1 -374.173 -257.862 cm
BT
/F16 10.909 Tf 109.907 244.144 Td[(41.)-250(Parallels)-250(and)-250(mid-points)-278(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 244.144 cm
0 g 0 G
1 0 0 1 -363.264 -244.144 cm
BT
/F16 10.909 Tf 363.264 244.144 Td[(25)]TJ
ET
1 0 0 1 374.173 244.144 cm
0 g 0 G
1 0 0 1 -374.173 -244.144 cm
BT
/F16 10.909 Tf 109.907 230.425 Td[(42.)-250(Division)-250(of)-250(segment)-250(into)-250(equal)-250(parts)-723(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 230.425 cm
0 g 0 G
1 0 0 1 -363.264 -230.425 cm
BT
/F16 10.909 Tf 363.264 230.425 Td[(26)]TJ
ET
1 0 0 1 374.173 230.425 cm
0 g 0 G
1 0 0 1 -374.173 -230.425 cm
BT
/F16 10.909 Tf 109.907 216.707 Td[(43.)-250(Numerical)-250(relations)-585(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 216.707 cm
0 g 0 G
1 0 0 1 -363.264 -216.707 cm
BT
/F16 10.909 Tf 363.264 216.707 Td[(26)]TJ
ET
1 0 0 1 374.173 216.707 cm
0 g 0 G
1 0 0 1 -374.173 -216.707 cm
BT
/F16 10.909 Tf 109.907 202.988 Td[(44.)-250(Algebraic)-250(formula)-250(connecting)-250(four)-250(harmonic)-250(points)]TJ
ET
1 0 0 1 363.264 202.988 cm
0 g 0 G
1 0 0 1 -363.264 -202.988 cm
BT
/F16 10.909 Tf 363.264 202.988 Td[(26)]TJ
ET
1 0 0 1 374.173 202.988 cm
0 g 0 G
1 0 0 1 -374.173 -202.988 cm
BT
/F16 10.909 Tf 109.907 189.27 Td[(45.)-250(Further)-250(formulae)-946(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 189.27 cm
0 g 0 G
1 0 0 1 -363.264 -189.27 cm
BT
/F16 10.909 Tf 363.264 189.27 Td[(28)]TJ
ET
1 0 0 1 374.173 189.27 cm
0 g 0 G
1 0 0 1 -374.173 -189.27 cm
BT
/F16 10.909 Tf 109.907 175.551 Td[(46.)-250(Anharmonic)-250(ratio)-668(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 175.551 cm
0 g 0 G
1 0 0 1 -363.264 -175.551 cm
BT
/F16 10.909 Tf 363.264 175.551 Td[(28)]TJ
ET
1 0 0 1 374.173 175.551 cm
0 g 0 G
1 0 0 1 -374.173 -175.551 cm
BT
/F16 10.909 Tf 109.907 161.833 Td[(PROBLEMS)-971(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 161.833 cm
0 g 0 G
1 0 0 1 -363.264 -161.833 cm
BT
/F16 10.909 Tf 363.264 161.833 Td[(29)]TJ
ET
1 0 0 1 374.173 161.833 cm
0 g 0 G
1 0 0 1 -374.173 -161.833 cm
BT
/F16 10.909 Tf 93.543 148.114 Td[(CHAPTER)-446(III)-446(-)-446(COMBINATION)-446(OF)-446(TW)-1(O)-446(PROJEC-)]TJ 15.273 -13.549 Td[(TIVELY)-250(RELATED)-250(FUNDAMENTAL)-250(FORMS)-685(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 134.565 cm
0 g 0 G
1 0 0 1 -363.264 -134.565 cm
BT
/F16 10.909 Tf 363.264 134.565 Td[(31)]TJ
ET
1 0 0 1 374.173 134.565 cm
0 g 0 G
1 0 0 1 -374.173 -134.565 cm
BT
/F16 10.909 Tf 109.907 120.847 Td[(47.)-2212(Superposed)-904(fundamental)-904(forms.)-2213(Self-)]TJ 25.091 -13.55 Td[(corresponding)-250(elements)-424(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 107.297 cm
0 g 0 G
1 0 0 1 -363.264 -107.297 cm
BT
/F16 10.909 Tf 363.264 107.297 Td[(31)]TJ
ET
1 0 0 1 374.173 107.297 cm
0 g 0 G
1 0 0 1 -374.173 -107.297 cm
BT
/F16 10.909 Tf 109.907 93.579 Td[(48.)-250(Special)-250(case)-585(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 93.579 cm
0 g 0 G
1 0 0 1 -363.264 -93.579 cm
BT
/F16 10.909 Tf 363.264 93.579 Td[(32)]TJ
ET
1 0 0 1 374.173 93.579 cm
0 g 0 G
1 0 0 1 -374.173 -93.579 cm
BT
/F16 10.909 Tf 109.907 79.86 Td[(49.)-250(Fundamental)-250(theorem.)-250(Postulate)-250(of)-250(continuity)-695(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 79.86 cm
0 g 0 G
1 0 0 1 -363.264 -79.86 cm
BT
/F16 10.909 Tf 363.264 79.86 Td[(33)]TJ
ET
1 0 0 1 374.173 79.86 cm
0 g 0 G
1 0 0 1 -374.173 -79.86 cm
BT
/F16 10.909 Tf 109.907 66.142 Td[(50.)-250(Extension)-250(of)-250(theorem)-250(to)-250(pencils)-250(of)-250(rays)-250(and)-250(planes)-281(.)]TJ
ET
1 0 0 1 363.264 66.142 cm
0 g 0 G
1 0 0 1 -363.264 -66.142 cm
BT
/F16 10.909 Tf 363.264 66.142 Td[(34)]TJ
ET
1 0 0 1 374.173 66.142 cm
0 g 0 G
1 0 0 1 -280.63 -27.36 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
53 0 obj <<
/Type /Page
/Contents 54 0 R
/Resources 52 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 41 0 R
>> endobj
52 0 obj <<
/Font << /F16 6 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
57 0 obj <<
/Length 11922
>>
stream
1 0 0 1 46.771 548.934 cm
0 g 0 G
1 0 0 1 -46.771 -548.934 cm
BT
/F16 10.909 Tf 46.771 548.934 Td[(Contents)-21391(xi)]TJ
ET
1 0 0 1 327.401 548.934 cm
0 g 0 G
1 0 0 1 -327.401 -548.934 cm
BT
/F16 10.909 Tf 63.135 518.175 Td[(51.)-302(Projectiv)-1(e)-267(point-rows)-268(having)-267(a)-268(self-corresponding)]TJ 25.091 -13.549 Td[(point)-250(in)-250(common)-866(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 504.626 cm
0 g 0 G
1 0 0 1 -316.492 -504.626 cm
BT
/F16 10.909 Tf 316.492 504.626 Td[(34)]TJ
ET
1 0 0 1 327.401 504.626 cm
0 g 0 G
1 0 0 1 -327.401 -504.626 cm
BT
/F16 10.909 Tf 63.135 490.918 Td[(52.)-250(Point-rows)-250(in)-250(perspective)-250(position)-806(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 490.918 cm
0 g 0 G
1 0 0 1 -316.492 -490.918 cm
BT
/F16 10.909 Tf 316.492 490.918 Td[(35)]TJ
ET
1 0 0 1 327.401 490.918 cm
0 g 0 G
1 0 0 1 -327.401 -490.918 cm
BT
/F16 10.909 Tf 63.135 477.211 Td[(53.)-250(Pencils)-250(in)-250(perspective)-250(position)-806(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 477.211 cm
0 g 0 G
1 0 0 1 -316.492 -477.211 cm
BT
/F16 10.909 Tf 316.492 477.211 Td[(35)]TJ
ET
1 0 0 1 327.401 477.211 cm
0 g 0 G
1 0 0 1 -327.401 -477.211 cm
BT
/F16 10.909 Tf 63.135 463.503 Td[(54.)-250(Axial)-250(pencils)-250(in)-250(perspective)-250(position)-640(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 463.503 cm
0 g 0 G
1 0 0 1 -316.492 -463.503 cm
BT
/F16 10.909 Tf 316.492 463.503 Td[(35)]TJ
ET
1 0 0 1 327.401 463.503 cm
0 g 0 G
1 0 0 1 -327.401 -463.503 cm
BT
/F16 10.909 Tf 63.135 449.796 Td[(55.)-250(Point-row)-250(of)-250(the)-250(second)-250(order)-308(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 449.796 cm
0 g 0 G
1 0 0 1 -316.492 -449.796 cm
BT
/F16 10.909 Tf 316.492 449.796 Td[(36)]TJ
ET
1 0 0 1 327.401 449.796 cm
0 g 0 G
1 0 0 1 -327.401 -449.796 cm
BT
/F16 10.909 Tf 63.135 436.088 Td[(56.)-250(Degeneration)-250(of)-250(locus)-419(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 436.088 cm
0 g 0 G
1 0 0 1 -316.492 -436.088 cm
BT
/F16 10.909 Tf 316.492 436.088 Td[(36)]TJ
ET
1 0 0 1 327.401 436.088 cm
0 g 0 G
1 0 0 1 -327.401 -436.088 cm
BT
/F16 10.909 Tf 63.135 422.38 Td[(57.)-250(Pencils)-250(of)-250(rays)-250(of)-250(the)-250(second)-250(order)-670(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 422.38 cm
0 g 0 G
1 0 0 1 -316.492 -422.38 cm
BT
/F16 10.909 Tf 316.492 422.38 Td[(36)]TJ
ET
1 0 0 1 327.401 422.38 cm
0 g 0 G
1 0 0 1 -327.401 -422.38 cm
BT
/F16 10.909 Tf 63.135 408.673 Td[(58.)-250(Degenerate)-250(case)-476(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 408.673 cm
0 g 0 G
1 0 0 1 -316.492 -408.673 cm
BT
/F16 10.909 Tf 316.492 408.673 Td[(37)]TJ
ET
1 0 0 1 327.401 408.673 cm
0 g 0 G
1 0 0 1 -327.401 -408.673 cm
BT
/F16 10.909 Tf 63.135 394.965 Td[(59.)-250(Cone)-250(of)-250(the)-250(second)-250(order)-697(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 394.965 cm
0 g 0 G
1 0 0 1 -316.492 -394.965 cm
BT
/F16 10.909 Tf 316.492 394.965 Td[(37)]TJ
ET
1 0 0 1 327.401 394.965 cm
0 g 0 G
1 0 0 1 -327.401 -394.965 cm
BT
/F16 10.909 Tf 63.135 381.258 Td[(PROBLEMS)-971(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 381.258 cm
0 g 0 G
1 0 0 1 -316.492 -381.258 cm
BT
/F16 10.909 Tf 316.492 381.258 Td[(38)]TJ
ET
1 0 0 1 327.401 381.258 cm
0 g 0 G
1 0 0 1 -327.401 -381.258 cm
BT
/F16 10.909 Tf 46.771 367.55 Td[(CHAPTER)-208(IV)-207(-)-208(POINT-ROWS)-208(OF)-207(THE)-208(SECOND)-208(ORDER)]TJ
ET
1 0 0 1 316.492 367.55 cm
0 g 0 G
1 0 0 1 -316.492 -367.55 cm
BT
/F16 10.909 Tf 316.492 367.55 Td[(42)]TJ
ET
1 0 0 1 327.401 367.55 cm
0 g 0 G
1 0 0 1 -327.401 -367.55 cm
BT
/F16 10.909 Tf 63.135 353.843 Td[(60.)-250(Point-row)-250(of)-250(the)-250(second)-250(order)-250(defined)-809(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 353.843 cm
0 g 0 G
1 0 0 1 -316.492 -353.843 cm
BT
/F16 10.909 Tf 316.492 353.843 Td[(42)]TJ
ET
1 0 0 1 327.401 353.843 cm
0 g 0 G
1 0 0 1 -327.401 -353.843 cm
BT
/F16 10.909 Tf 63.135 340.135 Td[(61.)-250(Tangent)-250(line)-473(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 340.135 cm
0 g 0 G
1 0 0 1 -316.492 -340.135 cm
BT
/F16 10.909 Tf 316.492 340.135 Td[(42)]TJ
ET
1 0 0 1 327.401 340.135 cm
0 g 0 G
1 0 0 1 -327.401 -340.135 cm
BT
/F16 10.909 Tf 63.135 326.428 Td[(62.)-250(Determination)-250(of)-250(the)-250(locus)-807(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 326.428 cm
0 g 0 G
