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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 334, page id 851387705:0354
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DE SECTIONIBUS PFODXXXI.
Item (propter Similia) EF. Ea:: DC. DO, hOc CA =, c:: Y d ~ +0c9
2dx = 0cq
odx
= DO9
e =. D0. ejusque quadraum  a N + 8 8 g + 207 d XC4e
8 ax - 8. 9 L 20y09 + 525
a 42 X
Tdeoque (urinque mulciplicando per s a de dividendo per e) y d2 N
 02c 92 + 207 dx C9 = 5 d N = 8 d ∞g = 207 d x69 F dEd N C. Et (de-
lendo utrinque = 207 d x C9, e transponendo) 02c 92 = 02 d X 92 = 8 d2 N
=v a2 4= F SE a XC2. Ft (quia o - y = d E, Per 5 C 2) 0 ∞ 9 + 8 d N G
= dEd N + dE d v c. Et (dixidendo urinque per d x + ~ = L f) o 9 = d E d X.
hoc est 3E V = 9. Constat erBO PrOPOtitum.
Illud Synihetice sic demonstratur, (rexeticis Analy seos veltixiis.) Ab F. IlipseoS
CentrO C ducatur recta Ca, acque Esiplin in puncto a concingat recta a F, diu-
metro cuilibet C A OccurrenS in F; ipsique parallela quaelibet OO rectae C a
(intra Fllipsin) occurrens in c diametroque C A in CC; DIaMeITO aurem C A
ordinarim applicetur a F, eique parallela Een _IAMEEIO OCCUrreNS in C. Fademque
maneane Cymbola qua PriUIS e, d, L, 17 6787676,7.
Sumantur aurem in diametro ucrinque a puncto c aequales rectae CD =, ,3 5 a X
atque ordinatim. DONantuE DO, DO, rectae OO occurrentes in OO. Adeoque
bisecantur tam DD in C (per conttruetionem) quam OO (propter paralle.
la5) in E.
Dieo rectam illam quamlibet OO (d recta Cia bisectam in 2) Estipsi in-
teripcam ette; hoc est puncta OO este in perimetro. Quod sic probatur.
Ouoniam sune (ut in Analy C demonstrarimus) P. F = --, eC = 7  4
CA = d + = _ ea = 1 -  =: Erit DC (= eG = CD) = 7 d  +, plav
=, eD2 = N -  = pEd +
2
e DA = d + = +  8E d
Clanerulum DA = DA = = a v. + 8Z~ = 8E 5 ~ L 2 7CY dEd~. (nempe, pro q
et q in amaluti; substiuendo YdEd C
.) vel (quia 5 = 5E =y per
SC2) eri D a , D 2 - 7 dr = dE8 L27CYSEdx
dd
Tum (propiee similia criangula) exit P. P. P. a:: DG. DO. hoc At, . c::
rdx LOY DEdX rax LeY dEdE e = DO. ejusque quactatum Y d .
odx :
dEd ~C =2ra XCY dEd X -Y dx + 83C = 27CYSEdY 8 = DO9.
02
a
Sed es cancundem elt quadrarum Ordinatim applicata puncto D. Nam (pro.
pter F. Hip(In) uE rectangulum P. A X F a ad rectangulum D A X D a; SIC (F ~G) qua-
dracum Ordinarim applicatae in E, ad quadrarum ordinarim applicatae in puncto
D. hoc CA a v. 2. d  + 53C + 2 rCVdEdx Y dv +3EC = 27CYdEd
d
quod igitur est quadratum ordinarim applicatae puncto D, eltque (ue modo olten.
tum clt) iptum DO9.
2