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# Title: Qua Continentur De Angulo Contactus & Semicirculi, Disquisitio Geometrica. De Sectionibus Conicis Tractatus. Arithmetica Infinitorum: sive de Curvilineorum quadraturâ, &c. Eclipseos Solaris Observatio (shelfmark Leibn. Marg. 84:2)
# Folio 52, page id 824573315:0136
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PROP. 23
Bctoenim Cob commanorem calculum) Pa = P, PA -d
hoc cA, 2d, 2d =a::
ad =ada + a2
4u
aa
(idc09; PF-- 2d,) PD--a3
(ideoq: DA- d = a, DF = 2d
a variatis nempe honist,
Dronc supponieur pon-
ccum D intra vel Capra pun-
etum P astumi.)
BPIEIZIEUE (DEODCeE PArA-
Bolam)PA. Da:: Pag. DO9.
hoc ett, d. d = a: : p2 4 a
DOg.
Ec C propter limilia exi-
angula) PF. DF: : Pa DY.
2d P =DF. hujusqi quadratum
EH isicur differentia guadearorum DF9 - DO9 =
a
. Ad  4da +, 2
+u
4dP. Oux quidem vel aliqua
ettus si puncta P, D, distent, (licq. Propcerea a quancitas rea-
lis;) vel ommino nulla, E coincidane puncta P, D; Cevanel
cence quippe quancitare a, adcog; et ixsius mulciplicibus om
nibus.) Hoc cA, Onadraca DPq, DOg. _ propcerea corum la.
cera DT, DO, vel aequalia lunc. si lumatur punctum D idem
aEq; P; vel illud majus est. E alibi lumatur D. EC Proptorca,
cum rectae at (quancumvis verinq: productae) singula puncta
iploa excepto, lime exera parabolam; ea Parabolam in unico
punctoa contineir. OuoderacDemonstrandum.
F.Hg; haec nostra demonstrario mulco expedicior, quam quae
ab Apollonio aliisgi, (adhibico Cono, variilq; lemmaris pex-
MmisIS) adducunEuT.
Si vero propolicio haec non fuisset ancehac excositata, sed a
nobis jam quaerenda: Iud Analytice sie fieri possit.
Supponamusrem quasi jam Factam; continsentem at, dia
mecro produeca occurrere in f: _ quaerenda sic lonsitudo recta
12
Recineatur eadem quae prius hgura; cademqi symbola, niti
quod.
De Sectionibus Conicis.