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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 548, page id 851387705:0568
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ea do es E
que composica teries momentorum V  in D = a: hoc est Va in V: D- a:
hoc es Series Va in Periem Va inverse ducta; cui convenit (ut Fupra) ratio +
ad 4F. Momentum itaque dicti spatii in luo liu (respectu PA rectae) cst ad
momentum quadrari P C in distantia FC suspenti, ut F ad 4H; adeoque ad mo-
mencum Cemicirculi sic Cuspenti, ut F ad 2: Hloc clt xequiponderat semicirculo
Cuspensa in distancia  F Cy hoc est ex puncto e centro; hoc elt in suo liru. Cum
isitur spacium illud Cissoidale in suo sicu aequiponderat Semicireulo in luo, (re-
specti rectae E A;) Licque spacium illud Semicirenti criplum: Pric distancia di-
stantiae Suberipla; hoc elbZ FC, vel SFC, nempe a recta P A; Adeoque 3FC,
vel ZF C, a recta Cia. ut peius.
28. 1
Aique hinc Ctarim collisimus; Solidum ex conrextione dicti spatii Cilsoidalis,
ad Sotidum, ex convertione Pemicireuli, circa eandem rectam Ca, esse ut 5 ad F,
(nempe uc planorum momenra respectu ejusdem Ca rectae:) Cirea rectam au
em FA (propter aequalia platorum momenca respectu liujus recta) aequalia
este Tolida.
Si quis autem quaerat, de Polidorum hujulmodi semiconvertione factorum,; cen-
eri graritatislinea, sire ejusdem ab F A vel Cg distantia: Id eodem plane modo
inveltisabitur. Ouippe cum semicslindrica Cuperticies rectarum L. Z Temiconver.
tione tactarum, Anc rectarum illarum momentis proportionales, hoc etb (respectu
rectae C. a) ver QL; suorumque cenrorum ab eadem recta, in ratione racio:
rum Ci L, hoc Mlta: cruncomnia momenta superticierum illarum semieslinerica.
Cujus seriei racio ad seriem aequalium.
sic colligitur. Series Var inverse ducta in
Series T. 4.  a
rationes =
242 27244,
a3. a4. c. dabit
2+24416
 2X2 +4. +6x8
d’BRHE OXLExHB BTLLMLZHIS, OTLLKLSELSHIZ
dec.
Adeoque cum series Va in seriem va inrecse ducta (ur ex inguisirione primum
tQH6 _ FO
terjecta loca ad hanc formam. Nempe series V a’inrerse ducta in e
series =
a
rationes. L)
111
. CCIS. LSI SOI O.S
2. Va. a. Va. a. V a3. Sec. dabit
7
242
2u2ua
115. d 11
31 p5. dec.
10) 645: 5 64D 9r+L 64D tZ BRTEXLS 649 72 14
Nomentum igitur supersicierum ominium ex rectarum L. Z. circa C a lemicon.
vertione factarum, in suo licu; hoc elt, Polidi ex semiconrertione sparii Ciltoidalis
cirea Cahiomencum in suo sieu; respectu Ca rectae; est, aet cotidem A qualia,
nempo momenca rocidem superticierum, rectis Ci F. lequalibus in distanciis C F semi-
convertio factarum, in Distancia maxima sispen Carums l=).S
35 ad 32B. F.R aucem mannido ad magnicudinem, av (5 ad 4 1, (momencis uii
que platiorum proportionales:) Pre distantia del distantiam ue 7 act 8: Hempe
ctius distanciae quam haber cenrum gravicatis Pemieireuli sradio C P. deteripri ab
ipso C: quae quidem non est roca C H recta, Sed (propter curraturam lemleirou-
Tarem) illa ejus pars quae est ad iocam ut Diameter ad Semiperipheniam 1103. si
Sitmiliter, Facta Conversione eired P As Lemieylindrica luper Heies rectis L. L. do-
scripea sunt VadiaV: D= a:(quippe momentis rectaruni proporrionales ;)
diltanciae vero centorum superticierum illarum sume rie racii conrertonis ire di
stantia D a; P reS Superticierum illatum momenta Cunv ut V a 3, in Z crv in
Y: D =a. Ave utD V a V a2In: D.  a. FHI autem (per Cupra dem on straLa)
Series DY a3 in V 4: sire series D V a in seriem V’a inverte, ad seriem
aequalium ut L ad 4 D: EL V a in Ya imverse, _L 5 ad. 32l: PO DY ad =Ya
in