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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 32, page id 797435492:0240
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lo 247 25.
1. 273 28
L E C Y. YV
lacum aequidistar recta, paricer omnibus aequidistar, ut in elemente
primo demontratur.
Operx pretium existimarie Apollonius hoc de parabola, ec hyper-
bola speciarim demonstrare.
V YII. Simili modo pater rectas quascunque CUEVaS FanSenCES Una
tantum excipitur, ad exrremum linex recurrentis. Vid. 28. hujus.
iidem parallelis occurrere. ( Etiam hoc, quoad sectiones conicas, uno
vel altero Theoremato demonstrarit Apollonins.
: IX. Ominimo rectx quaeris ipsam AZ secanres Cintra punctum
a supraque limirem, Eiquis exit, motus descensiri) curram
secabunt.
Cum enim omnes ipsi A Z parallelas secent eriam infinite prO-
duetae curram secene OpOrtet. FInjusmodi Symptomatis demonstra-
tioni in sectionibus conicis laboriolam operam impendie Apollonins.
X. Porro liquee applicatas ad rectam A Z, ipsi A Z parallelaS
C. quas nempe propolita currx sinus verlos appellare fas erit mi-
norem inter se rationem habere (minores cum majoribus. Comparan-
do, seu minores ancecedentium loco ponendo) quam habent re-
spectirx iplius A Y partes, iisdem remporibus decurlaxe (quas e currx
propolicx linus rectos appellare nil dubitem.) Nempe BM ad C H
minorem rarionem habet, quam A B ad A C, vel BM ad C P; quia
CNC CF. I Hoc de circulis, e aliis curris speciatim repexiatur
palsim octensum.
Ad sequentia nocandum, quod si recta trantversim d parallelaes
motaretroorade (d D puta vertus A per D A) moveri concipiatur,
ab aliquo currx propolira puneto, velut O, incipiens; eadem que sem-
per ratione dictum punctum ab O ascendens quond relociratem de-
crelcat, qua ad ipsum O descendens increverat, eadem curra pro.
ducetur. Ouidni? Cum idem motus sic, inverse tantum conside.
PAEHIS.
ZI. Suxponatur rectam lineam TMS propolitam curram in
puncto Mtangere (sic ut eam nempe non secet) Occurratque tangens
haec rectae AZ in T, ducaturque per M recta P M C ad AY parallela;
dico relocitarem puncti descendentis, eoque motu. curram deseriben-
tis, quam habet ad contactum M, aequari velocirati, qua recta
L. P describerur unitormiter eodem tempore, quo recta AQ Ferrur
Per