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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 96, page id 797435492:0324
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l. P C F. ZI.
VI. FTyperbolam AF. B, cujus Centrum C, tansanE duae rectae
BT, FS, _ reliqua ponantur ut in proxime praecedente; erit TD.
AD SP. AP
Nam est C A. CD:: CT. C A. unde C A - C T. CD.
C A:: CT. C A3 hOc CA TA. AD:: CT. C A. suppare dis-
CUxIU eAS A. AP:: CS. C A. Verum est C I. C A 2CS.
C a. quare I A. AD = 3S A. AP; seu componendo TD. AI
SF. AP.
VII. Circuli A EB (cujuS Centrum C) ex paraboliformis A F B
communes sint axis AD, e basISBD; CIE aurem paraboliformis ex-
Donens ; d AD:
C A (vel m =- n. M = 2n::
C A. AD) circulum verotansar recta BT; haec quoque paraboli-
formem A F B continget.
Nam quia BP circulum tangic, est CT. CA :: C A. CD. unde TA.
AD:: CACD. componendoque ID. AD:: C A. I CD. CD. lem, quo-
uiam est (ex hypothesi) C A. AD:: m.  n. m - 2 n; erit per ratio.
nis convertionem C A. C D :: m -- n. n. ee componendo C A. )
CD. CD:: m. n. HOC eATB. AD:: m. n. unde (a) palam FIL,
quod B Eparaboliformem AF Btansit.
VIII. Subnotetur, quod inverse, data ratione ipsius A D ad C A
designabitur hinc paraboliformis; quae Circulum A P. B ad B contin-
Bet. Nempe, A AD = -=, erir 2r --, dictx paraboliformis ex-
Ponens. Nam polito Fore
5  - 1
F - 5
mi exirideo (juxta crucem
mulciplicando) m F = m 5= 2 tn - -sn. _ transponendo mt
2nF = m s- n s. ac ideo (aqualicarem ad analogismum redisendo)
m = - n. m = 2 n : : t. s:: C A. A D. itaque constat ex anteceden
te Propolicu.
IX. Manente quoad exrera sexrimx hypocheli, paraboliformis
A F B extra circulum A F B tora cadet.
Nam uccunque ducatur recta O F F ad D B parallela. quxe secet
circulum ad F, parabolitormem in F; duetxque concipiantur rectx
ES circulum,  recta PR paraboliformem cominsentes; PAque
versa praxima sequitur gy AC
F18, 137.
F18. 138.
(4) 2 bajur a
E18, 239.