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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 97, page id 797435492:0333
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L. R C T. ZI.
RO. AC:: (a) m. n:: FD. AD (B) C SC. AO. quare RC (4) 2. Mga.
E SC. Unde (C) PaTCE FOTA A F B extra circulum A E B jacerc.
Z. Reliquis iridem Ptantibus, S ad balin 3 F (uccunque parallelam
ip(IDB) Sc axem AD concticuca intelligacur paraboliformis ejuldem cum FI8. 139.
ipla AEB generis (nempe cujus etiam exponens,) illa ad. ParteS A
supra GF, extra circulum cota jacebit.
Nam in arcu. A F accepto quocunque puncto M, ductague MP ad
FC parallelâ, _ M V circulum cansente; eAt V P. AP - 35C.
AC = = RO. AC:: m. n; (a) itaque rurtus liquet ProPOlI (a) 3. Bujus ap.
tum.
ZI. Consectatur etiam dictam (ip(I A F B coordinaram e ad ba-
Cin C. P constituram) paraboliformem intra 6 F. ad DB ProtraCtaM, Fi8. 139.
catenus inera Circulum cotam cadere,
Ouod intra Circulum Ctarim intra P C cadet ex eo pater, quod ipsam
tangens R F circulum secar (quia niempe S P circulum cangic). Quod
alibi C irculo non occurret hinc pater; quonium poliro quod occurrat
uspiam ad N, (a) cora supra N exrra circulum caderet, contra quam (a) 3. hujus ax.
modo dictum ac ostensum est.
XIL. POrTO, Fyperbolae A F B (CujuIS CeNEru C) _ parabolifor-
mis AF B, Cujus exponens
n n
n communes sinc axis AD, basISDB:
m- n CA; e B E hyperbolam TAHSAE; haeC
Sit autem AD = =
quoque paraboliformem AEB continset.
Nam est C:D. C A:: C A. C T. ac inde AD. TA:: CD. CA; inverséq.
componendo TD. AD :: C A - ]. C D. CD. Veruim ex hypo.
thesi, est m = n. 2 n = m:: C A. C D. adeoque inVerSE COMDO-
nendo C A. C D:: m - n. n; _ rurtus componendo C A -1 CD..
CD:: m. n. hoc est FD. AD:: m. n. unde B T hyperboliformem
conrinsit.
ZIII. Finc rursu dats ratione ip(uS A D ad C A, paraboliformis
ad punctum B hrpe bolam contingens dessgnabitur. nempe (IC AD =
C A; exit
M
S
5
Nam hoc suppolito erit (5avpnsor
mul.
ap
(B) 5. hujus aP.
(C) 3. bujus ap.
C18. 240.