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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 65, page id 797435492:0289
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# Lines: 43 recognised, mean confidence 0.89
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P. E C Y. VTII.
Nam (Facto ut prius) erit IL. IR: : FGo FF : : MO. MNI.
quapropter exit punctum R extra curram Y F N.
POCIThxec, ut praecedens, aliter octendi; sed verbis pluribuso
Curras ita litas concipe quales figura monstrat. nam seron giar cg0
ac actoneg ler fusitans casus prae caereris obrios ac Faciles arripiens pro-
Pono. Hloc ubique subnotatum relim.
VTI. Sit punctum datum D, curraque du ZF M, Y FN, iIL
relata, ut a D projecta quacunque recta DP F, habeant ad se rectae Piz. 81.
DE, D F rarionem semper eandem; unam vero Y F H cangat recta
FS; cui parallela (IE F R; tanser recta PR CUrVaM X F M.
Nam a D uccunque projiciatur recta DK (lineas intersecans, ut
vides). FAtque DR. DI:: DF. DF:: DEI. DM; ergo quum BIF
DRE DN; CxIEDIE DM; quare tora recta R P extra Curram
Z F M cadit.
RectX NIK, MI rarionem semper candem obtinene; unde res ali-
ter constat.
VITI. SinEEreS CHEVX Z F NI, Y FN, ZC O cales, ut SI ab alT∞
nato puncto D projiciatur urcunque recta DFFC, HaBCANEINFCrCCDEX
EC, F. F rationem semper eandem (puta quam R ad 5) tangant au- F18. 82.
tem rectae FY, C T currarum duas (DuTa X F MI, Z GO) in E, C;
OPOrEEt CurrX Y F N tangenrem ad F delignare.
Concipiatur curra TFV calis, ut a D urcunque projectâ rect à
DMKL, (qux secet rectaS TE, TC punctis I, L, _ iltam cur-
ra in R) habeane semper intercepeae IL, I R rarionem eandem datae
RadS; (a) eA isItURIRD IH; quaRECUEra I F K curvam YFN (4) 2 Lea.
ransic: (b) est anrem curra T FR hyporbola; hanc tansat PS; (6)
illa quoque curram X F NranSCF.
Duoniam hyperbolam cansentis hic primum injecta est mentio; hu-
jus Cuna cum aliarum omnium consimili ratione procreatarum seu re-
siprocarum linearum tansentibus) tangentem ita detiniemus.
TX. Sine V D recta linca, duXQUe CUEVA Z FM, Y F N ita re-
latx, ut ducta libere recta F D F ad positione datam parallela, sic P1G. 83.
Cemmper rectanentam ex DF, D E par eidem alicui spatio; TanGAE aU-
tem recta F T Curram X F. M in F, cum recta V D concurrens in T.
Tumaturque DS ==DT; d connectatur FS; hXC Curram Y FB
canse adE.
Nam uteunque ducatur IPV ad P. P parallela, lineas expolicas (c.
CarS.
2. Lea. VII.
VILI
(b) 4 Tect. VI.
(5) 2. hrojea