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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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PFOP. CLLLI.
Deoque, Circulus ad Duadratum Didmetri, (vel etiam Fllipsis quaelibet
ad Paralleloerammum sibi circumscriptum,) eam habet rationem, quam ha-
bent Radices Duadraticae universales Residuorum seriei infinitae A qualium
serie Secundanorum mulctatae, ad seriem illam A qualium.
Nam s circuli. Radius po-
natuER, (cujus pars intinice
Parra = = a, ) eique insistant
Perpendiculares tive sinus re-
cti numero intinici Ouactran
cem circuli complences; crunt
illa Perpendiculares medix
proporrionales inter Diametri
Seementa, (ut nocum elt; ) hoc elt.
inter R F0, R FTa, R + 24, R + 3a, dc
Ouorum Rectangula,
e
R - 0,
P
a3
R = 2a, R
3a,C
 R2 = 00, RZ = LN, R. - 44, R = Ga, C.
Eplaeqi media proporcionales V: R - 00. V: R = 24. V: R - 4u V: R =9a ec.
Ouam isitur rationem habet harum radicum univentalium Aggregatum, ad
cocidem maximae (Radio seil.) aequalium, eam haber Ouadrans Circuls (ex illIs
constans) ad Ouacratum Ractii (constans ex his;) Adeoque de cireulus inceser ad
quadracum Diamerri. Ouoderac oltendendum.
Acque idem de qualiber Ellipli (muratis mutandis) facile ostendetur; cum iptius
eriam ordinatim applicarae sine mediis proxorcionalibus (inter diametri tranversae
fexmenca) Propdrcionales, e quidem nonnunquam aequales, u ex conicorum do.
etrina nocum ett.
SC TTOF YV MI.
Ratio autem quam innuic haec proposicio (Cireuli nempe ad Quactrarum Dia-
metri,) ea est, quam habet Oniras ad numerum incermedium inter F ec Z in sccun-
da serie Transrerta Tabella PrOP. +27. Duomodo aueM InVENICTUE nuMErHS
ille (rel alius quixis illius seriei numeris incerponendus) deinceps inquirendum exit.
EROP. CXXII.
Corollarium.
Pproinde, s supponamus infinitas numero rectas semiparabolae cujusvis
in ejusdem continuationis aeque alta e titu inverso posuae rectas, respecti-
ve duci; quod provenit solidum ex infinitis illis Rectangulis constatum, (aut ex
Quadratis quae rectaneulis illis sint aequalia,) erit ad Parallelepipedum super
eadem base aeque altum, ut Circulus ad Quadratum Diametri. (Ft quidem
mediae proportionales erunt in subduplicata ratione ordinatim- applicatarum in
Circulo vel Fllipsi.)
Semiparabolam quamlibet A PO,
secet recta MIO (bati parallela) in
duo seomenta aque alta; e Recta
MO dICaLIIE VR. Frunt reliquae
ordinarim. applicacae in segmento
superiori alcendendo, V: R - a.
V: R = 2a. V: R = Z a. _C. FF in
segmento interiori descendendo,
J: R F a. V: R + 2a. V: R + 3a
_c. (propter quadrata ordinatim.
applicacarum in Parabola, arirtme.
LNFPN FTORW
XX7
Corollarium.
ROP.