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By Ferenc Kárteszi (Eds.)

ISBN-10: 0080872492

ISBN-13: 9780080872490

ISBN-10: 0444865284

ISBN-13: 9780444865281

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R i n F jes1=2xr, et pa- -- riter 0 (in F ) = w2(per fi intelligcndo F, s h e notum 3,1415926.. -1 u S' 22- (Fig*%Si ab fucrit I, ipsiits am h an; cttque -, A cab (e rocta a; B ee 1 0 1 in et c in tfarmi Iinea ( - ab composilus) b"; 10 ) . Juxta d6, tnm juxta (eratur prius ;;;r semper porro in infinitum: erit via ipsius Nam (posleriori I dicta) sit - c linea L ipsius em. punctum quodvis d in cd ; dnllf em, et 6 punctum ipsios L in ;;; cadens ~ erit 1m 0 am. et ac = 6d. adeoquc dll 0 em , eonsequ.

Et porest nbg ita coiiiputari, ut j a ab i quovis dato minus discre1 pet, cum nonnisi sin nbq= z-csse debeat. $sS. 1 ry , §. 39. ) Si fuerint (in plano) p 9 et s t II rectae mn (. i (forsan tnixtilinci) ecp ,cut congruent, atque ec= ca. Si yorro cf=ag, erit A a c f G A c a g , et utrum que puadriluteri fagc tliniidiuin cst. ), adeoque etfam cag+acg+cga=2R ; 'itaque i n quavis einsmodi At0 acg summa 3 I\lotum =2R. Sive in ug (quae II mn) ceciderit autem recta ar, sive non : Alorum rcctihheorum age, ugh, tam ~ ~ S O T Uqwam ~ stcmmarum Alorum ipsoruadem, aequakifar in aperto est.

For a long time, no other results of his were known. He has remained isolated to the end of his life. Not by his fault, but by the social conditions of that time. This page intentionally left blank PART I1 THE ABSOLUTE GEOMETRY OF JANOS BOLYAI, THE APPENDIX This page intentionally left blank A P P E N SCJBNTIAM SPAT11 D 1 X. absolute yeram exhibens : o votitots aut fafsiiate Axiomatis X I Euclidei haud 'unpuarn decidenda) independentea: adjecta ad casum Tale sitatis, quadralura circuli gc o m e I r ica.

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Appendix: The Theory of Space by Ferenc Kárteszi (Eds.)


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