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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)
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618. 6.
L CEBLCADE
cum est; cum s opus eHt, sic more nodro poreric demonsrari: Si
incelligaeur CZ C 2 Sector, ex aequalibus similibus que criangulis
numero infiniris conslari, quae rotidem radii reprasentenE; Pet
horum omnium cenera gravitatis quae cransie cuiva, adeoque ra
diorum illorum duas cereras abscindie, erie similis arcus circuli
radium habentis = (3 C; cujus quidem arcus singula pun Sta CUE-
Pore aequalium criangulorum centra gravicatis) cum supponenda
SinE aeque onerara, idem erit cum hujus aecus, eum expositi se
etoris, centrum gravieatis: Aujus aurem aecuis cenerum gravita-
eis habCEUE, S Hac (quod modo dictum ct ec mox piobubIEuT) ut
arCuS ilte ad SUAM IVBTeNCa (HOC CHE, UE AECUS FIIIIIS Z C Z, 20
SUBSECNTAI CuaM ZZ,) Sic eadius dicti arcus = C3 C (nempe Z F2
dii Sectoris expolici) ad quarra, quae eric G P: FIt itaque pun-
ctum F cum hujus arcus, cum proprerea Sectoris expolici,
cenerum gravieatis: Duod octendendum erat. Q.od aurem arcUS
cenerum gravicacisaillud est quod diximus; SIC prohAtUE. OVOM-
am parallela plana eadem ratione secane superticiem Sphaericam,
qua secant axem, (quod ab Archimede de aliis demonstri
cum est;) Manifestum est, portionem superticiei Sphaericae
quae areu 2 C 2 Semicirculum non excedente circa b b axem
converso describitur, eam racionem ad cocam sphaerx superficiem
habere, quam habet 22 subrenta (vel axis porcio huic respon-
dens) ad D B aXCM INECOFUI : PUEA, vE axis D, ad SuBTeNFII S;
(C FOTa SphXEX Superficies D P, ad POrtionem arcu desCripEAM;
qua itaque estsP. Oux quidem porcio h, per magnicudinem
arcus a dividacur, prodibic = P periphetia cenero seavicatis
iltius arcus descripra, adeoque hujus peripherix radius, hoc est
dictantia ceneri gravicatis dicti arcus a cenero circuli, R;
Nempe ea parsradii C C = R; guxe est ad EOrI, uE s2d a,
Tubcensa dicti arcus ad ipsum arcum: Onod probandum suscepi-
mus. Ex similiter de cenero stavicatis Sectoris Z C C (auC 2
lius cujusvis) eodem processu conttabit. Fe speciarim, semicir-
culi centrum gravicaris, a circuli cenero distat, 3 ~
Nempeuc = P ad D = 2 R, sic = R ac
2
Dacto
vere