1 0 0 1 -316.492 -326.428 cm
BT
/F16 10.909 Tf 316.492 326.428 Td[(43)]TJ
ET
1 0 0 1 327.401 326.428 cm
0 g 0 G
1 0 0 1 -327.401 -326.428 cm
BT
/F16 10.909 Tf 63.135 312.72 Td[(63.)-250(Restatement)-250(of)-250(the)-250(problem)-418(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 312.72 cm
0 g 0 G
1 0 0 1 -316.492 -312.72 cm
BT
/F16 10.909 Tf 316.492 312.72 Td[(43)]TJ
ET
1 0 0 1 327.401 312.72 cm
0 g 0 G
1 0 0 1 -327.401 -312.72 cm
BT
/F16 10.909 Tf 63.135 299.012 Td[(64.)-250(Solution)-250(of)-250(the)-250(fundamental)-250(problem)-473(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 299.012 cm
0 g 0 G
1 0 0 1 -316.492 -299.012 cm
BT
/F16 10.909 Tf 316.492 299.012 Td[(43)]TJ
ET
1 0 0 1 327.401 299.012 cm
0 g 0 G
1 0 0 1 -327.401 -299.012 cm
BT
/F16 10.909 Tf 63.135 285.305 Td[(65.)-250(Different)-250(constructions)-250(for)-250(the)-250(figure)-476(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 285.305 cm
0 g 0 G
1 0 0 1 -316.492 -285.305 cm
BT
/F16 10.909 Tf 316.492 285.305 Td[(44)]TJ
ET
1 0 0 1 327.401 285.305 cm
0 g 0 G
1 0 0 1 -327.401 -285.305 cm
BT
/F16 10.909 Tf 63.135 271.597 Td[(66.)-250(Lines)-250(joining)-250(four)-250(points)-250(of)-250(the)-250(locus)-250(to)-250(a)-250(fifth)-473(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 271.597 cm
0 g 0 G
1 0 0 1 -316.492 -271.597 cm
BT
/F16 10.909 Tf 316.492 271.597 Td[(45)]TJ
ET
1 0 0 1 327.401 271.597 cm
0 g 0 G
1 0 0 1 -327.401 -271.597 cm
BT
/F16 10.909 Tf 63.135 257.89 Td[(67.)-250(Restatement)-250(of)-250(the)-250(theorem)-474(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 257.89 cm
0 g 0 G
1 0 0 1 -316.492 -257.89 cm
BT
/F16 10.909 Tf 316.492 257.89 Td[(45)]TJ
ET
1 0 0 1 327.401 257.89 cm
0 g 0 G
1 0 0 1 -327.401 -257.89 cm
BT
/F16 10.909 Tf 63.135 244.182 Td[(68.)-250(Further)-250(important)-250(theorem)-890(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 244.182 cm
0 g 0 G
1 0 0 1 -316.492 -244.182 cm
BT
/F16 10.909 Tf 316.492 244.182 Td[(45)]TJ
ET
1 0 0 1 327.401 244.182 cm
0 g 0 G
1 0 0 1 -327.401 -244.182 cm
BT
/F16 10.909 Tf 63.135 230.475 Td[(69.)-250(Pascal's)-250(theorem)-349(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 230.475 cm
0 g 0 G
1 0 0 1 -316.492 -230.475 cm
BT
/F16 10.909 Tf 316.492 230.475 Td[(45)]TJ
ET
1 0 0 1 327.401 230.475 cm
0 g 0 G
1 0 0 1 -327.401 -230.475 cm
BT
/F16 10.909 Tf 63.135 216.767 Td[(70.)-250(Permutation)-250(of)-250(points)-250(in)-250(Pascal's)-250(theorem)-904(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 216.767 cm
0 g 0 G
1 0 0 1 -316.492 -216.767 cm
BT
/F16 10.909 Tf 316.492 216.767 Td[(46)]TJ
ET
1 0 0 1 327.401 216.767 cm
0 g 0 G
1 0 0 1 -327.401 -216.767 cm
BT
/F16 10.909 Tf 63.135 203.059 Td[(71.)-250(Harmonic)-250(points)-250(on)-250(a)-250(point-row)-250(of)-250(the)-250(second)-250(order)]TJ
ET
1 0 0 1 316.492 203.059 cm
0 g 0 G
1 0 0 1 -316.492 -203.059 cm
BT
/F16 10.909 Tf 316.492 203.059 Td[(47)]TJ
ET
1 0 0 1 327.401 203.059 cm
0 g 0 G
1 0 0 1 -327.401 -203.059 cm
BT
/F16 10.909 Tf 63.135 189.352 Td[(72.)-250(Determination)-250(of)-250(the)-250(locus)-807(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 189.352 cm
0 g 0 G
1 0 0 1 -316.492 -189.352 cm
BT
/F16 10.909 Tf 316.492 189.352 Td[(48)]TJ
ET
1 0 0 1 327.401 189.352 cm
0 g 0 G
1 0 0 1 -327.401 -189.352 cm
BT
/F16 10.909 Tf 63.135 175.644 Td[(73.)-250(Circles)-250(and)-250(conics)-250(as)-250(point-rows)-250(of)-250(the)-250(second)-250(order)]TJ
ET
1 0 0 1 316.492 175.644 cm
0 g 0 G
1 0 0 1 -316.492 -175.644 cm
BT
/F16 10.909 Tf 316.492 175.644 Td[(48)]TJ
ET
1 0 0 1 327.401 175.644 cm
0 g 0 G
1 0 0 1 -327.401 -175.644 cm
BT
/F16 10.909 Tf 63.135 161.937 Td[(74.)-250(Conic)-250(through)-250(five)-250(points)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 161.937 cm
0 g 0 G
1 0 0 1 -316.492 -161.937 cm
BT
/F16 10.909 Tf 316.492 161.937 Td[(49)]TJ
ET
1 0 0 1 327.401 161.937 cm
0 g 0 G
1 0 0 1 -327.401 -161.937 cm
BT
/F16 10.909 Tf 63.135 148.229 Td[(75.)-250(Tangent)-250(to)-250(a)-250(conic)-335(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 148.229 cm
0 g 0 G
1 0 0 1 -316.492 -148.229 cm
BT
/F16 10.909 Tf 316.492 148.229 Td[(51)]TJ
ET
1 0 0 1 327.401 148.229 cm
0 g 0 G
1 0 0 1 -327.401 -148.229 cm
BT
/F16 10.909 Tf 63.135 134.522 Td[(76.)-250(Inscribed)-250(quadrangle)-836(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 134.522 cm
0 g 0 G
1 0 0 1 -316.492 -134.522 cm
BT
/F16 10.909 Tf 316.492 134.522 Td[(51)]TJ
ET
1 0 0 1 327.401 134.522 cm
0 g 0 G
1 0 0 1 -327.401 -134.522 cm
BT
/F16 10.909 Tf 63.135 120.814 Td[(77.)-250(Inscribed)-250(triangle)-724(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 120.814 cm
0 g 0 G
1 0 0 1 -316.492 -120.814 cm
BT
/F16 10.909 Tf 316.492 120.814 Td[(53)]TJ
ET
1 0 0 1 327.401 120.814 cm
0 g 0 G
1 0 0 1 -327.401 -120.814 cm
BT
/F16 10.909 Tf 63.135 107.106 Td[(78.)-250(Degenerate)-250(conic)-781(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 107.106 cm
0 g 0 G
1 0 0 1 -316.492 -107.106 cm
BT
/F16 10.909 Tf 316.492 107.106 Td[(53)]TJ
ET
1 0 0 1 327.401 107.106 cm
0 g 0 G
1 0 0 1 -327.401 -107.106 cm
BT
/F16 10.909 Tf 63.135 93.399 Td[(PROBLEMS)-971(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 93.399 cm
0 g 0 G
1 0 0 1 -316.492 -93.399 cm
BT
/F16 10.909 Tf 316.492 93.399 Td[(54)]TJ
ET
1 0 0 1 327.401 93.399 cm
0 g 0 G
1 0 0 1 -327.401 -93.399 cm
BT
/F16 10.909 Tf 46.771 79.691 Td[(CHAPTER)-293(V)-292(-)-293(PENCILS)-292(OF)-293(RAYS)-292(OF)-293(THE)-293(SECOND)]TJ 15.273 -13.549 Td[(ORDER)-711(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 66.142 cm
0 g 0 G
1 0 0 1 -316.492 -66.142 cm
BT
/F16 10.909 Tf 316.492 66.142 Td[(56)]TJ
ET
1 0 0 1 327.401 66.142 cm
0 g 0 G
1 0 0 1 -280.63 -27.36 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
56 0 obj <<
/Type /Page
/Contents 57 0 R
/Resources 55 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 41 0 R
>> endobj
55 0 obj <<
/Font << /F16 6 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
60 0 obj <<
/Length 12278
>>
stream
1 0 0 1 93.543 548.934 cm
0 g 0 G
1 0 0 1 -93.543 -548.934 cm
BT
/F16 10.909 Tf 93.543 548.934 Td[(xii)-1893(An)-250(Ele)-1(mentary)-250(Course)-250(in)-250(Synthetic)-250(Projective)-250(Geometry)]TJ
ET
1 0 0 1 374.173 548.934 cm
0 g 0 G
1 0 0 1 -374.173 -548.934 cm
BT
/F16 10.909 Tf 109.907 518.175 Td[(79.)-250(Pencil)-250(of)-250(rays)-250(of)-250(the)-250(second)-250(order)-250(defined)-810(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 518.175 cm
0 g 0 G
1 0 0 1 -363.264 -518.175 cm
BT
/F16 10.909 Tf 363.264 518.175 Td[(56)]TJ
ET
1 0 0 1 374.173 518.175 cm
0 g 0 G
1 0 0 1 -374.173 -518.175 cm
BT
/F16 10.909 Tf 109.907 504.472 Td[(80.)-250(Tangents)-250(to)-250(a)-250(circle)-641(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 504.472 cm
0 g 0 G
1 0 0 1 -363.264 -504.472 cm
BT
/F16 10.909 Tf 363.264 504.472 Td[(56)]TJ
ET
1 0 0 1 374.173 504.472 cm
0 g 0 G
1 0 0 1 -374.173 -504.472 cm
BT
/F16 10.909 Tf 109.907 490.77 Td[(81.)-250(Tangents)-250(to)-250(a)-250(conic)-696(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 490.77 cm
0 g 0 G
1 0 0 1 -363.264 -490.77 cm
BT
/F16 10.909 Tf 363.264 490.77 Td[(57)]TJ
ET
1 0 0 1 374.173 490.77 cm
0 g 0 G
1 0 0 1 -374.173 -490.77 cm
BT
/F16 10.909 Tf 109.907 477.067 Td[(82.)-250(Generating)-250(point-rows)-250(lines)-250(of)-250(the)-250(system)-752(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 477.067 cm
0 g 0 G
1 0 0 1 -363.264 -477.067 cm
BT
/F16 10.909 Tf 363.264 477.067 Td[(58)]TJ
ET
1 0 0 1 374.173 477.067 cm
0 g 0 G
1 0 0 1 -374.173 -477.067 cm
BT
/F16 10.909 Tf 109.907 463.365 Td[(83.)-250(Determination)-250(of)-250(the)-250(pencil)-474(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 463.365 cm
0 g 0 G
1 0 0 1 -363.264 -463.365 cm
BT
/F16 10.909 Tf 363.264 463.365 Td[(58)]TJ
ET
1 0 0 1 374.173 463.365 cm
0 g 0 G
1 0 0 1 -374.173 -463.365 cm
BT
/F16 10.909 Tf 109.907 449.662 Td[(84.)-250(Brianchon's)-250(theorem)-988(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 449.662 cm
0 g 0 G
1 0 0 1 -363.264 -449.662 cm
BT
/F16 10.909 Tf 363.264 449.662 Td[(59)]TJ
ET
1 0 0 1 374.173 449.662 cm
0 g 0 G
1 0 0 1 -374.173 -449.662 cm
BT
/F16 10.909 Tf 109.907 435.959 Td[(85.)-250(Permutations)-250(of)-250(lines)-250(in)-250(Brianchon's)-250(theorem)-960(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 435.959 cm
0 g 0 G
1 0 0 1 -363.264 -435.959 cm
BT
/F16 10.909 Tf 363.264 435.959 Td[(59)]TJ
ET
1 0 0 1 374.173 435.959 cm
0 g 0 G
1 0 0 1 -374.173 -435.959 cm
BT
