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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)
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DL BECTIONIBUS PEOP. LLAX
Tum (ProPter Fangencem) D F q = DOq (nempe aequalia, s DE pun-
cta coinciclane; vel, s secus, illud majus,) hoc est, S = a = 2f a
+ d = a2 = a2 = + a = 2 d a
+d -
erit f2+ d = f2 d2 = 1d a = d a = 2f+ d a = 2f d a = f2 1 a = f2 d2-
a
Ff2 7a =2fda. FL (deleris urrinque f2 + d -- f= d, acque diridendo per L a)
erit = +d a = d2 a = 2fY a = 2f d= = f2 a = f21 - 2f2 d.
Denique, ponendo D F. idem este punctum, (ut Craneseat quantitas a = F. D,
adcoque e ipsius mulciplicia + dan d’’an f a exit 2f1 d - 2fd 2 = f2 1 - 2f2 d.
Ec (diridendo per 2f) +d = d2 = 2f+ - fd. (hoc est, D AF a == D CK F)
vel 3t- d. t - d:: d. f. hoc estu F C. F. a:: P. A. E. F. vel (alternando) FC.
F. A:: F. a. F F. Ouod crat inquirendum.
duod Theorema sie inventum hoc est. Si sit Ordinatim axplicata in
FllipE P aq alque ab applicationis puncto P. FllipseOS diameter per
propiorem verticem A continuetur ad P: sitque, uc distantia puncti-
applicationis a CentrO F. C, ad diametrum intexceptam F. A, sic re
liduum transrer(x dliametri P. an ad diametrum interceptam continua-
tam P. F: recta a F Ellipim in puncto a continget.
Demonstratio (si Opus) insticui pocerit repeciris Analyseos vestioiis.
Sed ee hinc concludi porest quod modo aliunde oltentum erat: nempe quod
Recta F. lipsin in diametri vertice continsens diametro conjueatae parallela est, eique
nunguam occursura. Nam, cum sL F. C. P A:: F. a. F. V. S (propeer coinciden-
tiam punctorum F C) prima F C nulla Cic (sire nullius maonicudinis) quarta P. F
(vel C F) crir intinita (ex utravis parte supponatur diameter produei, sire per
A, Tire per an inditterenter enim se Pangens habet ad utrumque rerricem propier
applicationem in centro,) hoc est, F. P a F nUnquam CONCUTTENE (propier inf
ntam distantiam suppotui puncti concursus F,) adeoque sune parallela.
Patet etiam, Interceptam. diametrum P A (inter ap.
plicationis punctum es verricem propiorem) ipsuis con-
tinuatione AF (inter verricem illum ec tangentis cum
diametro concurtum,) minorem esse. Cum enim (E.
EC. F a = F. C f C a : F. A. F. F = F A f AF: EXII
etiam (dividendo) FC. C 2:: F. A. A F. AC F C minor
clt quam C a vel C A (ParS 1OCO,) erBO d F A minor
quam AP.
Sed de (ponendo C A = , + = 5, _ C. F. = 5 1 - d = 5,
ideo que L. A = d = 5 - c,  F. a = 1 = d = 5 + 6,)
CxIEF. P = -
1 d
 =C _CF (=FF + FC)
=; hoc cAt CF. C. A: : C A. CF.
Sed d hinc docemur Rectam a F dusere quae F.lipsin in dato puncto a con-
sineat. Nempe, ducta Ordinatim applicata a F, Fiar ut B. C ad E. a SIC F A ad
EL. Juncta enim La Ellipen in a concingit.
Trem A dato exira puncto P rectam ducere Pa quae F.llipsin contineat. Nem-
De, juncta PC, ec concinuata, (quae Ellipli in A a punetis occurrat,) ui habea-
cur F punctum in diametri Ra continuatione; Ouoniam est (ut modo dictum
est) F C. C a = C. A:: F A. AF. ideoque E A. AC:: AF.. FC; Si diridatUr AC
In E, sicuc dividitur PC in A; ec ducatur Ordinatim applicaIa F a; recta F a
juncta Fllipln contingit.
Alia liceret hie Corollaria adjuneere, qualia de Parabola innuimus prOP. 23.
Sed ea brevitatis ergo omuienda judico.
PROP