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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)
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DE WOTCHOTDK
vero Sectoris cujusris Z O C, Xc2 C O crianguli, cum magnitu
dinibus cum centris gravieacis, dacur etiam cenerum gravitacis
scomenei 2 C. Dacis aurem cum segmenri 2C, cum crianguli
2C Y, mionicudinibus ex graricatum ceneris, dacur eriam cen-
crum graritacis aegregari 2 Y C. Fe similicer de Sectorisz FC,
aliusre, cenero gravicatis conttabie.
70. In porrionibus Spherae, cenerum gravitatis sic colligitur. Centrum
Ouadrarum rectae 2 Y fs. 6. Xquac ubique quadratum Radii mi- Gravicatis
nus quadrato (3 X, (quod PateL.) Dicamus aurem, uc alibi, Ra- Sectoris, vel
dium R, ejusque parrem aliquoram infinire exionamr. Frune i- Sermenti
Sicur quadrara omnium Z Y (quadrancem b CO complencium) Spharici
R=, R Z , 2, R 2 - 4 Y = R Z = 9r E, _C U(que ad R = - Z =
(quod est punctum verricis C.) Sin pro duadraris hisce substi-
cuamus ubique circulos, laceribus quadrarorum ue Radiis descri-
PEOS, (adeoque quadraris illis proporrionales:) pro omnibus R2
habebimus circulos Cylindri, hemisphaerio circumseripri; pro
omnibus 00, r =, 4r 3, 9r  _c, Circulos Coni, cujus verrex (+
centrum Sphaerae, balis eadem cum base CHlindri, in plano quod
Sphaeram in C tangie; prouerorumque vero differeniis R 2 -O.
RZ - p2 R= = 4r 2, R = = 9r  ec, Circulos hemisphaerii
(quadracis utique rectarum 2 L provoitionales;) qui propterea
aequales deprehenduneur planis annulis crlindei conice excavaci:
Sed e eadem habebune graviratis cenera, (nempe respectira
puncta X, in recta C C:) aequiponderabune ieaque cum singula
lingulis respectire, cum omnia omnibus; idemque erit cen-
erum gravitaris elindri hujus conice excaraci, acque hemisphae-
rii: Nempe in eo axis hemisphaerii puncto quo ira dividitur, ue
pars ad cenerum Sphaerae sic ad reliquam uc 3 ad5, sve Z Foriuss
Id enim ob dacum cum C plindri, cum exempei coni, magnitudi
nes ex gravicatis cenrra Facile colligieur.
72. Velsc. Cum circuli hemisphaerium complences, CIHE
quod modo dictum est) uE R = -r 2, R2- 4 r2 R=  9r a
_c, (hoc est, juxca noltram Rrichmeticam Infinitorum, uc se
ries Aqualium dempra Perie Secundanorum, quae ad correspon-
dencem seriem Aqualium, elt uE L  Z ad X, hoc es uc Z ad L,
dive uc 2 ad 3; quae iraque est ratio Hemisphaerii ad circumseri-
peum Cylindrum;) Eintque corundem Circulorum distantix à
cenero SphaerK, UET, 2753r, C, nempe series Primanorum:
F18C