/F16 10.909 Tf 109.907 422.257 Td[(86.)-250(Construction)-250(of)-250(the)-250(penvil)-250(by)-250(Brianchon's)-250(theorem)-266(.)]TJ
ET
1 0 0 1 363.264 422.257 cm
0 g 0 G
1 0 0 1 -363.264 -422.257 cm
BT
/F16 10.909 Tf 363.264 422.257 Td[(60)]TJ
ET
1 0 0 1 374.173 422.257 cm
0 g 0 G
1 0 0 1 -374.173 -422.257 cm
BT
/F16 10.909 Tf 109.907 408.554 Td[(87.)-250(Point)-250(of)-250(contact)-250(of)-250(a)-250(tangent)-250(to)-250(a)-250(conic)-558(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 408.554 cm
0 g 0 G
1 0 0 1 -363.264 -408.554 cm
BT
/F16 10.909 Tf 363.264 408.554 Td[(60)]TJ
ET
1 0 0 1 374.173 408.554 cm
0 g 0 G
1 0 0 1 -374.173 -408.554 cm
BT
/F16 10.909 Tf 109.907 394.851 Td[(88.)-250(Circumscribed)-250(quadrilateral)-308(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 394.851 cm
0 g 0 G
1 0 0 1 -363.264 -394.851 cm
BT
/F16 10.909 Tf 363.264 394.851 Td[(60)]TJ
ET
1 0 0 1 374.173 394.851 cm
0 g 0 G
1 0 0 1 -374.173 -394.851 cm
BT
/F16 10.909 Tf 109.907 381.149 Td[(89.)-250(Circumscribed)-250(triangle)-807(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 381.149 cm
0 g 0 G
1 0 0 1 -363.264 -381.149 cm
BT
/F16 10.909 Tf 363.264 381.149 Td[(61)]TJ
ET
1 0 0 1 374.173 381.149 cm
0 g 0 G
1 0 0 1 -374.173 -381.149 cm
BT
/F16 10.909 Tf 109.907 367.446 Td[(90.)-250(Use)-250(of)-250(Brianchon's)-250(theorem)-350(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 367.446 cm
0 g 0 G
1 0 0 1 -363.264 -367.446 cm
BT
/F16 10.909 Tf 363.264 367.446 Td[(61)]TJ
ET
1 0 0 1 374.173 367.446 cm
0 g 0 G
1 0 0 1 -374.173 -367.446 cm
BT
/F16 10.909 Tf 109.907 353.744 Td[(91.)-250(Harmonic)-250(tangents)-918(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 353.744 cm
0 g 0 G
1 0 0 1 -363.264 -353.744 cm
BT
/F16 10.909 Tf 363.264 353.744 Td[(61)]TJ
ET
1 0 0 1 374.173 353.744 cm
0 g 0 G
1 0 0 1 -374.173 -353.744 cm
BT
/F16 10.909 Tf 109.907 340.041 Td[(92.)-250(Projectivity)-250(and)-250(perspectivity)-473(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 340.041 cm
0 g 0 G
1 0 0 1 -363.264 -340.041 cm
BT
/F16 10.909 Tf 363.264 340.041 Td[(62)]TJ
ET
1 0 0 1 374.173 340.041 cm
0 g 0 G
1 0 0 1 -374.173 -340.041 cm
BT
/F16 10.909 Tf 109.907 326.338 Td[(93.)-250(Degenerate)-250(case)-476(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 326.338 cm
0 g 0 G
1 0 0 1 -363.264 -326.338 cm
BT
/F16 10.909 Tf 363.264 326.338 Td[(62)]TJ
ET
1 0 0 1 374.173 326.338 cm
0 g 0 G
1 0 0 1 -374.173 -326.338 cm
BT
/F16 10.909 Tf 109.907 312.636 Td[(94.)-250(Law)-250(of)-250(duality)-362(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 312.636 cm
0 g 0 G
1 0 0 1 -363.264 -312.636 cm
BT
/F16 10.909 Tf 363.264 312.636 Td[(62)]TJ
ET
1 0 0 1 374.173 312.636 cm
0 g 0 G
1 0 0 1 -374.173 -312.636 cm
BT
/F16 10.909 Tf 109.907 298.933 Td[(PROBLEMS)-971(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 298.933 cm
0 g 0 G
1 0 0 1 -363.264 -298.933 cm
BT
/F16 10.909 Tf 363.264 298.933 Td[(62)]TJ
ET
1 0 0 1 374.173 298.933 cm
0 g 0 G
1 0 0 1 -374.173 -298.933 cm
BT
/F16 10.909 Tf 93.543 285.23 Td[(CHAPTER)-250(VI)-250(-)-250(POLES)-250(AND)-250(POLARS)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 285.23 cm
0 g 0 G
1 0 0 1 -363.264 -285.23 cm
BT
/F16 10.909 Tf 363.264 285.23 Td[(69)]TJ
ET
1 0 0 1 374.173 285.23 cm
0 g 0 G
1 0 0 1 -374.173 -285.23 cm
BT
/F16 10.909 Tf 109.907 271.528 Td[(95.)-250(Inscribed)-250(and)-250(circumscribed)-250(quadrilaterals)-477(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 271.528 cm
0 g 0 G
1 0 0 1 -363.264 -271.528 cm
BT
/F16 10.909 Tf 363.264 271.528 Td[(69)]TJ
ET
1 0 0 1 374.173 271.528 cm
0 g 0 G
1 0 0 1 -374.173 -271.528 cm
BT
/F16 10.909 Tf 109.907 257.825 Td[(96.)-250(Definition)-250(of)-250(the)-250(polar)-250(line)-250(of)-250(a)-250(point)-446(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 257.825 cm
0 g 0 G
1 0 0 1 -363.264 -257.825 cm
BT
/F16 10.909 Tf 363.264 257.825 Td[(69)]TJ
ET
1 0 0 1 374.173 257.825 cm
0 g 0 G
1 0 0 1 -374.173 -257.825 cm
BT
/F16 10.909 Tf 109.907 244.123 Td[(97.)-250(Further)-250(defining)-250(properties)-724(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 244.123 cm
0 g 0 G
1 0 0 1 -363.264 -244.123 cm
BT
/F16 10.909 Tf 363.264 244.123 Td[(70)]TJ
ET
1 0 0 1 374.173 244.123 cm
0 g 0 G
1 0 0 1 -374.173 -244.123 cm
BT
/F16 10.909 Tf 109.907 230.42 Td[(98.)-250(Definition)-250(of)-250(the)-250(pole)-250(of)-250(a)-250(line)-835(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 230.42 cm
0 g 0 G
1 0 0 1 -363.264 -230.42 cm
BT
/F16 10.909 Tf 363.264 230.42 Td[(70)]TJ
ET
1 0 0 1 374.173 230.42 cm
0 g 0 G
1 0 0 1 -374.173 -230.42 cm
BT
/F16 10.909 Tf 109.907 216.717 Td[(99.)-250(Fundamental)-250(theorem)-250(of)-250(poles)-250(and)-250(polars)-919(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 216.717 cm
0 g 0 G
1 0 0 1 -363.264 -216.717 cm
BT
/F16 10.909 Tf 363.264 216.717 Td[(70)]TJ
ET
1 0 0 1 374.173 216.717 cm
0 g 0 G
1 0 0 1 -374.173 -216.717 cm
BT
/F16 10.909 Tf 109.907 203.015 Td[(100.)-250(Conjugate)-250(points)-250(and)-250(lines)-361(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 203.015 cm
0 g 0 G
1 0 0 1 -363.264 -203.015 cm
BT
/F16 10.909 Tf 363.264 203.015 Td[(71)]TJ
ET
1 0 0 1 374.173 203.015 cm
0 g 0 G
1 0 0 1 -374.173 -203.015 cm
BT
/F16 10.909 Tf 109.907 189.312 Td[(101.)-250(Construction)-250(of)-250(the)-250(polar)-250(line)-250(of)-250(a)-250(given)-250(point)-918(.)-500(.)]TJ
ET
1 0 0 1 363.264 189.312 cm
0 g 0 G
1 0 0 1 -363.264 -189.312 cm
BT
/F16 10.909 Tf 363.264 189.312 Td[(71)]TJ
ET
1 0 0 1 374.173 189.312 cm
0 g 0 G
1 0 0 1 -374.173 -189.312 cm
BT
/F16 10.909 Tf 109.907 175.609 Td[(102.)-250(Self-polar)-250(triangle)-696(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 175.609 cm
0 g 0 G
1 0 0 1 -363.264 -175.609 cm
BT
/F16 10.909 Tf 363.264 175.609 Td[(72)]TJ
ET
1 0 0 1 374.173 175.609 cm
0 g 0 G
1 0 0 1 -374.173 -175.609 cm
BT
/F16 10.909 Tf 109.907 161.907 Td[(103.)-250(Pole)-250(and)-250(polar)-250(projectively)-250(related)-975(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 161.907 cm
0 g 0 G
1 0 0 1 -363.264 -161.907 cm
BT
/F16 10.909 Tf 363.264 161.907 Td[(72)]TJ
ET
1 0 0 1 374.173 161.907 cm
0 g 0 G
1 0 0 1 -374.173 -161.907 cm
BT
/F16 10.909 Tf 109.907 148.204 Td[(104.)-250(Duality)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 148.204 cm
0 g 0 G
1 0 0 1 -363.264 -148.204 cm
BT
/F16 10.909 Tf 363.264 148.204 Td[(72)]TJ
ET
1 0 0 1 374.173 148.204 cm
0 g 0 G
1 0 0 1 -374.173 -148.204 cm
BT
/F16 10.909 Tf 109.907 134.502 Td[(105.)-250(Self-dual)-250(theorems)-418(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 134.502 cm
0 g 0 G
1 0 0 1 -363.264 -134.502 cm
BT
/F16 10.909 Tf 363.264 134.502 Td[(73)]TJ
ET
1 0 0 1 374.173 134.502 cm
0 g 0 G
1 0 0 1 -374.173 -134.502 cm
BT
/F16 10.909 Tf 109.907 120.799 Td[(106.)-250(Other)-250(correspondences)-309(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 120.799 cm
0 g 0 G
1 0 0 1 -363.264 -120.799 cm
BT
/F16 10.909 Tf 363.264 120.799 Td[(74)]TJ
ET
1 0 0 1 374.173 120.799 cm
0 g 0 G
1 0 0 1 -374.173 -120.799 cm
BT
/F16 10.909 Tf 109.907 107.096 Td[(PROBLEMS)-971(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 107.096 cm
0 g 0 G
1 0 0 1 -363.264 -107.096 cm
BT
/F16 10.909 Tf 363.264 107.096 Td[(74)]TJ
ET
1 0 0 1 374.173 107.096 cm
0 g 0 G
1 0 0 1 -374.173 -107.096 cm
BT
/F16 10.909 Tf 93.543 93.394 Td[(CHAPTER)-446(VII)-445(-)-446(METRICAL)-446(PROPERTIES)-446(OF)-446(THE)]TJ 15.273 -13.55 Td[(CONIC)-250(SECTIONS)-461(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 79.844 cm
0 g 0 G
1 0 0 1 -363.264 -79.844 cm
BT
/F16 10.909 Tf 363.264 79.844 Td[(76)]TJ
ET
1 0 0 1 374.173 79.844 cm
0 g 0 G
1 0 0 1 -374.173 -79.844 cm
BT
/F16 10.909 Tf 109.907 66.142 Td[(107.)-250(Diameters.)-250(Center)-724(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 66.142 cm
0 g 0 G
1 0 0 1 -363.264 -66.142 cm
BT
/F16 10.909 Tf 363.264 66.142 Td[(76)]TJ
ET
1 0 0 1 374.173 66.142 cm
0 g 0 G
1 0 0 1 -280.63 -27.36 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
59 0 obj <<
/Type /Page
/Contents 60 0 R
/Resources 58 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 41 0 R
>> endobj
58 0 obj <<
/Font << /F16 6 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
63 0 obj <<
/Length 11001
>>
stream
1 0 0 1 46.771 548.934 cm
0 g 0 G
1 0 0 1 -46.771 -548.934 cm
BT
/F16 10.909 Tf 46.771 548.934 Td[(Contents)-20835(xiii)]TJ
ET
1 0 0 1 327.401 548.934 cm
0 g 0 G
1 0 0 1 -327.401 -548.934 cm
BT
