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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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De Sectionibus Conicis.
PROP. XL. VI.
PROP. 46.
De recta Paraboloides Cubicale contirgente.
Y Parabo oides Cubieale Aa, in puncto quoris
a continrae recta aF, diamCtRO PA OCCUETeNS
in F, Ccq; eidem diametro ordinatim- applicata
aD: erit recta AF Cdinmetri continuatio) dupla di-
ametri interceptae PA: hoc elt, diameter continuota
PE, tripla dianceri PA.
Nam, Cumpeoubiris (in caden diametro) punctoD, cui
ordinacim applicetur DO, cangenti e F’occurrens in T: Pun-
Atum T (DrOPterFangentem) vel eric idem cum punctó a, (sI
nempe P, D, coincidane;) vel CE (CCUS) erit P exCra curram:
E (pTOPFCrCA) DF = DO (nempe aequales, A D, P, coinci-
dant; vel, A lecue, DY longior erit.)
Ponamus aurem (ob commodiorem calculum) Pa =P, PA
=d. PF = f, PD = a. Prit ergo (per det. praeced.) Pd. DA
: PaC. DCC. hoc est d. d = a:: p.
du
p. =- DOc. Icem
(Dropcer similia eriangula) PF. Po:: DF. DT. hoc est f. p::
 a. F
a
 P = DT. Pjalq; cubus
(=-DTC)  (DOC =
2
f2 a + 2 f a + 
p5
d P. Ec Cuerinqe mulcipii
cendo per f. d, e dividendo per p2) erie f. d L 3F2da +
3faa = d a 2 = f3d +f a. Tum Cauterendo verinq: F. d, &
diridendo per  a) erie 3 f2 d =+ 3fd a Y da = = f. Denia
vonendo puncta PD coincidere, CHe eranelcac quencicas a,
adco9; ee ipsus molciplicia + 3 fda, Y d a 2 0) eric 372 d = f.
hoc cA3d-- f. Duod crac demonstrandum.
R