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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 (shelfmark Leibn. Marg. 103)
# Folio 24, page id 85138403X:0040
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F18. 6.
l C2C L110
cum est; tum (I opus est, sic more nostro porerie demonstrari: Si
incelligatur (7Z C Z Sector, ex aequalibus similibusque criangulis
numero intinitis consari, quae toridem racii reprasentent; per
horum omnium cenera grarieatis quae eran(IE curra, adeoque FA
diorum illorum duas cerrias abscindie, erie Cmilis arcus circuli
radium habentis = 5 C; cujus quidem arcus lingula punta C ut-
Poce aqualium eriansulorum centra gravitaris) cum surponenda
mE aequeo oneraca, idem eric cum hujus aECUS, TuI exFOliti Se-
ctoris, centrum gravicatis: Eujus aurem arclis cenerum gravita-
EiS habOEUE, A AaE (quod modo dictum est Q mox probaBIEUF) UE
arcus ille ad Tuam subrentam (hoc el, VE AECUS GIMLIIS Z C Z, 20
TuBCenSaM SUaM Z2,) Sic radius dicti arcus = C, C (nemDe = F2
dii Sectoris expoliti) ad quaream, quae erit O F: EK itaque pun-
ctum E cum hujus arcus, cum proprerea Sectoris expoiici,
centrum gravicatis: Ouod octendendum erac. Quod aurem arcus
centrum gravicarisaillud est quod diximus; sIc prohatur. Quoni-
am parallela planz eadem rarione secone superticiem Sphaericam,
qua secane arem, (quod ab Archimede ex aliis demonstra
cum elt;) Manifeltum est, porrionem Cuperkciei Sphaericx
Qu∞ AECU 2 C Z Semicirculum non excedence circa b b axem
converso describicur, eam rationem ad eocam sphaerx superficiem
habere, quam habet 22 subcenta (vel axis portio huic respon
dens) ad bb axem inceerum: Pura, ue axis D, ad subrentims;
siC cora Sphaerx superficies D P, ad portionem arcu. deseriptam;
quae ieaque elts P. Oux quidem porcio li, per magnicudinem
atcus a dividacur, prodibie-P Deripheria CenErO GraVIEAtIS
istius arcus descripea, adeoque hujus Deripherix radius, hoc est
distancia ceneri gravicaris dicti arcus a cenero circuli, 
Nempe eapars radii CC = R; gux est ad EOrUM, ve sad a,
subrensa dicti arcus ad ipsum arcum: Ouod probandum suscepi-
us. Fesimilicer de cenero gravitaris Sectoris ZGC (auF a
lius cujusris) eodem processu constabie. Ec speciatim, semicii-
culi cenerum gravitatis, a circuli centro distat,
Nempeut = P ad D = 2 R, GC Z X ac
RZ
B R
PR, C
D.
D
c