/F16 10.909 Tf 63.135 518.175 Td[(108.)-250(Various)-250(theorems)-918(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 518.175 cm
0 g 0 G
1 0 0 1 -316.492 -518.175 cm
BT
/F16 10.909 Tf 316.492 518.175 Td[(76)]TJ
ET
1 0 0 1 327.401 518.175 cm
0 g 0 G
1 0 0 1 -327.401 -518.175 cm
BT
/F16 10.909 Tf 63.135 504.444 Td[(109.)-250(Conjugate)-250(diameters)-501(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 504.444 cm
0 g 0 G
1 0 0 1 -316.492 -504.444 cm
BT
/F16 10.909 Tf 316.492 504.444 Td[(76)]TJ
ET
1 0 0 1 327.401 504.444 cm
0 g 0 G
1 0 0 1 -327.401 -504.444 cm
BT
/F16 10.909 Tf 63.135 490.713 Td[(110.)-250(Classification)-250(of)-250(conics)-862(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 490.713 cm
0 g 0 G
1 0 0 1 -316.492 -490.713 cm
BT
/F16 10.909 Tf 316.492 490.713 Td[(77)]TJ
ET
1 0 0 1 327.401 490.713 cm
0 g 0 G
1 0 0 1 -327.401 -490.713 cm
BT
/F16 10.909 Tf 63.135 476.982 Td[(111.)-250(Asymptotes)-972(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 476.982 cm
0 g 0 G
1 0 0 1 -316.492 -476.982 cm
BT
/F16 10.909 Tf 316.492 476.982 Td[(77)]TJ
ET
1 0 0 1 327.401 476.982 cm
0 g 0 G
1 0 0 1 -327.401 -476.982 cm
BT
/F16 10.909 Tf 63.135 463.251 Td[(112.)-250(Various)-250(theorems)-918(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 463.251 cm
0 g 0 G
1 0 0 1 -316.492 -463.251 cm
BT
/F16 10.909 Tf 316.492 463.251 Td[(77)]TJ
ET
1 0 0 1 327.401 463.251 cm
0 g 0 G
1 0 0 1 -327.401 -463.251 cm
BT
/F16 10.909 Tf 63.135 449.52 Td[(113.)-250(Theorems)-250(concerning)-250(asymptotes)-558(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 449.52 cm
0 g 0 G
1 0 0 1 -316.492 -449.52 cm
BT
/F16 10.909 Tf 316.492 449.52 Td[(78)]TJ
ET
1 0 0 1 327.401 449.52 cm
0 g 0 G
1 0 0 1 -327.401 -449.52 cm
BT
/F16 10.909 Tf 63.135 435.789 Td[(114.)-250(Asymptotes)-250(and)-250(conjugate)-250(diameters)-752(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 435.789 cm
0 g 0 G
1 0 0 1 -316.492 -435.789 cm
BT
/F16 10.909 Tf 316.492 435.789 Td[(79)]TJ
ET
1 0 0 1 327.401 435.789 cm
0 g 0 G
1 0 0 1 -327.401 -435.789 cm
BT
/F16 10.909 Tf 63.135 422.058 Td[(115.)-260(Segments)-253(cut)-253(off)-253(on)-253(a)-254(chord)-253(by)-253(hyperbola)-253(and)-254(its)]TJ 25.091 -13.549 Td[(asymptotes)-950(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 408.509 cm
0 g 0 G
1 0 0 1 -316.492 -408.509 cm
BT
/F16 10.909 Tf 316.492 408.509 Td[(79)]TJ
ET
1 0 0 1 327.401 408.509 cm
0 g 0 G
1 0 0 1 -327.401 -408.509 cm
BT
/F16 10.909 Tf 63.135 394.778 Td[(116.)-250(Application)-250(of)-250(the)-250(theorem)-946(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 394.778 cm
0 g 0 G
1 0 0 1 -316.492 -394.778 cm
BT
/F16 10.909 Tf 316.492 394.778 Td[(79)]TJ
ET
1 0 0 1 327.401 394.778 cm
0 g 0 G
1 0 0 1 -327.401 -394.778 cm
BT
/F16 10.909 Tf 63.135 381.047 Td[(117.)-712(Triangle)-403(formed)-404(by)-404(the)-404(two)-404(asymptotes)-404(and)-404(a)]TJ 25.091 -13.55 Td[(tangent)-256(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 367.497 cm
0 g 0 G
1 0 0 1 -316.492 -367.497 cm
BT
/F16 10.909 Tf 316.492 367.497 Td[(80)]TJ
ET
1 0 0 1 327.401 367.497 cm
0 g 0 G
1 0 0 1 -327.401 -367.497 cm
BT
/F16 10.909 Tf 63.135 353.766 Td[(118.)-250(Equation)-250(of)-250(hyperbola)-250(referred)-250(to)-250(the)-250(asymptotes)-393(.)]TJ
ET
1 0 0 1 316.492 353.766 cm
0 g 0 G
1 0 0 1 -316.492 -353.766 cm
BT
/F16 10.909 Tf 316.492 353.766 Td[(81)]TJ
ET
1 0 0 1 327.401 353.766 cm
0 g 0 G
1 0 0 1 -327.401 -353.766 cm
BT
/F16 10.909 Tf 63.135 340.035 Td[(119.)-250(Equation)-250(of)-250(parabola)-363(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 340.035 cm
0 g 0 G
1 0 0 1 -316.492 -340.035 cm
BT
/F16 10.909 Tf 316.492 340.035 Td[(81)]TJ
ET
1 0 0 1 327.401 340.035 cm
0 g 0 G
1 0 0 1 -327.401 -340.035 cm
BT
/F16 10.909 Tf 63.135 326.304 Td[(120.)-458(Equation)-320(of)-319(central)-319(conics)-320(referred)-319(to)-320(conjugate)]TJ 25.091 -13.549 Td[(diameters)-812(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 312.755 cm
0 g 0 G
1 0 0 1 -316.492 -312.755 cm
BT
/F16 10.909 Tf 316.492 312.755 Td[(83)]TJ
ET
1 0 0 1 327.401 312.755 cm
0 g 0 G
1 0 0 1 -327.401 -312.755 cm
BT
/F16 10.909 Tf 63.135 299.024 Td[(PROBLEMS)-971(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 299.024 cm
0 g 0 G
1 0 0 1 -316.492 -299.024 cm
BT
/F16 10.909 Tf 316.492 299.024 Td[(84)]TJ
ET
1 0 0 1 327.401 299.024 cm
0 g 0 G
1 0 0 1 -327.401 -299.024 cm
BT
/F16 10.909 Tf 46.771 285.293 Td[(CHAPTER)-250(VIII)-250(-)-250(INVOLUTION)-920(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 285.293 cm
0 g 0 G
1 0 0 1 -316.492 -285.293 cm
BT
/F16 10.909 Tf 316.492 285.293 Td[(88)]TJ
ET
1 0 0 1 327.401 285.293 cm
0 g 0 G
1 0 0 1 -327.401 -285.293 cm
BT
/F16 10.909 Tf 63.135 271.562 Td[(121.)-250(Fundamental)-250(theorem)-751(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 271.562 cm
0 g 0 G
1 0 0 1 -316.492 -271.562 cm
BT
/F16 10.909 Tf 316.492 271.562 Td[(88)]TJ
ET
1 0 0 1 327.401 271.562 cm
0 g 0 G
1 0 0 1 -327.401 -271.562 cm
BT
/F16 10.909 Tf 63.135 257.831 Td[(122.)-250(Linear)-250(construction)-946(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 257.831 cm
0 g 0 G
1 0 0 1 -316.492 -257.831 cm
BT
/F16 10.909 Tf 316.492 257.831 Td[(89)]TJ
ET
1 0 0 1 327.401 257.831 cm
0 g 0 G
1 0 0 1 -327.401 -257.831 cm
BT
/F16 10.909 Tf 63.135 244.1 Td[(123.)-250(Definition)-250(of)-250(involution)-250(of)-250(points)-250(on)-250(a)-250(line)-722(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 244.1 cm
0 g 0 G
1 0 0 1 -316.492 -244.1 cm
BT
/F16 10.909 Tf 316.492 244.1 Td[(90)]TJ
ET
1 0 0 1 327.401 244.1 cm
0 g 0 G
1 0 0 1 -327.401 -244.1 cm
BT
/F16 10.909 Tf 63.135 230.369 Td[(124.)-250(Double-points)-250(in)-250(an)-250(involution)-944(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 230.369 cm
0 g 0 G
1 0 0 1 -316.492 -230.369 cm
BT
/F16 10.909 Tf 316.492 230.369 Td[(90)]TJ
ET
1 0 0 1 327.401 230.369 cm
0 g 0 G
1 0 0 1 -327.401 -230.369 cm
BT
/F16 10.909 Tf 63.135 216.638 Td[(125.)-488(Desargues's)-329(theorem)-329(concerning)-329(conics)-330(through)]TJ 25.091 -13.549 Td[(four)-250(points)-339(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 203.089 cm
0 g 0 G
1 0 0 1 -316.492 -203.089 cm
BT
/F16 10.909 Tf 316.492 203.089 Td[(91)]TJ
ET
1 0 0 1 327.401 203.089 cm
0 g 0 G
1 0 0 1 -327.401 -203.089 cm
BT
/F16 10.909 Tf 63.135 189.358 Td[(126.)-250(Degenerate)-250(conics)-250(of)-250(the)-250(system)-309(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 189.358 cm
0 g 0 G
1 0 0 1 -316.492 -189.358 cm
BT
/F16 10.909 Tf 316.492 189.358 Td[(92)]TJ
ET
1 0 0 1 327.401 189.358 cm
0 g 0 G
1 0 0 1 -327.401 -189.358 cm
BT
/F16 10.909 Tf 63.135 175.626 Td[(127.)-250(Conics)-250(through)-250(four)-250(points)-250(touching)-250(a)-250(given)-250(line)-584(.)]TJ
ET
1 0 0 1 316.492 175.626 cm
0 g 0 G
1 0 0 1 -316.492 -175.626 cm
BT
/F16 10.909 Tf 316.492 175.626 Td[(92)]TJ
ET
1 0 0 1 327.401 175.626 cm
0 g 0 G
1 0 0 1 -327.401 -175.626 cm
BT
/F16 10.909 Tf 63.135 161.895 Td[(128.)-250(Double)-250(correspondence)-781(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 161.895 cm
0 g 0 G
1 0 0 1 -316.492 -161.895 cm
BT
/F16 10.909 Tf 316.492 161.895 Td[(93)]TJ
ET
1 0 0 1 327.401 161.895 cm
0 g 0 G
1 0 0 1 -327.401 -161.895 cm
BT
/F16 10.909 Tf 63.135 148.164 Td[(129.)-250(Steiner's)-250(construction)-904(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 148.164 cm
0 g 0 G
1 0 0 1 -316.492 -148.164 cm
BT
/F16 10.909 Tf 316.492 148.164 Td[(93)]TJ
ET
1 0 0 1 327.401 148.164 cm
0 g 0 G
1 0 0 1 -327.401 -148.164 cm
BT
/F16 10.909 Tf 63.135 134.433 Td[(130.)-634(Application)-378(of)-378(Steiner's)-378(construction)-378(to)-378(double)]TJ 25.091 -13.549 Td[(correspondence)-675(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 120.884 cm
0 g 0 G
1 0 0 1 -316.492 -120.884 cm
BT
/F16 10.909 Tf 316.492 120.884 Td[(94)]TJ
ET
1 0 0 1 327.401 120.884 cm
0 g 0 G
1 0 0 1 -327.401 -120.884 cm
BT
/F16 10.909 Tf 63.135 107.153 Td[(131.)-253(Involution)-250(of)-251(points)-251(on)-251(a)-251(point-row)-251(of)-251(the)-251(second)]TJ 25.091 -13.549 Td[(order.)-840(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 93.604 cm
0 g 0 G
1 0 0 1 -316.492 -93.604 cm
BT
/F16 10.909 Tf 316.492 93.604 Td[(95)]TJ
ET
1 0 0 1 327.401 93.604 cm
0 g 0 G
1 0 0 1 -327.401 -93.604 cm
BT
/F16 10.909 Tf 63.135 79.873 Td[(132.)-250(Involution)-250(of)-250(rays)-834(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 79.873 cm
0 g 0 G
1 0 0 1 -316.492 -79.873 cm
BT
/F16 10.909 Tf 316.492 79.873 Td[(96)]TJ
ET
1 0 0 1 327.401 79.873 cm
