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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 333, page id 851387705:0353
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PFOP. XXXI.
ON IC IS.
P RO P. XXXI.
De Fllipseos Diametris.
T a puncto quoris a in F.Iip(eoS curra A an ducatur ad Centrum
C recta a C; erit haec ejusdem FMlipseos diameter, cujus rertex
an ejusque Ordinatim applicatae rectae ipsi a P, Ellipsn in puncto a
contingenci, parallela.
Fibet hanc propolicionem (ut prius prop. 24.) pri-
mo Analycice eximinare, deinde et Synthetice demon-
Strarc.
Supponamus igicur rem este ut perhibetur; adeoque
inscripiam quamlibet OO tanSeNE a F paralletam, 2
recta aC (per contactum e cencrum cranleunte) bi-
sectam in A. Sintque rectae OD, OD, a F, diametro
AF. ordinatim applicatae, adeoque invicem parallela
quibus etiam parallela ducatur se eidem diamerro in c
Occurrens quae propterea (ob parallelas) bilecabie (ut
OO in E, lic) DD in c. Denique recta OO, diame.
ErO AF, (VErISque R opuS est productis,) Occurrat in
C. (Salcem si Parallela sic, uE non pOlIE OCCUERerE; reS
ipsa jam demonstrata est, PrOP. 29.
Supponemus etiam imprasentiarum, rercieum A a (dia-
merri AF,) verticem A propiorem, 2 remoriorem, Puncto R: Trem punctume
intra puncta a C incidere: rectamque OO diametro A F producta exera F. Iip-
TIm OcCurrere: Si aurem horum alicui concrarium concinsat, (quod quidem tieri
Docclt) nihilo camen minus res succeder mutatis tancum aliquories lignis. + -
quod operationis prosressum neuciquam curbabit
Dieancur autem (ob commodiorem calculum) F. a = C, P. A = d A a = 1
Ca (= + - 4) = ∞, C C. (= Zt - 4) = C, CD = 9, 2_ = dy 4. C =0726 - d =E
C (=0 - 5
Tum (per praeced.) EC. F. A: : Ba. F. F. hoc est 5. d: : v.  = FF. EL
(proprer parallelas, et similia triangula) C a. E9.:: C. F.. CF.. hoc est 0. 5:: c.
E=CF. ELC4. C5:: F. a. Cc: : F F. CC. hoc elt, 0. 7: : e.  = c,:: d 7d X
A
= d +  de ca = 1 =  , ideoque DA (= e A = C D) = d. +   = 9, de
D2 =∞ -  = = g. EL rectanentum D A L D a =
=0 dg + 205c9 + 05 v0 - 05 dc = s2 02
2x = 8 9 +2809+20809+2055
20 - 8 = E
a d  -69-2012 16
de
q
+
2 xq
(vel, Guia X = d = 26
Cvel, quia 0 - 5 = 7, e
Deinde, (quia, propter FIiplin, Ouadrata ordinarim applicacarum sunt rectan.
gulis segmentorum diametri crantrerlae proportionalia) E A X E a = d N. D AXD2
:: Fag = c. D09 = = dx - 89 + 207c9 + 5E6
Trem