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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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PROP. 47.
De Sectionibus Conicis.
l
duCatuT recta  C (diREErO AP OCCurrenS in C) Paralscta
cansenci at (quae eidem diamerro occurrie in t.) Wico aX
ejuldem Paraboloideoo diameerum esse, eigi ordinacim poli-
EABL NC.
Diametro AP ordinacism opplicetur oe, eiq: parallela du-
Catur rp (eidem dismeero occurrens in p.) Ec lunco Cymbola
Pa = p. PA - d. FC - a = PD- 5.
Tum Cumantur in diamecro, ucrinq; a puncto p, aqualesre.
AXPD =PD =-9 VETAG; nempe canca, quonra est radix hujus
aequacionis 9d92 -+ 92 = 27d 8. PF punctis D, D, ordina-
EIMI DOnANEUE reCCA DO, DO, reCtE X G OcCurrenceS in C, O:
quae cum para Hlela snC reCta P, GICNE reCtA VD (ex constru-
ctione) bilceatur in D, eric ideo OO (propcer Parallelas) bi
sectainn.
Superestigitur ut octendam rectam OO (bilectam in x) ea
raboloidi inscripeam esse (nc nemve ax recta bisecans sit dia-
meter) hoc eA, puncta C, , elle in Paraboloideos curra; nem-
De rectas DO, DO, (diamecro A P ordinacim. BOLEAS, Cx CON
Fructione,) ordinacim applicatis c’ad eadem diameeri puncta)
aequales elle, adeoq; in cu. ra terminari. Ouod sic ostenditur.
FA PA = PA + PP- -d F C. DA - PA + PD = d t 3 + g. DO
=-DF = 3d. DO - DC + DI - 3d + 9.
Tum (propeer Paraboloides cabicale) at PA, ad DA; SIC Cu-
busrectae Pa puncto P ordinacim applicaca, ad cubum ordi-
nacim. applicacae puncto D. Hoc eA d. d F 8 +, 9:: p.
quiisitur cutrus est ordinatim applicatx puncto D.
NB 9, 2
Scd _ cancundem est cubus rectae DO. Nam Cpropeer hmi-
Lia criangula) PF. Pa :: DC. DV. hOC eA 3d. P: : 5d, + 9.
3 d
-
Ba
P=-DO. Ejulq: cubus DOC-
274 + 27a 9t 9d9 = 4
274
D2 Vel (PrO gd g = = 9=, lubRicuendo 27d 8, QuX Per CON
dructionem lune aequalias)
2 7d3
L. 27d 9+ 272
27a
vel deniqi (abbreviando trachionen per 27 d
a -= 9+B, 3
=DOc. 2d209; rect+ DO, DO, ordinarim- applICALE TunE
puncis. D, Iad Paraboloideos curram cerminatae in C, ;
et
de