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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 553, page id 851387705:0573
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It
11II
PT IInanouoS.
parabolae segmentum A LLIB =
Zist aurem rectaneulum BR = =. F S Llun  BL, ad parabola
Seementum AR FTB; adeoque (ut supra probatum est) AB recta, ad curvam
ACF; Ut 27 aC2, adt 9C + 4 a in V: 96+ 4 a. minus 8a. Quod erat de
monstrandum.
iplaque AD, D: Frunc ordinatim applicatae dp = V a L; iplaque DP = V DL:
18 ab0 +8 a b,
Meam denique hanc habe.
in Y. 90 + 4 a. minus 16 a b
Fsto ADP PataboIa Lecla, Cisco Laccto LCc WCacuI e Accogce, sumpris
diametris Ad, Ad, ecc. arichmerice proporcionalibus, quae sigillarim dicantur d:
29. 2G
Ft parabolae abscista A d p =. Z d V dL; adeoque ad invicem, ut aY d, vel V 23:
Ec ddp rectansula (quae, sumpris dd parriculis infinice exisuis, quae dicantur
Q Parabolarum disterentiis aequipollent) AV aL; qua itaque cunc ad inricem,
UE Va, (lire ut ipa dp ordinatim applicatae;) aique ad parabolas suas, ut
A ad Zd
Ducatur denique curra A CF (parabo la in P OccurrenS,) ea lege ut singula
de rectae, sinc A dp parabolis proporrionales; adeogne ut dV d, sive Y a3
Duam isitur curram, ex P’arabolocidum genere esse constat; quam Semicubicalem
appellemus: urpoce cujus Ordinarim applicata Diamerrorum, A POnaEuT AD dia.
mecer; vel, Diameeri Ordinatim applicacarum, _ Donarus diameles A A; funt in
ratione sub duplicata criplicatae.
Cum igicur sine de ad invicem, ut a Y d; SiIguE DF = DP = V DL: Frun
de = = V aL. Nempe, ut D Y D ad aY L; SiC V D L. ad = V a L.
Cumque sint de, parabolis Adp proportionales; crunt d disferentix disteren-
iiis proporrionales: Adeoque difterentise Fe, cum inter se, cum ad incegras de.
ealdem habebunt rationes, quas parabolarum differentix, cum inter se, cum ad
suas parabolas: Nempe illic, ut V d ad Vd; hic, uE A ad 3 a. Adeoque F F.
ZOVDL = CF:)
X FC = 3 = YLL = Y F aL. Ouibus isicur si ponaneur equales de erit
42Y
ADC pacabola, cujus lacus rectum . =: quod nempe in diametcos a ducrum,
quadraris ordinarim axplicatarum de equabitur.
Eacundtem vero se quacteaca d a L , quadraris da hoc ett a. adlica, extis.
bent rectarum ee quadrata A f Dd L . Ouorum quidem quadratorum aue
menta supra  cum sinc iplis a proportionalia; s rectis ce ponancur aequales db,
eric AbB D nuncus parabolas cujus laus rectum est idem . . ordinacim ap
2 2
plicar