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# Title: [Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica (shelfmarks Leibn. Marg. 100:1/2, Stück 1; Leibn. Marg. 100:1/2)
# Folio 324, page id 851387705:0344
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DE SECPIONIDUS PFOPXXIV.
Tum substituris (ob commodiorem calculum) idoneis symbolis, elto P a = p.
P A = d. (ideoque per praeced. P L = pC = 2d.) PD = a X = VG = g. (CrSO
DA = P A F DP = a f8.) PD =9. (ideoque D A = D A F PD = 4 + 5 +9.
e DO = pG F PD = 2d
Fric ixitur (Propier Pacabolam) P A. D A:: P ag. DO4. hoc cst d. d + 8
g:: p
S= 2p = D04.
Trem (proprer similia criangula) PF. Pa:: DC. DO. hoc CA 2d. p: : 2 d F, 9.
2d di
2d
Lp =DO. FI Cromendo quadlata) 44 L a dq + E p = D04
a + 5Eq
Fireo (mrinque dividendo per pe dt mulciplicando per 4 d2) 4 d + 4. ag + 9
=4 a + 4a8 =4 dg. hoc est (Tublaris utrinque aequalibus) 9= 4 d e. Adeo-
que inventa elt quanciras q. adeoque et puncta D, D, quibus Ordinacim appli.
CantuT DO, DO. Vera isitur est propolitio.
Illud Synthetice sie demonstrabimus, premendo Analyseos vestisia.
Diametro AP ducatur parallela a ∞, per cujus punctum quodvis (intra pa-
rabolam)  ducatur recta n G diametro occurrens in C, ee parallela taneenti a F
occurreni diametro in P. Dico an ejuldem Parabolx diametrum elte cique or-
dinacim poni rC.
Digmerro AP ordinatim applicetur à P, eique parallela dueatur xP diametro
occurrens in p. Iic Funto (ymbola P a = p, P A = d. FC == a x = P P = 8
Tum sumantur in diametro utrinque d puncto p, aequales rectae pD = (V 4 d e =)
2Vd 8. (hoc est, duplum media provorcionalis inter AP, a n, rectas.) acque
punetis D, D, ordinatim. ponantur DO, DO, rectae x C Occurrentes in O, O;
quae cum paralletae linc rectae p, Sicut recta DD (ex constructione) bilcca-
tur in p, erit ideo e OO (propier parallelas) Bilecta iH H.
Rectat ue ostendam rectam illam OO (bisectam in m) Parabola inseriptam
este, (ut an recta bisecans sic diameter,) hoc ett, puncta OO este in Parabola
Curra. Quod Ec probatuE.
2d. D = DC  DD = 2d + 2Vde
applicata puncto P, ad quadracum ordinacim applicacae pugclo D: hoc est d. d + 5
+2Vde:: p
Duncto D.
8
ZYde
d
P. quod isiur est quadiacum ordinacim applicatae
e1
Sed e camcundem elt quadiacum recta DO. Nam (popter similia triangula)
PF.
Fst pA = P A + PP = d F f. DR = BA =B 18 16. DC = DF
de