0 g 0 G
1 0 0 1 -327.401 -79.873 cm
BT
/F16 10.909 Tf 63.135 66.142 Td[(133.)-250(Double)-250(rays)-890(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 316.492 66.142 cm
0 g 0 G
1 0 0 1 -316.492 -66.142 cm
BT
/F16 10.909 Tf 316.492 66.142 Td[(96)]TJ
ET
1 0 0 1 327.401 66.142 cm
0 g 0 G
1 0 0 1 -280.63 -27.36 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
62 0 obj <<
/Type /Page
/Contents 63 0 R
/Resources 61 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 64 0 R
>> endobj
61 0 obj <<
/Font << /F16 6 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
67 0 obj <<
/Length 11519
>>
stream
1 0 0 1 93.543 548.934 cm
0 g 0 G
1 0 0 1 -93.543 -548.934 cm
BT
/F16 10.909 Tf 93.543 548.934 Td[(xiv)-1671(An)-250(E)-1(lementary)-250(Course)-250(in)-250(Synthetic)-250(Projective)-250(Geometry)]TJ
ET
1 0 0 1 374.173 548.934 cm
0 g 0 G
1 0 0 1 -374.173 -548.934 cm
BT
/F16 10.909 Tf 109.907 518.175 Td[(134.)-250(Conic)-250(through)-250(a)-250(fixed)-250(point)-250(touching)-250(four)-250(lines)-390(.)-500(.)]TJ
ET
1 0 0 1 363.264 518.175 cm
0 g 0 G
1 0 0 1 -363.264 -518.175 cm
BT
/F16 10.909 Tf 363.264 518.175 Td[(96)]TJ
ET
1 0 0 1 374.173 518.175 cm
0 g 0 G
1 0 0 1 -374.173 -518.175 cm
BT
/F16 10.909 Tf 109.907 504.457 Td[(135.)-250(Double)-250(correspondence)-781(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 504.457 cm
0 g 0 G
1 0 0 1 -363.264 -504.457 cm
BT
/F16 10.909 Tf 363.264 504.457 Td[(97)]TJ
ET
1 0 0 1 374.173 504.457 cm
0 g 0 G
1 0 0 1 -374.173 -504.457 cm
BT
/F16 10.909 Tf 109.907 490.738 Td[(136.)-250(Pencils)-250(of)-250(rays)-250(of)-250(the)-250(second)-250(order)-250(in)-250(involution)-780(.)]TJ
ET
1 0 0 1 363.264 490.738 cm
0 g 0 G
1 0 0 1 -363.264 -490.738 cm
BT
/F16 10.909 Tf 363.264 490.738 Td[(97)]TJ
ET
1 0 0 1 374.173 490.738 cm
0 g 0 G
1 0 0 1 -374.173 -490.738 cm
BT
/F16 10.909 Tf 109.907 477.02 Td[(137.)-365(Theore)-1(m)-288(concerning)-289(pencils)-288(of)-289(the)-288(second)-289(order)]TJ 25.091 -13.55 Td[(in)-250(involution)-310(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 463.47 cm
0 g 0 G
1 0 0 1 -363.264 -463.47 cm
BT
/F16 10.909 Tf 363.264 463.47 Td[(97)]TJ
ET
1 0 0 1 374.173 463.47 cm
0 g 0 G
1 0 0 1 -374.173 -463.47 cm
BT
/F16 10.909 Tf 109.907 449.752 Td[(138.)-250(Involution)-250(of)-250(rays)-250(determined)-250(by)-250(a)-250(conic)-725(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 449.752 cm
0 g 0 G
1 0 0 1 -363.264 -449.752 cm
BT
/F16 10.909 Tf 363.264 449.752 Td[(98)]TJ
ET
1 0 0 1 374.173 449.752 cm
0 g 0 G
1 0 0 1 -374.173 -449.752 cm
BT
/F16 10.909 Tf 109.907 436.033 Td[(139.)-250(Statement)-250(of)-250(theorem)-890(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 436.033 cm
0 g 0 G
1 0 0 1 -363.264 -436.033 cm
BT
/F16 10.909 Tf 363.264 436.033 Td[(98)]TJ
ET
1 0 0 1 374.173 436.033 cm
0 g 0 G
1 0 0 1 -374.173 -436.033 cm
BT
/F16 10.909 Tf 109.907 422.315 Td[(140.)-250(Dual)-250(of)-250(the)-250(theorem)-724(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 422.315 cm
0 g 0 G
1 0 0 1 -363.264 -422.315 cm
BT
/F16 10.909 Tf 363.264 422.315 Td[(98)]TJ
ET
1 0 0 1 374.173 422.315 cm
0 g 0 G
1 0 0 1 -374.173 -422.315 cm
BT
/F16 10.909 Tf 109.907 408.596 Td[(PROBLEMS)-971(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 363.264 408.596 cm
0 g 0 G
1 0 0 1 -363.264 -408.596 cm
BT
/F16 10.909 Tf 363.264 408.596 Td[(99)]TJ
ET
1 0 0 1 374.173 408.596 cm
0 g 0 G
1 0 0 1 -374.173 -408.596 cm
BT
/F16 10.909 Tf 93.543 394.878 Td[(CHAPTER)-353(IX)-354(-)-353(METRICAL)-353(PROPERTIES)-353(OF)-354(INVO-)]TJ 15.273 -13.549 Td[(LUTIONS)-573(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 381.329 cm
0 g 0 G
1 0 0 1 -357.81 -381.329 cm
BT
/F16 10.909 Tf 357.81 381.329 Td[(104)]TJ
ET
1 0 0 1 374.173 381.329 cm
0 g 0 G
1 0 0 1 -374.173 -381.329 cm
BT
/F16 10.909 Tf 109.907 367.61 Td[(141.)-250(Introduction)-250(of)-250(infinite)-250(point;)-250(center)-250(of)-250(involution)]TJ
ET
1 0 0 1 357.81 367.61 cm
0 g 0 G
1 0 0 1 -357.81 -367.61 cm
BT
/F16 10.909 Tf 357.81 367.61 Td[(104)]TJ
ET
1 0 0 1 374.173 367.61 cm
0 g 0 G
1 0 0 1 -374.173 -367.61 cm
BT
/F16 10.909 Tf 109.907 353.892 Td[(142.)-250(Fundamental)-250(metrical)-250(theorem)-974(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 353.892 cm
0 g 0 G
1 0 0 1 -357.81 -353.892 cm
BT
/F16 10.909 Tf 357.81 353.892 Td[(105)]TJ
ET
1 0 0 1 374.173 353.892 cm
0 g 0 G
1 0 0 1 -374.173 -353.892 cm
BT
/F16 10.909 Tf 109.907 340.173 Td[(143.)-250(Existence)-250(of)-250(double)-250(points)-362(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 340.173 cm
0 g 0 G
1 0 0 1 -357.81 -340.173 cm
BT
/F16 10.909 Tf 357.81 340.173 Td[(106)]TJ
ET
1 0 0 1 374.173 340.173 cm
0 g 0 G
1 0 0 1 -374.173 -340.173 cm
BT
/F16 10.909 Tf 109.907 326.455 Td[(144.)-250(Existence)-250(of)-250(double)-250(rays)-391(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 326.455 cm
0 g 0 G
1 0 0 1 -357.81 -326.455 cm
BT
/F16 10.909 Tf 357.81 326.455 Td[(106)]TJ
ET
1 0 0 1 374.173 326.455 cm
0 g 0 G
1 0 0 1 -374.173 -326.455 cm
BT
/F16 10.909 Tf 109.907 312.736 Td[(145.)-250(Construction)-250(of)-250(an)-250(involution)-250(by)-250(means)-250(of)-250(circles)]TJ
ET
1 0 0 1 357.81 312.736 cm
0 g 0 G
1 0 0 1 -357.81 -312.736 cm
BT
/F16 10.909 Tf 357.81 312.736 Td[(107)]TJ
ET
1 0 0 1 374.173 312.736 cm
0 g 0 G
1 0 0 1 -374.173 -312.736 cm
BT
/F16 10.909 Tf 109.907 299.018 Td[(146.)-250(Circular)-250(points)-528(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 299.018 cm
0 g 0 G
1 0 0 1 -357.81 -299.018 cm
BT
/F16 10.909 Tf 357.81 299.018 Td[(108)]TJ
ET
1 0 0 1 374.173 299.018 cm
0 g 0 G
1 0 0 1 -374.173 -299.018 cm
BT
/F16 10.909 Tf 109.907 285.299 Td[(147.)-454(Pairs)-318(in)-318(an)-318(involution)-318(of)-318(rays)-318(which)-318(are)-318(at)-318(right)]TJ 25.091 -13.549 Td[(angles.)-250(Circular)-250(involution)-756(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 271.75 cm
0 g 0 G
1 0 0 1 -357.81 -271.75 cm
BT
/F16 10.909 Tf 357.81 271.75 Td[(109)]TJ
ET
1 0 0 1 374.173 271.75 cm
0 g 0 G
1 0 0 1 -374.173 -271.75 cm
BT
/F16 10.909 Tf 109.907 258.032 Td[(148.)-250(Axes)-250(of)-250(conics)-557(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 258.032 cm
0 g 0 G
1 0 0 1 -357.81 -258.032 cm
BT
/F16 10.909 Tf 357.81 258.032 Td[(109)]TJ
ET
1 0 0 1 374.173 258.032 cm
0 g 0 G
1 0 0 1 -374.173 -258.032 cm
BT
/F16 10.909 Tf 109.907 244.313 Td[(149.)-544(Points)-348(at)-348(which)-348(the)-348(involution)-348(determined)-348(by)-349(a)]TJ 25.091 -13.549 Td[(conic)-250(is)-250(circular)-563(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 230.764 cm
0 g 0 G
1 0 0 1 -357.81 -230.764 cm
BT
/F16 10.909 Tf 357.81 230.764 Td[(110)]TJ
ET
1 0 0 1 374.173 230.764 cm
0 g 0 G
1 0 0 1 -374.173 -230.764 cm
BT
/F16 10.909 Tf 109.907 217.045 Td[(150.)-250(Properties)-250(of)-250(such)-250(a)-250(point)-779(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 217.045 cm
0 g 0 G
1 0 0 1 -357.81 -217.045 cm
BT
/F16 10.909 Tf 357.81 217.045 Td[(110)]TJ
ET
1 0 0 1 374.173 217.045 cm
0 g 0 G
1 0 0 1 -374.173 -217.045 cm
BT
/F16 10.909 Tf 109.907 203.327 Td[(151.)-250(Position)-250(of)-250(such)-250(a)-250(point)-805(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 203.327 cm
0 g 0 G
1 0 0 1 -357.81 -203.327 cm
BT
/F16 10.909 Tf 357.81 203.327 Td[(111)]TJ
ET
1 0 0 1 374.173 203.327 cm
0 g 0 G
1 0 0 1 -374.173 -203.327 cm
BT
/F16 10.909 Tf 109.907 189.608 Td[(152.)-250(Discovery)-250(of)-250(the)-250(foci)-250(of)-250(the)-250(conic)-559(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 189.608 cm
0 g 0 G
1 0 0 1 -357.81 -189.608 cm
BT
/F16 10.909 Tf 357.81 189.608 Td[(112)]TJ
ET
1 0 0 1 374.173 189.608 cm
0 g 0 G
1 0 0 1 -374.173 -189.608 cm
BT
/F16 10.909 Tf 109.907 175.89 Td[(153.)-250(The)-250(circle)-250(and)-250(the)-250(parabola)-865(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 175.89 cm
0 g 0 G
1 0 0 1 -357.81 -175.89 cm
BT
/F16 10.909 Tf 357.81 175.89 Td[(114)]TJ
ET
1 0 0 1 374.173 175.89 cm
0 g 0 G
1 0 0 1 -374.173 -175.89 cm
BT
/F16 10.909 Tf 109.907 162.171 Td[(154.)-250(Focal)-250(properties)-250(of)-250(conics)-641(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 162.171 cm
0 g 0 G
1 0 0 1 -357.81 -162.171 cm
BT
/F16 10.909 Tf 357.81 162.171 Td[(114)]TJ
ET
1 0 0 1 374.173 162.171 cm
0 g 0 G
1 0 0 1 -374.173 -162.171 cm
BT
/F16 10.909 Tf 109.907 148.453 Td[(155.)-250(Case)-250(of)-250(the)-250(parabola)-558(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 148.453 cm
0 g 0 G
1 0 0 1 -357.81 -148.453 cm
