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# Title: [Johannis Wallisii SS. Th. D. Geometriae Professoris Saviliani Oxoniae, Tractatus Duo] Johannis Wallisii SS. Th. D. Geometriæ Professoris Saviliani Oxoniæ, Tractatus Duo (shelfmarks Leibn. Marg. 84:1, Stück 2; Leibn. Marg. 84:1)
# Folio 86, page id 826605435:0106
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DF CTSSOTDE.
suOSIEU, VE 5 ad Y. Epatium IBIEUIE FCZ AF in luO Seu, XquipOn
derac quintuplo semicirculi in sicu suo, sire in distantia CC su-
lvenso; adeoque semicirculo in distancix CO quincupla. FF
consequenter (proprer diltantias magnicudimbus reciproce PrO-
porcionales) cum spatium sic semicirculi criplum, erie diltancia
diltancia suberipla, hoc est = C 6, vel S C F, nempe a recta C a:
Adeoque Z C C vel ZC F a recta F A. Tancundem icaque distat
iltius spacii linea centri gravicaris (_, siquod est, ipsum gravica-
EiS CentruM) a rectis illis C a F A. Ouod erat oMendendum.
Idem eodem modo colligicur, sumpea ab inicio, aequilibrii
linea F A. Nempe cum series magnicudinum L Z SIC ~
_ distantiarum D= a; F.I ex uerisque compolica series momen-
Eorum V p in D = a: hoc est V a in V: D = a: hoc est
series aa in seriem a’a inverse ducta; cui convenit (uE supFA)
ratio = ad 4 ∞. Momentum ieaque dicti spacii in Tuo sieu (respe-
ctu F A reCtX) est ad momentum quadraci F C in diltancia FC
Suipens ue Z ad 4 B; adeoque ad momentum semicirculi (C su-
Spen(i, uc X ad 2: Hlo.est, aequiponderac semicirculo suspenso in
diltancia Z F C, hoc est ex puncto C centro, ho- est in suO SItu.
Cum igitur spacium illud Cissoidale in suo lieu requiponderat Se-
micirculo in TVO, (reSpeCTU FeCtX F A;) Sicque Spacium illud Se
micirculi criplum. Frie diltancia distanciae suberipla; hoc est
EF C, vel Z F C, nempe a recta FA; Adeoque Z F C, vel ZFC,
a recta C a. UEpriuS.
Aeque hinc Ratim collioimus; Solidum ex conversione dicti
Spatii Cissoidalis, ad solidu ex convertione semicirculi, circa ean-
dem rectam C a, esse uE 5 ad Y, (NEMPC UE DLANOEUML IOMIeMCA
respectu ejusdem Ca rectae:) CIrCA RCCFAML AUFCM FA (PFOPECI X
qualia planoru momenta respectu hujus rectae) equalia esse Colida.
Si quis aurem quaerat, de solidorum hujusmodi lemiconrerlio-
ne factorum, ceneri gravicatis linea, sive ejusdem ab F A vel C a
diltantia: Id eodem plane modo invellisabitur. Ouippe cum se
miclindricae superticies rectarum L. Z. semiconversione FaCTarum,
linc rectarum illarum momentis proportionales, hoc est (respestu
Fec C a) u V
Tuorumque cenerorum ab eadem recta,