By Ferenc Kárteszi (Eds.)

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Additional info for Appendix: The Theory of Space

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Que cp1I1w-z ; est (per $. ) In S vero nttlla 3 puncta u, d, c ipsiris L vel It' i n recta sunt. gr. am) inrra duos rcliquos cadit ; et tunc (per S;. ) tam l a m yuarn cam It'. 0 IT. 1, est etianc in S fitlea, et F stqerficies. ) ~d nullum alium axem Jn. Lre est. ) quodvis punctum ipsius F in J'? 12), quaecunque puricta a,6 fuerint in eo, ita s i l i congcuere poterit, ut a in b cadat; e s ~igitur F suy e r f i c i e s unilfovmis. Patet lrinc (per 11. et 12) L esse lineam iintlfOrrnem. 7). Cujusris ylani, per punctum a ipsius Fad axem am oblique positi,sectio cum F in S yeriphert'a circulr' est.

He got acquainted 32 with the ideas of GAUSSonly after the Appendix had been published, and he took notice of a (single) work of LOBACHEVSKY even later, in 1848 (these circumstances have already been pointed out by STACKEL*). The stimulating effect of scholarly environment, the interest shown by colleagues working in related fields, acquaintance with the methods of other scientists are all solid supports and strong impulses for an effective and stout research work. Bolyai had no share of them. The first written document from which we can draw conclusions regarding the progress of his ideas is dated from 1820.

7. ); adeoque et rzp, Ld se mutuo - v Y r y < - 9 secant. Patet exhinc Axiorna Xf. 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.

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