BT
/F16 10.909 Tf 357.81 148.453 Td[(115)]TJ
ET
1 0 0 1 374.173 148.453 cm
0 g 0 G
1 0 0 1 -374.173 -148.453 cm
BT
/F16 10.909 Tf 109.907 134.734 Td[(156.)-250(Parabolic)-250(reflector)-586(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 134.734 cm
0 g 0 G
1 0 0 1 -357.81 -134.734 cm
BT
/F16 10.909 Tf 357.81 134.734 Td[(116)]TJ
ET
1 0 0 1 374.173 134.734 cm
0 g 0 G
1 0 0 1 -374.173 -134.734 cm
BT
/F16 10.909 Tf 109.907 121.016 Td[(157.)-250(Directrix.)-250(Principal)-250(axis.)-250(Vertex)-447(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 121.016 cm
0 g 0 G
1 0 0 1 -357.81 -121.016 cm
BT
/F16 10.909 Tf 357.81 121.016 Td[(116)]TJ
ET
1 0 0 1 374.173 121.016 cm
0 g 0 G
1 0 0 1 -374.173 -121.016 cm
BT
/F16 10.909 Tf 109.907 107.297 Td[(158.)-250(Another)-250(definition)-250(of)-250(a)-250(conic)-891(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 107.297 cm
0 g 0 G
1 0 0 1 -357.81 -107.297 cm
BT
/F16 10.909 Tf 357.81 107.297 Td[(117)]TJ
ET
1 0 0 1 374.173 107.297 cm
0 g 0 G
1 0 0 1 -374.173 -107.297 cm
BT
/F16 10.909 Tf 109.907 93.579 Td[(159.)-250(Eccentricity)-918(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 93.579 cm
0 g 0 G
1 0 0 1 -357.81 -93.579 cm
BT
/F16 10.909 Tf 357.81 93.579 Td[(119)]TJ
ET
1 0 0 1 374.173 93.579 cm
0 g 0 G
1 0 0 1 -374.173 -93.579 cm
BT
/F16 10.909 Tf 109.907 79.86 Td[(160.)-250(Sum)-250(or)-250(difference)-250(of)-250(focal)-250(distances)-282(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 79.86 cm
0 g 0 G
1 0 0 1 -357.81 -79.86 cm
BT
/F16 10.909 Tf 357.81 79.86 Td[(119)]TJ
ET
1 0 0 1 374.173 79.86 cm
0 g 0 G
1 0 0 1 -374.173 -79.86 cm
BT
/F16 10.909 Tf 109.907 66.142 Td[(PROBLEMS)-971(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 357.81 66.142 cm
0 g 0 G
1 0 0 1 -357.81 -66.142 cm
BT
/F16 10.909 Tf 357.81 66.142 Td[(120)]TJ
ET
1 0 0 1 374.173 66.142 cm
0 g 0 G
1 0 0 1 -280.63 -27.36 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
66 0 obj <<
/Type /Page
/Contents 67 0 R
/Resources 65 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 64 0 R
>> endobj
65 0 obj <<
/Font << /F16 6 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
70 0 obj <<
/Length 10666
>>
stream
1 0 0 1 46.771 548.934 cm
0 g 0 G
1 0 0 1 -46.771 -548.934 cm
BT
/F16 10.909 Tf 46.771 548.934 Td[(Contents)-21169(xv)]TJ
ET
1 0 0 1 327.401 548.934 cm
0 g 0 G
1 0 0 1 -327.401 -548.934 cm
BT
/F16 10.909 Tf 46.771 518.175 Td[(CHAPTER)-430(X)-430(-)-430(ON)-430(THE)-430(HISTORY)-430(OF)-430(SYNTHETIC)]TJ 15.273 -13.549 Td[(PROJECTIVE)-250(GEOMETRY)-656(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 504.626 cm
0 g 0 G
1 0 0 1 -311.038 -504.626 cm
BT
/F16 10.909 Tf 311.038 504.626 Td[(122)]TJ
ET
1 0 0 1 327.401 504.626 cm
0 g 0 G
1 0 0 1 -327.401 -504.626 cm
BT
/F16 10.909 Tf 63.135 491.077 Td[(161.)-250(Ancient)-250(results)-473(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 491.077 cm
0 g 0 G
1 0 0 1 -311.038 -491.077 cm
BT
/F16 10.909 Tf 311.038 491.077 Td[(122)]TJ
ET
1 0 0 1 327.401 491.077 cm
0 g 0 G
1 0 0 1 -327.401 -491.077 cm
BT
/F16 10.909 Tf 63.135 477.528 Td[(162.)-250(Unifying)-250(principles)-945(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 477.528 cm
0 g 0 G
1 0 0 1 -311.038 -477.528 cm
BT
/F16 10.909 Tf 311.038 477.528 Td[(126)]TJ
ET
1 0 0 1 327.401 477.528 cm
0 g 0 G
1 0 0 1 -327.401 -477.528 cm
BT
/F16 10.909 Tf 63.135 463.978 Td[(163.)-250(Desargues)-835(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 463.978 cm
0 g 0 G
1 0 0 1 -311.038 -463.978 cm
BT
/F16 10.909 Tf 311.038 463.978 Td[(127)]TJ
ET
1 0 0 1 327.401 463.978 cm
0 g 0 G
1 0 0 1 -327.401 -463.978 cm
BT
/F16 10.909 Tf 63.135 450.429 Td[(164.)-250(Poles)-250(and)-250(polars)-695(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 450.429 cm
0 g 0 G
1 0 0 1 -311.038 -450.429 cm
BT
/F16 10.909 Tf 311.038 450.429 Td[(127)]TJ
ET
1 0 0 1 327.401 450.429 cm
0 g 0 G
1 0 0 1 -327.401 -450.429 cm
BT
/F16 10.909 Tf 63.135 436.88 Td[(165.)-488(Desargues's)-329(theorem)-329(concerning)-329(conics)-330(through)]TJ 25.091 -13.549 Td[(four)-250(points)-339(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 423.331 cm
0 g 0 G
1 0 0 1 -311.038 -423.331 cm
BT
/F16 10.909 Tf 311.038 423.331 Td[(128)]TJ
ET
1 0 0 1 327.401 423.331 cm
0 g 0 G
1 0 0 1 -327.401 -423.331 cm
BT
/F16 10.909 Tf 63.135 409.782 Td[(166.)-249(Extension)-249(of)-248(the)-248(theory)-248(of)-249(poles)-248(and)-248(polars)-248(to)-249(space)]TJ
ET
1 0 0 1 311.038 409.782 cm
0 g 0 G
1 0 0 1 -311.038 -409.782 cm
BT
/F16 10.909 Tf 311.038 409.782 Td[(128)]TJ
ET
1 0 0 1 327.401 409.782 cm
0 g 0 G
1 0 0 1 -327.401 -409.782 cm
BT
/F16 10.909 Tf 63.135 396.232 Td[(167.)-250(Desargues's)-250(method)-250(of)-250(describing)-250(a)-250(conic)-407(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 396.232 cm
0 g 0 G
1 0 0 1 -311.038 -396.232 cm
BT
/F16 10.909 Tf 311.038 396.232 Td[(129)]TJ
ET
1 0 0 1 327.401 396.232 cm
0 g 0 G
1 0 0 1 -327.401 -396.232 cm
BT
/F16 10.909 Tf 63.135 382.683 Td[(168.)-250(Reception)-250(of)-250(Desargues's)-250(work)-823(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 382.683 cm
0 g 0 G
1 0 0 1 -311.038 -382.683 cm
BT
/F16 10.909 Tf 311.038 382.683 Td[(129)]TJ
ET
1 0 0 1 327.401 382.683 cm
0 g 0 G
1 0 0 1 -327.401 -382.683 cm
BT
/F16 10.909 Tf 63.135 369.134 Td[(169.)-250(Conservatism)-250(in)-250(Desargues's)-250(time)-460(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 369.134 cm
0 g 0 G
1 0 0 1 -311.038 -369.134 cm
BT
/F16 10.909 Tf 311.038 369.134 Td[(130)]TJ
ET
1 0 0 1 327.401 369.134 cm
0 g 0 G
1 0 0 1 -327.401 -369.134 cm
BT
/F16 10.909 Tf 63.135 355.585 Td[(170.)-250(Desargues's)-250(style)-250(of)-250(writing)-655(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 355.585 cm
0 g 0 G
1 0 0 1 -311.038 -355.585 cm
BT
/F16 10.909 Tf 311.038 355.585 Td[(131)]TJ
ET
1 0 0 1 327.401 355.585 cm
0 g 0 G
1 0 0 1 -327.401 -355.585 cm
BT
/F16 10.909 Tf 63.135 342.036 Td[(171.)-250(Lack)-250(of)-250(appreciation)-250(of)-250(Desargues)-977(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 342.036 cm
0 g 0 G
1 0 0 1 -311.038 -342.036 cm
BT
/F16 10.909 Tf 311.038 342.036 Td[(132)]TJ
ET
1 0 0 1 327.401 342.036 cm
0 g 0 G
1 0 0 1 -327.401 -342.036 cm
BT
/F16 10.909 Tf 63.135 328.486 Td[(172.)-250(Pascal)-250(and)-250(his)-250(theorem)-307(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 328.486 cm
0 g 0 G
1 0 0 1 -311.038 -328.486 cm
BT
/F16 10.909 Tf 311.038 328.486 Td[(132)]TJ
ET
1 0 0 1 327.401 328.486 cm
0 g 0 G
1 0 0 1 -327.401 -328.486 cm
BT
/F16 10.909 Tf 63.135 314.937 Td[(173.)-250(Pascal's)-250(essay)-960(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 314.937 cm
0 g 0 G
1 0 0 1 -311.038 -314.937 cm
BT
/F16 10.909 Tf 311.038 314.937 Td[(133)]TJ
ET
1 0 0 1 327.401 314.937 cm
0 g 0 G
1 0 0 1 -327.401 -314.937 cm
BT
/F16 10.909 Tf 63.135 301.388 Td[(174.)-250(Pascal's)-250(originality)-459(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 301.388 cm
0 g 0 G
1 0 0 1 -311.038 -301.388 cm
BT
/F16 10.909 Tf 311.038 301.388 Td[(134)]TJ
ET
1 0 0 1 327.401 301.388 cm
0 g 0 G
1 0 0 1 -327.401 -301.388 cm
BT
/F16 10.909 Tf 63.135 287.839 Td[(175.)-250(De)-250(la)-250(Hire)-250(and)-250(his)-250(work)-669(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 287.839 cm
0 g 0 G
1 0 0 1 -311.038 -287.839 cm
BT
/F16 10.909 Tf 311.038 287.839 Td[(134)]TJ
ET
1 0 0 1 327.401 287.839 cm
0 g 0 G
1 0 0 1 -327.401 -287.839 cm
BT
/F16 10.909 Tf 63.135 274.29 Td[(176.)-250(Descartes)-250(and)-250(his)-250(influence)-781(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 274.29 cm
0 g 0 G
1 0 0 1 -311.038 -274.29 cm
BT
/F16 10.909 Tf 311.038 274.29 Td[(135)]TJ
ET
1 0 0 1 327.401 274.29 cm
0 g 0 G
1 0 0 1 -327.401 -274.29 cm
BT
/F16 10.909 Tf 63.135 260.74 Td[(177.)-250(Newton)-250(and)-250(Maclaurin)-280(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 260.74 cm
0 g 0 G
1 0 0 1 -311.038 -260.74 cm
BT
/F16 10.909 Tf 311.038 260.74 Td[(136)]TJ
ET
1 0 0 1 327.401 260.74 cm
0 g 0 G
1 0 0 1 -327.401 -260.74 cm
BT
/F16 10.909 Tf 63.135 247.191 Td[(178.)-250(Maclaurin's)-250(construction)-377(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 247.191 cm
0 g 0 G
1 0 0 1 -311.038 -247.191 cm
BT
/F16 10.909 Tf 311.038 247.191 Td[(137)]TJ
ET
1 0 0 1 327.401 247.191 cm
0 g 0 G
1 0 0 1 -327.401 -247.191 cm
BT
/F16 10.909 Tf 63.135 233.642 Td[(179.)-250(Descriptive)-250(geometry)-250(and)-250(the)-250(second)-250(revival)-643(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 233.642 cm
