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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 797, page id 851387705:0817
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PFOD ZIX. DeCalculo Centri Cravitatis.
aciemre habentis A a momentum respectu bB; d a B = 3 a R = : ad v. Aciem. Fi8. 169
que habentis bB, momencum respectu bB; acienire habencis A a respectu A en 170
momencum, Z a3 B = 3 a R = = a V
Haec icaque. ex respectivis momencis Ongularum A BBa (S K. invenris,) sub.
ducta; relinquunt relpectira Ongularum A b B momenta.
Nempe; Ingulae A BB, aciem habentis b K, momentum respectu Aa, aciemre
habentis Aa momencum respectu BK; = 2 C R 3 = a v R  = Ea 3 R +
Aciemque habencis b R momentum re spectu b K, 2C R3 = 5 a3 R F 5a 3V: Aciem.
que habentis Aa momencum respectu Aa, (hoc elt, Omn. 343, eo spectancia,)
2CR3 = 2 aVR 2 = 3 a 3 R + a2 5 R f 3 a 3v.
Adeoque, (proprer illius magnicudinem, = 3 a R = v R2 + Z a 20; hujusque
==a2R F aSR = V R = = Za =V; per S T. prOp. 17.) Vnoulae ABB, aciem la-
beneis bB, Dillancia Ceneri oravicaris ab A0, = 12 C R f 6avR - a R + a v
abe
22eR = 22 R + 242
3a R F 60R 2 F 3a 2V
=3a R = 6V F F 34: Aciemq; habentis Aa. Distamia Ceniri gravit. d bk,
22eR + 6avR- aR + av
35 P +6as R -60 + 307 2b 1u 1 2eR 12auX 20 8 + 6aes t 2a0
-3a R + 6a5R 60N + 3aV
Atque his, in Pisurae Sinuum vertorum AFa ejusre parrium, Ongulis, (ic ex-
Dediris: L’adem opera, eadem in Fisurae Sinuum Rectorum arn expedumrur. P IL
enim (ut Set. prOP. 27. Oltencum elC,) Figura Sinuum Rectorum Onins quadran.
eis a sn eadem plane figura arque d D A, Ficurx Sinuum versorum portio. Adeo.
que ex magniudine, Momentis, Ingulisque, tiourx d D A (quae FGUTA A r a parS
elt,) e parcium ejuldem; Paeile erie tionra adn, adeoque de àr u parciumque
illius, Magnicudines, Momenta, Onsulalque, quaeque hinc dependene, derirare. s
Veleriam, line ope ligurae ATa, ejutre porcionis d D A; DolLunE iPLIUS a Xn
parciumque hujus, Ungula, (utS V. prop. 17. Ostentum clt,) carumque momen
ta, tacile obrineri.
Cum enim rectae BV, Erilineum aB. complentes, sinc arenum avichetice pro
porcionalium (ipsIs aB respectire xgualium) linus Recti: Dua Ongulam aβ0
aciem ha
miguadrar
aa
lei
cu ipta aB0 angula aciem habens ar, seu plani momentum respectu recta
ar, elt Z C R = F =SV R, Per SO. PrOP. 17.  AIque eorundem semiquacratorum
252, Seu planorum Friansulorum momencum respectu iptius ar, (Propter 25, Vis
Itanciam Centri Bravicatis a T a, per prOP. 5. hujus) sune, Omnia, 553: (PrOPter
352XZ 5 == 353.) AULCtIam (PEOPter S = VB,) Omn. 35Vb. Hoc est Omp
35V R -= 55V2: Cumpeis a arichmerice proporcionalibus.
Sune aurem Omn. 53; (sumpris a arictimecice proporrionalibus,) idem deque
Omn. V R: (per BV. prOP. L3.) seu Omn. S2 R, Cumpris v arichmerice proDOr.
cionalibus: Hloc est, duplum momenei (respectu A a.) legmenti semicircusi AB V
tig. 169. in R ductum; (Tunc enim Omn. Z5: sumpes v arichmetiee proporcia
nalibus, momentum illud:) HOc cst, (per S R. prOP. 15.) ZVR3 -- 5 S2 R= +
352VR = ZV2 R2 = ZS2 VR. FFBO; Omn. 353: =
vR
S2 R2 + 552V R,
seu 3V2 R = 352 V R, est Ungulae a B0 aciem habencis a r, momentum respectu
ar. Adeoque (propier magnicudinem L C R 2 + a sv R, per BO. PrOB, 17. ) Di-
Pancia Ceniri Graricatis a ra, est 4v R + 45 V
OcR + 95V
Vel sic eriam; Sunc Omn. 353: = Omn. 3 5vh; (propies B I meciam pr opoi.
cionalem invex A V et Va; hoc est, s. inier v et B; ) leu (prOprex b = 2  = 2,)
Omn. = 5V R - 3 5V
Sune aucem Omn. su: (sumpris a arichmerice proporiionalibus, ) 3 v E. A = 2R
R2
(per S L. PrOB. 18.) Adeoque Omm. 35V R. = 3V1 R1 = 3V R3
AI AhHH 3
N.
TIet,