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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)
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PR OP. 24.
De Sectionibus Conicis.
applicacae puncto D; adcogs recta DO ipsi ordinacim epplicacae
aequalis. Sed de puncto D ordinacim- vonitur recta DO (ex
constructione) ergo ordinacim applicata cAt: punctag; O
propcerea Cune in ipla Parabola cuere, adeoq; O rectâ PZr2
bola inscripta. Sed _ cam C acq; codem rarione iph parallelas
inscripeas omnes) bilecat recta ar. F. R igitur (per det.) ax
diamerer, eiq; ordlinacim. applicara r O, C ordinatim. in (CriDEX
Cemissis.) Ouod erar demonstrandum.
Monendum autem hic eA, quod cum (eam in AnalyEiguam
in Synches) dicimus duarum rectarum DC, alceram quidem
aequalem cHepC vPD, hoc ett, differencia rectarum PG, PD,
fieri quidem pocest ne quandoq; De (nempe quoties rectaOO
diameerum AP nOn EraN(IC) quandoq; DD (nempe ubi OO
Eran(IEAP) major esse: Adlcoq; DC ~PD, nUINC Per PC PD,
nune per pPdL PC, incerprecanduerit. Verimhoc calculum non
omnino perturbar; quonis ca quancitas in operacionis progrelsu
uadranda occurrit: quo calu, aerumris concineat, cadem qua
2d.4
draca prodibune. Nempe cum sc in Analyli 24
De exDOnatUE
Eire-
+2
2d
Iu + G
P = DO, (.
Q p = DO (vEubI OO nOn Eran(IC AP,)
2d
p = DO (nE ubi Exan(iE, ) ucrorio modo erie
=+ ada p = DO9. Ex paricer concinsie in Demon-
Aratione Synthecica. Quod monvisse sufticie.
Possene hic alia Theoremaca mulra Cigillarim oftendi, Purn.
Duodlibet Curvae Parabolicae punctum alienius Diemerri verricem
esse.
adeoq; In qualibet Parabola infeniios esse Verrices, aiqe Diame
eros infinitas.
IECM; Parabola Diametros omnes esse invicem Paralletas.
EE; Duamlibet rectam (in eodem plano) cuilibet Parabolae Diame-
ero parallolam, ejusdem Parabola Diametrum eriem esse; eique in uno ali-
quo, e quidem unico, puncto occurrere.
Tcem; Duamlibet in eodem plano rectam, per aliquod intra Parabo-
lam punctum transeuntem, Dramerro non parallelami, in binis punsis Pa
rabola occurrere; es alicui Dimmetre Ordinarim. Posiram esse.