0 g 0 G
1 0 0 1 -311.038 -233.642 cm
BT
/F16 10.909 Tf 311.038 233.642 Td[(137)]TJ
ET
1 0 0 1 327.401 233.642 cm
0 g 0 G
1 0 0 1 -327.401 -233.642 cm
BT
/F16 10.909 Tf 63.135 220.093 Td[(180.)-250(Duality,)-250(homology,)-250(continuity,)-250(contingent)-250(relations)]TJ
ET
1 0 0 1 311.038 220.093 cm
0 g 0 G
1 0 0 1 -311.038 -220.093 cm
BT
/F16 10.909 Tf 311.038 220.093 Td[(138)]TJ
ET
1 0 0 1 327.401 220.093 cm
0 g 0 G
1 0 0 1 -327.401 -220.093 cm
BT
/F16 10.909 Tf 63.135 206.544 Td[(181.)-250(Poncelet)-250(and)-250(Cauchy)-307(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 206.544 cm
0 g 0 G
1 0 0 1 -311.038 -206.544 cm
BT
/F16 10.909 Tf 311.038 206.544 Td[(139)]TJ
ET
1 0 0 1 327.401 206.544 cm
0 g 0 G
1 0 0 1 -327.401 -206.544 cm
BT
/F16 10.909 Tf 63.135 192.994 Td[(182.)-250(The)-250(work)-250(of)-250(Poncelet)-863(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 192.994 cm
0 g 0 G
1 0 0 1 -311.038 -192.994 cm
BT
/F16 10.909 Tf 311.038 192.994 Td[(140)]TJ
ET
1 0 0 1 327.401 192.994 cm
0 g 0 G
1 0 0 1 -327.401 -192.994 cm
BT
/F16 10.909 Tf 63.135 179.445 Td[(183.)-1143(The)-547(debt)-548(which)-547(analytic)-548(geometry)-547(owes)-548(to)]TJ 25.091 -13.549 Td[(synthetic)-250(geometry)-812(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 165.896 cm
0 g 0 G
1 0 0 1 -311.038 -165.896 cm
BT
/F16 10.909 Tf 311.038 165.896 Td[(140)]TJ
ET
1 0 0 1 327.401 165.896 cm
0 g 0 G
1 0 0 1 -327.401 -165.896 cm
BT
/F16 10.909 Tf 63.135 152.347 Td[(184.)-250(Steiner)-250(and)-250(his)-250(work)-501(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 152.347 cm
0 g 0 G
1 0 0 1 -311.038 -152.347 cm
BT
/F16 10.909 Tf 311.038 152.347 Td[(141)]TJ
ET
1 0 0 1 327.401 152.347 cm
0 g 0 G
1 0 0 1 -327.401 -152.347 cm
BT
/F16 10.909 Tf 63.135 138.798 Td[(185.)-250(Von)-250(Staudt)-250(and)-250(his)-250(work)-306(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 138.798 cm
0 g 0 G
1 0 0 1 -311.038 -138.798 cm
BT
/F16 10.909 Tf 311.038 138.798 Td[(142)]TJ
ET
1 0 0 1 327.401 138.798 cm
0 g 0 G
1 0 0 1 -327.401 -138.798 cm
BT
/F16 10.909 Tf 63.135 125.248 Td[(186.)-250(Recent)-250(developments)-918(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 125.248 cm
0 g 0 G
1 0 0 1 -311.038 -125.248 cm
BT
/F16 10.909 Tf 311.038 125.248 Td[(142)]TJ
ET
1 0 0 1 327.401 125.248 cm
0 g 0 G
1 0 0 1 -327.401 -125.248 cm
BT
/F16 10.909 Tf 46.771 111.699 Td[(INDEX)-890(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ
ET
1 0 0 1 311.038 111.699 cm
0 g 0 G
1 0 0 1 -311.038 -111.699 cm
BT
/F16 10.909 Tf 311.038 111.699 Td[(144)]TJ
ET
1 0 0 1 327.401 111.699 cm
0 g 0 G
1 0 0 1 -280.63 -72.917 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
69 0 obj <<
/Type /Page
/Contents 70 0 R
/Resources 68 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 64 0 R
>> endobj
68 0 obj <<
/Font << /F16 6 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
73 0 obj <<
/Length 126
>>
stream
1 0 0 1 93.543 548.934 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
1 0 0 1 -280.63 -510.152 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
72 0 obj <<
/Type /Page
/Contents 73 0 R
/Resources 71 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 64 0 R
>> endobj
71 0 obj <<
/ProcSet [ /PDF ]
>> endobj
74 0 obj
<< /S /GoTo /D (index3) >>
endobj
77 0 obj
(CHAPTER I - ONE-TO-ONE CORRESPONDENCE)
endobj
78 0 obj
<< /S /GoTo /D (index4) >>
endobj
81 0 obj
()
endobj
82 0 obj
<< /S /GoTo /D (index5) >>
endobj
85 0 obj
()
endobj
88 0 obj <<
/Length 3059
>>
stream
1 0 0 1 46.771 548.934 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
1 0 0 1 -280.63 -19.8 cm
0 g 0 G
1 0 0 1 -46.771 -529.134 cm
BT
/F16 7.97 Tf 337.795 512.811 Td[([1])]TJ/F16 18.959 Tf -291.024 -65.712 Td[(CHAPTER)-265(I)-265(-)-266(ONE-TO-ONE)]TJ 0 -24.647 Td[(CORRESPONDENCE)]TJ/F39 10.909 Tf 0 -73.574 Td[(1.)-592(Definition)-365(of)-364(one-to-one)-364(correspondence.)]TJ/F16 10.909 Tf 213.907 0 Td[(Given)-364(any)-364(two)]TJ -213.907 -13.55 Td[(sets)-177(of)-178(individuals,)-192(if)-177(it)-178(is)-177(possible)-177(to)-178(set)-177(up)-178(such)-177(a)-178(correspondence)]TJ 0 -13.549 Td[(between)-203(the)-202(two)-203(sets)-202(that)-203(to)-202(any)-203(individual)-202(in)-203(one)-202(set)-203(corresponds)]TJ 0 -13.549 Td[(one)-190(and)-189(only)-190(one)-190(individual)-189(in)-190(the)-190(other,)-201(then)-190(the)-190(two)-189(sets)-190(are)-190(said)]TJ 0 -13.549 Td[(to)-221(be)-221(in)]TJ/F20 10.909 Tf 34.498 0 Td[(one-to-one)-221(correspondence)]TJ/F16 10.909 Tf 121.752 0 Td[(with)-221(each)-221(other.)-240(This)-221(notion,)]TJ -156.25 -13.549 Td[(simple)-325(as)-324(it)-325(is,)-343(is)-324(of)-325(fundamental)-324(importance)-325(in)-325(all)-324(branches)-325(of)]TJ 0 -13.549 Td[(science.)-305(The)-268(process)-268(of)-269(counting)-268(is)-268(nothing)-268(but)-269(a)-268(setting)-268(up)-268(of)-269(a)]TJ 0 -13.55 Td[(one-to-one)-175(correspondence)-175(between)-175(the)-174(objects)-175(to)-175(be)-175(counted)-175(and)]TJ 0 -13.549 Td[(certain)-251(words,)-251('one,')-251('two,')-251('three,')-251(etc.,)-251(in)-251(the)-250(mind.)-253(Many)-251(savage)]TJ 0 -13.549 Td[(peoples)-346(have)-347(discovered)-346(no)-347(better)-346(method)-346(of)-347(counting)-346(than)-347(by)]TJ 0 -13.549 Td[(setting)-355(up)-355(a)-356(one-to-one)-355(correspondence)-355(between)-355(the)-355(objects)-356(to)]TJ 0 -13.549 Td[(be)-341(counted)-342(and)-341(their)-342(fingers.)-524(The)-341(scientist)-342(who)-341(busies)-342(himself)]TJ 0 -13.55 Td[(with)-267(naming)-267(and)-267(classifying)-267(the)-267(objects)-267(of)-267(nature)-267(is)-268(only)-267(setting)]TJ 0 -13.549 Td[(up)-265(a)-265(one-to-one)-266(correspondence)-265(between)-265(the)-265(objects)-265(and)-266(certain)]TJ 0 -13.549 Td[(words)-286(which)-286(serve,)-295(not)-286(as)-286(a)-286(means)-286(of)-286(counting)-286(the)-573(objects,)-295(but)]TJ/F16 7.97 Tf 291.024 0 Td[([2])]TJ/F16 10.909 Tf -291.024 -13.549 Td[(of)-379(listing)-380(them)-379(in)-379(a)-380(convenient)-379(way.)-638(Thus)-379(he)-380(may)-379(be)-379(able)-380(to)]TJ 0 -13.549 Td[(marshal)-274(and)-274(array)-274(his)-274(material)-274(in)-274(such)-274(a)-274(way)-274(as)-274(to)-274(bring)-274(to)-274(light)]TJ 0 -13.55 Td[(relations)-262(that)-262(may)-261(exist)-262(between)-262(the)-262(objects)-261(themselves.)-286(Indeed,)]TJ 0 -13.549 Td[(the)-195(whole)-195(notion)-195(of)-195(language)-195(springs)-195(from)-195(this)-195(idea)-196(of)-195(one-to-one)]TJ 0 -13.549 Td[(correspondence.)]TJ
ET
1 0 0 1 46.771 38.782 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
87 0 obj <<
/Type /Page
/Contents 88 0 R
/Resources 86 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 64 0 R
>> endobj
89 0 obj <<
/D [87 0 R /XYZ 46.771 518.175 null]
>> endobj
75 0 obj <<
/D [87 0 R /XYZ 46.771 518.175 null]
>> endobj
79 0 obj <<
/D [87 0 R /XYZ 46.771 379.284 null]
>> endobj
90 0 obj <<
/D [87 0 R /XYZ 46.771 362.459 null]
>> endobj
93 0 obj <<
/D [87 0 R /XYZ 273.488 159.189 null]
>> endobj
83 0 obj <<
/D [87 0 R /XYZ 46.771 66.142 null]
>> endobj
86 0 obj <<
/Font << /F16 6 0 R /F39 92 0 R /F20 29 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
94 0 obj
<< /S /GoTo /D (index6) >>
endobj
97 0 obj
()
endobj
98 0 obj
<< /S /GoTo /D (index7) >>
endobj
101 0 obj
()
endobj
106 0 obj <<
/Length 3792
>>
stream
1 0 0 1 93.543 548.934 cm
0 g 0 G
1 0 0 1 -93.543 -548.934 cm
BT
/F16 10.909 Tf 93.543 548.934 Td[(2)-2449(An)-250(E)-1(lementary)-250(Course)-250(in)-250(Synthetic)-250(Projective)-250(Geometry)]TJ
ET
1 0 0 1 374.173 548.934 cm
0 g 0 G
1 0 0 1 -374.173 -548.934 cm
BT
