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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 55, page id 797435492:0271
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# Lines: 38 recognised, mean confidence 0.89
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L B C Y VI.
irem PO ad Y F. Parallela. F Aque F F 9 = F O g(C P9) )- OF9
=1 2E OXOF (=L 2CPXOF). Verum obC P. C A:: OP.
OF:: C F. OF; Cs C P XOF = C A X CF; ergO FF9=
CP9-)n OFg.) 2C A X CF. item est AF9 = C Fg.)
C A9 - = 2 C A X C F; quapropter est F F9.) AF 9 = C P9.).
C A9 - ] OF9 C F g. hoc estE C9 == (AP9. 1- PF g =
CV 9 ]. PF 4. vel ECg - PF4 = CV 4. Verum est CF.
(PO). PF: : CP. AP:: C P. CV; unde FC9.
CVC
CPC
CFg
CV 9; adesque linea C V C est hyperbola, cujus centrum C; se-
MIaXES CV, C P.
Nor Ducta recta F O ad TH perpendiculari, sumptaque O R =
AE; _E CONMEKa CR; exit C R hyperbola V GC perpendicularis,
mihi praesta sistidem; aut ipse rem ad Calculum exise; co verba
non protundam.
XXVI. Positione dara SInE ReCEX A C, BD (se intersecantes in Z)
quas decusset recta A B; cum ducta utcunque recti PRL ad A B FI8. 59.
varallela, (quae rectas A C, BD seceE punCtiS P, R) SITP L aequa-
lisipli BK; erit linea A L. L recta.
Nam, (duCta Z O ad B A paralleli, est AO. AP:: (BZ.
BR::) OX. P L: ersolinea AL. L est recta.
XXVTI. Postione data sir recta A X, _C punctum D. Reque non
linea DNN talis; ut per D ductâ quacunque recta MN (quare. F18. 60.
ctam A X secet in M, _C lineam D N AI in N) sic perperim rectangu-
lum ex D MI, DEI aequale dato (puca quadrato Cx Z); erie linea
DN N circularis.
Nam ducatur D B ad A X perpendicularis; sitque DB. Z:: L.
DF; SE COnneCtATUE N F; LCt jaM D ML X D N = Z 9 =- DBX
DE; quare D M. D B:: D E. D N. ergo triangula D B M, DN F
similia sunc; quaproxter angulus D NI P rectus est; itaque linea DHIN
est circularis: (ad circuluun perrinens, cnjus Diameter D F).
Vides nedum rectam e hyperbolam; sed _ suo modo rectam ac
circulum cibilineas esse reciprocas. Verum hic, ethi praeludiis no-
Aris nondum absoluris, paulum subsiCtamuS.
EC X. VL