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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 53, page id 824573315:0137
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PROP. 23
DeSectionibus Comeis.
quod proPE (nondum cognica) substicnaturs, adeogi pro
DE, f=La. Fruncigicur (uE prius) PA. DA : : Pag. DO
a
P. PEPF. DF:: Pa. DF. (hOC ett, f. f=
DT. F
+2fata
EA IIEM (DFOPICKFAnGenCem) DT = DO (hoc eH, DT ∞.
qualis rel major quam DO; illud quidem s B, P, Coincidant;
hOC, A(CCHS) _ DFg= DO9 hoc eA
2fata
 d a
 e
Cuerumq: multiplicando in d(2 _ diridendo per p) crit
ds +2dat da= ds2 +f= a: _ auterendo ucrinqi df2, 2c9; divi-
dendo per =4) 24f + da = f.
Denig: ponendo D P idem punctum Cuc evanelcac quanti
cas a- adeoq, _ das) eric 20f f, hoc est 2d- f. Ouod cst ip.
dum Theorema quod inreltisandum erar, quodq: modo de-
montcarimus.
Conrerta propolicionis propolicx; nempe Parabolae tancentem
aF diametro P A productae occursuram, es quidem itant obscindat rectam
AF ipsi AP aequalem; ex dictis Facis paret, vel inde salcem tacile
deduci pocest.
ACq. etiam; Rectam AF Parabolam in unico puncto contincere.
Icem, ab eodem puncto P, atque ad easdem partes, rectam aliam quae
Parabolam contine at duei non posse.
Ec, Parabolam in eodem puncto a non nisc unicam rectam contingere
posse.
Adeoq; In locam inter curvam ae A rectamque contingentem aF, aliam
reciam lineam cadere non posse: (Hoc eA, prout c80 alibi peculiari
traccatu Fusius demonstrari, Anculum qui Contactus dicitur, esse an
culum nullius maeniiudinis, (ive non- anculum.)
Verum cum ea non difficulter calculo demonstrari possine
(demonstracionibus praecedenei non absimilibus) ceo, parcim
ut erronibus quo le exerceant relinguam. parcins ne aliis cae-
dio sim, eis sigillasim demonstrandis suver(cdeo.