/F39 10.909 Tf 93.543 518.175 Td[(2.)-751(Consequences)-418(of)-417(one-to-one)-417(correspondence.)]TJ/F16 10.909 Tf 237.898 0 Td[(The)-417(most)]TJ -237.898 -13.549 Td[(useful)-248(and)-247(interesting)-248(problem)-247(that)-248(may)-247(arise)-248(in)-247(connection)-248(with)]TJ 0 -13.549 Td[(any)-175(one-to-one)-174(correspondence)-175(is)-174(to)-175(determine)-174(just)-175(what)-175(relations)]TJ 0 -13.549 Td[(existing)-501(between)-500(the)-501(individuals)-501(of)-501(one)-500(assemblage)-501(may)-501(be)]TJ 0 -13.55 Td[(carried)-200(over)-200(to)-200(another)-200(assemblage)-200(in)-200(one-to-one)-200(correspondence)]TJ 0 -13.549 Td[(with)-332(it.)-495(It)-332(is)-332(a)-332(favorite)-332(error)-331(to)-332(assume)-332(that)-332(whatever)-332(holds)-332(for)]TJ 0 -13.549 Td[(one)-268(set)-269(must)-268(also)-268(hold)-268(for)-269(the)-268(other.)-305(Magicians)-268(are)-268(apt)-268(to)-269(assign)]TJ 0 -13.549 Td[(magic)-284(properties)-284(to)-284(many)-283(of)-284(the)-284(words)-284(and)-284(symbols)-284(which)-284(they)]TJ 0 -13.549 Td[(are)-286(in)-286(the)-285(habit)-286(of)-286(using,)-295(and)-285(scientists)-286(are)-286(constantly)-286(confusing)]TJ 0 -13.55 Td[(objective)-251(things)-250(with)-251(the)-250(subjective)-251(formulas)-250(for)-251(them.)-251(After)-251(the)]TJ 0 -13.549 Td[(physicist)-258(has)-258(set)-258(up)-258(correspondences)-258(between)-258(physical)-258(facts)-258(and)]TJ 0 -13.549 Td[(mathematical)-284(formulas,)-292(the)-284("interpretation")-284(of)-284(these)-284(formulas)-284(is)]TJ 0 -13.549 Td[(his)-250(most)-250(important)-250(and)-250(difficult)-250(task.)]TJ/F39 10.909 Tf 0 -49.877 Td[(3.)]TJ/F16 10.909 Tf 16.414 0 Td[(In)-418(mathematics,)-460(effo)-1(rt)-418(is)-418(constantly)-418(being)-418(made)-419(to)-418(set)-418(up)]TJ -16.414 -13.549 Td[(one-to-one)-381(correspondences)-381(between)-381(simple)-381(notions)-381(and)-381(more)]TJ 0 -13.55 Td[(complicated)-177(ones,)-191(or)-176(between)-177(the)-176(well-explored)-177(fields)-176(of)-177(research)]TJ 0 -13.549 Td[(and)-510(fields)-509(less)-510(known.)-1029(Thus,)-575(by)-509(mea)-1(ns)-509(of)-510(the)-510(mechanism)]TJ 0 -13.549 Td[(employed)-288(in)-288(analytic)-288(geometry,)-298(algebraic)-288(theorems)-288(are)-288(made)-288(to)]TJ 0 -13.549 Td[(yield)-286(geometric)-287(ones,)-295(and)-286(vice)-286(versa.)-359(In)-287(geometry)-286(we)-286(get)-286(at)-287(the)]TJ 0 -13.549 Td[(properties)-384(of)-384(the)-384(conic)-384(sections)-384(by)-384(means)-384(of)-384(the)-385(properties)-384(of)]TJ 0 -13.55 Td[(the)-285(straight)-286(line,)-294(and)-285(cubic)-285(surfaces)-285(are)-286(studied)-285(by)-285(means)-285(of)-286(the)]TJ 0 -13.549 Td[(plane.)]TJ/F16 7.97 Tf -72.755 0 Td[([3])]TJ/F39 10.909 Tf 84.711 -76.975 Td[(4.)-369(One-to-one)-290(correspondence)-290(and)-290(enumeration.)]TJ/F16 10.909 Tf 230.857 0 Td[(If)-290(a)-290(one-)]TJ -242.813 -13.549 Td[(to-one)-371(correspondence)-372(has)-371(been)-372(set)-371(up)-371(between)-372(the)-371(objects)-372(of)]TJ 0 -13.549 Td[(one)-369(set)-370(and)-369(the)-369(objects)-369(of)-370(another)-369(set,)-399(then)-369(the)-369(inference)-370(may)]TJ 0 -13.55 Td[(usually)-216(be)-216(drawn)-215(that)-216(they)-216(have)-216(the)-216(same)-215(number)-216(of)-216(elements.)-239(If,)]TJ 0 -13.549 Td[(however,)-234(there)-230(is)-230(an)-230(infinite)-230(number)-230(of)-230(individuals)-230(in)-230(each)-231(of)-230(the)]TJ
ET
1 0 0 1 93.543 38.782 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
105 0 obj <<
/Type /Page
/Contents 106 0 R
/Resources 104 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 64 0 R
>> endobj
107 0 obj <<
/D [105 0 R /XYZ 93.543 529.134 null]
>> endobj
95 0 obj <<
/D [105 0 R /XYZ 93.543 331.999 null]
>> endobj
108 0 obj <<
/D [105 0 R /XYZ 93.543 316.89 null]
>> endobj
109 0 obj <<
/D [105 0 R /XYZ 93.543 194.947 null]
>> endobj
99 0 obj <<
/D [105 0 R /XYZ 93.543 173.729 null]
>> endobj
110 0 obj <<
/D [105 0 R /XYZ 105.499 120.339 null]
>> endobj
104 0 obj <<
/Font << /F16 6 0 R /F39 92 0 R >>
/ProcSet [ /PDF /Text ]
>> endobj
111 0 obj
<< /S /GoTo /D (index8) >>
endobj
114 0 obj
()
endobj
117 0 obj <<
/Length 4790
>>
stream
1 0 0 1 46.771 548.934 cm
0 g 0 G
1 0 0 1 -46.771 -548.934 cm
BT
/F16 10.909 Tf 46.771 548.934 Td[(4.)-250(One-to-one)-250(correspondence)-250(and)-250(enumeration)-6203(3)]TJ
ET
1 0 0 1 327.401 548.934 cm
0 g 0 G
1 0 0 1 -280.63 -19.8 cm
0 g 0 G
1 0 0 1 5.605 -184.904 cm
q 2.67513 0 0 2.67513 0 0 cm
1 0 0 1 2.727 0 cm
q 1 0 0 1 0 0 cm
q
96.9596 0 0 69.1197 0 0 cm
/Im1 Do
Q
Q
1 0 0 1 -2.727 0 cm
Q
1 0 0 1 -52.376 -344.23 cm
BT
/F16 10.909 Tf 174.29 325.226 Td[(F)]TJ/F16 7.97 Tf 6.066 0 Td[(IG)]TJ/F16 10.909 Tf 8.408 0 Td[(.)-269(1)]TJ
ET
1 0 0 1 46.771 319.668 cm
0 g 0 G
1 0 0 1 -46.771 -319.668 cm
BT
/F16 10.909 Tf 46.771 296.478 Td[(two)-294(sets,)-306(the)-294(notion)-295(of)-294(counting)-294(is)-295(necessarily)-294(ruled)-294(out.)-383(It)-295(may)]TJ 0 -13.549 Td[(be)-264(possible,)-268(nevertheless,)-267(to)-264(set)-264(up)-264(a)-264(one)-1(-to-one)-264(correspondence)]TJ 0 -13.549 Td[(between)-479(the)-478(elements)-478(of)-479(two)-478(sets)-479(even)-478(when)-479(the)-478(number)-479(is)]TJ 0 -13.549 Td[(infinite.)-244(Thus,)-235(it)-232(is)-231(easy)-232(to)-231(set)-232(up)-231(such)-232(a)-231(correspondence)-232(between)]TJ 0 -13.549 Td[(the)-193(points)-193(of)-193(a)-193(line)-193(an)-192(inch)-193(long)-193(and)-193(the)-193(points)-193(of)-193(a)-193(line)-193(two)-193(inches)]TJ 0 -13.55 Td[(long.)-284(For)-261(let)-262(the)-261(lines)-261(\050Fig.)-284(1\051)-261(be)]TJ/F20 10.909 Tf 145.72 0 Td[(AB)]TJ/F16 10.909 Tf 16.181 0 Td[(and)]TJ/F20 10.909 Tf 18.604 0 Td[(A'B')]TJ/F16 10.909 Tf 18 0 Td[(.)-261(Join)]TJ/F20 10.909 Tf 26.613 0 Td[(AA')]TJ/F16 10.909 Tf 18.516 0 Td[(and)]TJ/F20 10.909 Tf 18.604 0 Td[(BB')]TJ/F16 10.909 Tf 15.665 0 Td[(,)]TJ -277.903 -13.549 Td[(and)-288(let)-288(these)-288(joining)-288(lines)-288(meet)-288(in)]TJ/F20 10.909 Tf 152.288 0 Td[(S)]TJ/F16 10.909 Tf 5.455 0 Td[(.)-288(For)-288(every)-288(point)]TJ/F20 10.909 Tf 77.104 0 Td[(C)]TJ/F16 10.909 Tf 10.417 0 Td[(on)]TJ/F20 10.909 Tf 14.051 0 Td[(AB)]TJ/F16 10.909 Tf 16.472 0 Td[(a)]TJ -275.786 -13.549 Td[(point)]TJ/F20 10.909 Tf 25.653 0 Td[(C')]TJ/F16 10.909 Tf 12.834 0 Td[(may)-296(be)-295(found)-296(on)]TJ/F20 10.909 Tf 78.34 0 Td[(A'B')]TJ/F16 10.909 Tf 21.224 0 Td[(by)-296(joining)]TJ/F20 10.909 Tf 48.273 0 Td[(C)]TJ/F16 10.909 Tf 10.5 0 Td[(to)]TJ/F20 10.909 Tf 11.712 0 Td[(S)]TJ/F16 10.909 Tf 8.678 0 Td[(and)-296(noting)-295(the)]TJ -217.214 -13.549 Td[(point)]TJ/F20 10.909 Tf 24.976 0 Td[(C')]TJ/F16 10.909 Tf 12.158 0 Td[(where)]TJ/F20 10.909 Tf 29.198 0 Td[(CS)]TJ/F16 10.909 Tf 15.279 0 Td[(meets)]TJ/F20 10.909 Tf 27.998 0 Td[(A'B')]TJ/F16 10.909 Tf 18 0 Td[(.)-234(Similarly,)-236(a)-234(point)]TJ/F20 10.909 Tf 83.567 0 Td[(C)]TJ/F16 10.909 Tf 9.824 0 Td[(may)-234(be)-233(found)]TJ -221 -13.549 Td[(on)]TJ/F20 10.909 Tf 14.715 0 Td[(AB)]TJ/F16 10.909 Tf 17.135 0 Td[(for)-349(any)-349(point)]TJ/F20 10.909 Tf 62.32 0 Td[(C')]TJ/F16 10.909 Tf 13.415 0 Td[(on)]TJ/F20 10.909 Tf 14.715 0 Td[(A'B')]TJ/F16 10.909 Tf 18 0 Td[(.)-349(The)-349(correspondence)-349(is)-349(clearly)]TJ -140.3 -13.55 Td[(one-to-one,)-349(but)-330(it)-329(would)-330(be)-329(absurd)-330(to)-329(infer)-330(from)-329(this)-330(that)-330(there)]TJ 0 -13.549 Td[(were)-306(just)-306(as)-306(many)-306(points)-307(on)]TJ/F20 10.909 Tf 127.904 0 Td[(AB)]TJ/F16 10.909 Tf 16.67 0 Td[(as)-306(on)]TJ/F20 10.909 Tf 26.675 0 Td[(A'B')]TJ/F16 10.909 Tf 18 0 Td[(.)-306(In)-306(fact,)-320(it)-306(would)-307(be)]TJ -189.249 -13.549 Td[(just)-309(as)-309(reasonable)-308(to)-309(infer)-309(that)-309(there)-308(were)-309(twice)-309(as)-309(many)-309(points)]TJ 0 -13.549 Td[(on)]TJ/F20 10.909 Tf 14.468 0 Td[(A'B')]TJ/F16 10.909 Tf 21.558 0 Td[(as)-326(on)]TJ/F20 10.909 Tf 27.115 0 Td[(AB)]TJ/F16 10.909 Tf 13.331 0 Td[(.)-326(For)-326(if)-327(we)-326(bend)]TJ/F20 10.909 Tf 76.268 0 Td[(A'B')]TJ/F16 10.909 Tf 21.558 0 Td[(into)-326(a)-327(circle)-326(with)-326(center)]TJ -174.298 -13.549 Td[(at)]TJ/F20 10.909 Tf 12.287 0 Td[(S)]TJ/F16 10.909 Tf 9.864 0 Td[(\050Fig.)-713(2\051,)-443(we)-404(see)-405(that)-404(for)-404(every)-405(point)]TJ/F20 10.909 Tf 174.195 0 Td[(C)]TJ/F16 10.909 Tf 11.685 0 Td[(on)]TJ/F20 10.909 Tf 15.32 0 Td[(AB)]TJ/F16 10.909 Tf 17.74 0 Td[(there)-404(are)]TJ -241.091 -13.55 Td[(two)-264(points)-265(on)]TJ/F20 10.909 Tf 62.596 0 Td[(A'B')]TJ/F16 10.909 Tf 18 0 Td[(.)-264(Thus)-529(it)-264(is)-265(seen)-264(that)-264(the)-265(notion)-264(of)-264(one-to-one)]TJ/F16 7.97 Tf 210.427 0 Td[([4])]TJ/F16 10.909 Tf -291.023 -13.549 Td[(correspondence)-358(is)-359(more)-358(extensive)-359(than)-358(the)-359(notion)-358(of)-359(counting,)]TJ 0 -13.549 Td[(and)-306(includes)-306(the)-306(notion)-306(of)-306(counting)-306(only)-306(when)-306(applied)-306(to)-306(finite)]TJ
ET
1 0 0 1 46.771 38.782 cm
0 g 0 G
1 0 0 1 280.63 0 cm
0 g 0 G
endstream
endobj
116 0 obj <<
/Type /Page
/Contents 117 0 R
/Resources 115 0 R
/MediaBox [0 0 419.528 595.276]
/Parent 119 0 R
>> endobj
102 0 obj <<
/Type /XObject
/Subtype /Image
/Width 404
/Height 288
/BitsPerComponent 8
/ColorSpace /DeviceRGB
/Length 349056
>>
stream
ÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿÿ
|