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# Title: [Lectiones XVIII, Cantabrigiae in Scholis publicis habitae] Lectiones XVIII, Cantabrigiæ in Scholis publicis habitæ (shelfmarks Leibn. Marg. 0; ZEN Leibn. Marg. 0)
# Folio 42, page id 797435492:0074
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.92
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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E. B C Y. V.
tioribus minores line. de quod cuiris ea majori binx pares incerteri
pollune, ad ejus urramque parrem Cingula. nimirum hxc c superiori
constructione luculente patent; pauxillum expende Sodes; e per-
spicies; operamquemeam non deliderabis.
ZII. EIis praestratis ad Principale construendum Problema reverti-
Eis. 55,50. mur; e reliqua derexenda. Scilicet imprimis a daro puncto A pro-
diens radius est delignandus, cujus retractus per darum punctum X
exanlibit. I) hoc ita conficitur. Per A, X ducancur retringenti perpen-
diculares AB, X P. tum inprimo casu tat AB. YB:: VIg - Rg.
I. neque non Aat Z P. T:: V Ig = R9. R. d per punctum Y
transadisatur recta NC subrendens angulum APF, e iplam Y ex
aequans; _ conne tantur AN, XI. dicofactum; Peu rectam XV
incidentis A N retractum esse. I Ftenim estZ P. RB:: NP. NB::
NO. NIY. permurandoque ZP. NO:: RB. NZ. hoc est ZP.
NO (vel NI9 - Rg. R):: KB. YN. itaque per theorema pra-
missum liquet R N ipsius A N retractum esse: (. FF.
Flaud ablimilirer in secundo casu; HaLX P. Y P:: V R9 - Ig. R,
itemque AB. T:: VR9 -- P9. I; anguloque AB F Per Y tranSI
ens, ipsamque T adaequans inseratur recta NC; connectanturque
AN, XNI; Factum eric. ) Nam iplam X P prorractam secet A N in
5. eAtque SP. YNI:: AB. GN:: AB. T:: V R9- 19. I. unde
consequitur e praemonstraris Fore X N iplius SN retractum C. F. F.
XIII. Exhinc, Se praemissa respiciendo Pacis diluceseir non ulera
duos ad unas pervendicularis A B parres incidentium retractos in uno
puneto convenire. nam (ur supra declararum) per puncum X (quod
universis hujusmodi constructionibus commune, vel invariatum per-
perlistie; in primo casu quoad omnes ab A incidentes; in secundo
gnoad omnes per X transeuntes retractos) plures duabus sibi pares
duabus sibi pares rectae angulo recro XP F, vel A B F interleri ne-
queunt; adeoque nec plures relracri per ipsum X rransibunt.
XIV. Porro, cum e dicris definita habeatur recta, in qua puneti
A Imaso verlatur; ilte nimirum retractus qui per oculi centrum
eransit, modo jam expolito ducendus; ipsum jam punctum decermi-
nandum venit, ad quod illa pracise consultit; id quod ctiam eprxce
dentibus haud difticulrer eliciemus.
XV. Sumacur, in calu primo, punerum Y condirione prxdicum
iat