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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 120, page id 797435492:0192
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L E C Y. ZVII
hOC CA AZ X CB = 2 A C XC Z; vel 2 AZX CF = 2 AC
X CZ; unde AZ. AC:: CZ. CB; hoc eAZHI. CF:: C Z.
C F. Quapropter estX H = = CZ: QuodF. D.
Ouoad radiationem ad parres concaras, plane similis est discursus.
examinetis ip(i, Peto.
VII. Fxhine eridenrer liquer, (I fuerir C AL CF; quod om-
nes punctorum F limires, leu Foci (quales Z) ad elliplin existune;
cujus focns C, et cujus axis TV epraemissis, non unomodo, deter-
minatur. irem si C A = C F, limites Z ad parabolam consistene
cujus foens C, axis CT = Z CF, vertex T. denuo, si C A ~C B.
pincta Z ad hyperbolas esse constat, quarum icidem focs C; e axis
TV Facile de modo (vel alibi) didtis rexeritur; cunctarum vero secti-
onum Parameter ip(I C B X quatur.
VIII. Tinc in singulis respectire calibus, ejusmodi sectiones. co-
nicae lunt rectarum FaC absolutae imasines; quin e cxdem verx
sunt imagines ad oculum relatae in speculi centro constitutum; ex re-
Rectione scilicet ad concaras speculi parres effectae; qua solx oculo
sic polito conspieux sunt.
IX. Patet autem si recta F a C infinire distet, quod ellipsis in cir-
culum abic. uei quoque sI F a C per centrum cranseat, quod hyperbola
iltae in rectam lineam degenerant.
Z. Subnoretur etiam in casu quum imaco fit hyperbolica, quod
hyperbolae Y T Y ParS ZP P Y, neque non tota EV E ad circuli partes
MBIIperinent; (nempe l centro C per P descriptus circulus iplam
FC inter secet punctis R, cota hyperbola C VC rectam interceptam R R
reteret; ex hyperbolica linea alterius pars superior Y F P Y quod
reliquum est repra sentabit hinc inde protensae rectae FC) pars autem
ET E ad partem concaram MD i spectat. id quod sufecerit ad-
monitum.
XI. Ft haec quidem de rectae F AC imaginibus absolutis; c qui-
bus commodius de relatis judicum fet. SIE, instantix loco, oculusO.
ad quem (conrexis e partibus) ab F, _E G rCAeCtANEUE O. M R,
ONL; _ Sic ellipsiS Z V Y T absoluta (qualem modo detinirimus)
rectae FA C imaso; quam dustxe PC, CC punctis Z, Y secent.
iraque punctorum F, C imagines ad O relat (pUTA P, eF y) extra
ellipsim
F18. 193
194, 195
218. 196.