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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 889, page id 851387705:0909
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Ouo itaque habeantur Omnia a 3 V; HoCCll, Omnes _, (seu BV recta Figuram
_ vEV7, _C. ComplentES) respectiris a (serie Pertianorum) onulta: Incellisa
mus, juxra doctrinam prop. 10. hujus, (quam Cepius in auxilium adrocarimus,
Singulas an B, 7, ecc. H15. 135. aequaliter ab invicem remotas, coridem elle respectiras FiB. 135
x rectas; adeoque ipsam AF onustam, scu Omnia, a + B F 7 _c. = Omp. x
=5 R, ut jam oltentum est, Cx S B. pFOP. 17.
Florumque omnium momenta respectu axis A; hoc CH, Omn: a N; TUNE ipL
onustae rectae, AF f BF F CF, ecc. hoc elt, roridem A H, dempris omnitus A B
= AC, _c. HTOC CH, (PrOPrer A F = s R,) cocidem sR ultimis (Teu a sR,
dempris omnibus sR anrccedentibus, pro arcubus arichimerice proporcionalibus
V(que ad a ulcimum.
Sunc aucem (pro aceubusa arichmecice proporcionalibus) omn s, =u R, per
8O. PrOP. X7. (utpotC ipsa aBV F3. 270.) Adeoque Omn. SR, = V R3. HOC
itaque ex as R subducto, habetur a S.R = V R2 = Omn: a v.
1L
Incelligantur deinde eadem an B, 7, _c. Hx. 135. tanquam cocidem aN: adeoque
onuctq recta AB. =Omn. a N, = aS R- V R 2. PTorumque omnium momenta re
spectu iplius A; hoc est Omn. a = N; Func ip (a AF f BF. F CF, Sc. rectae sC
onusta. Hloc est, rocidem AF, (= a7S R  aV RZ,) dempris Omnihus AB F
AC, Ccc. hoc et, omnibus asR = 2 R?, pro arcubus a arithmetiee proporciona.
Libus.) 3.5p0
Sunt autem (pro arenbus a arichmetice proportionalibus) Omn. a5, = - e R 2
+ av _ per SO. PrOP. 27. Curpore momentum ipsius aB.fg. 270. respeCt 1C
ctae Aa;) adeoque Omn. asR, = - e R3 = a V R2.
Tiem Omn. V, = e R, per SB. prop. L7. (uipore iptut A B R crilineum, 1.8.
270.) adeoque Omn. - v R
ErGO, Omn. a s R = v R2: = - 2C R3 + av R - - 2 a R3 + 25R + avse
HIoc itaque, ex a SR = a V R, Tubducto; habetuE Z a R 3 25 R 1 2aV R
 a25R = Omn. a2 X.
Incellisaneur denique eadem a, B, 7, dec. fig. +35. Catigliam coridem a: allloque
onulta recta AH, =Omn. a 2 ∞, = 2 a R3 = 25 R =, 2a V R 2 + a 2 5 R. IIO
rum itagiie omnium momenta respectu axis A, hocCsL, Omn. a X; TunC iI A P.
= BF. F CF, Sc. SCOnultX: FTOC CHL, coridem AF,  (= 24Z R3, = 2as R3 -
2 a 2 V R + as R,) dempris A B f A C, dec. TTOC elt, omnibus, 2 a R 3 = 25R3
2aV R 2.  a = s X, pro arcubus a arichmetice provorrionatibus. P2 13g 15. 11
Sune aucem (pro. a arichmetice provorrionalibus) Omn. an FF ZaV, DEN DEOP. 5.
hujus. Adeoque Omn. 2. a 13, == a Z R3.) essd 5 esistosieB esdso elisiin e
Tiem, Omn. S, = v R, Per SO. prOP. 17. adeoque Omn: , 2. SR3 =2 1(2 ∞ R
mtrem, Omn. a v, = 3 a = R -- a 5 R = V R~, Per SFI. prOP. E7. (uipore momen-
cum cilinei AbK. HB. 1 70. respectu Aai) adeoque Omm. = 2 av R2, = = a R.
245R3 = 2V R2.
Trem, Omn. a2 s, = = a  R2 + 2 a s R + a e v R  2. y R2, per S, O. BFOP. 19.
(nempe Onculae a Bv fz. 270. aciem habentis Aa, monrentum relpectu Aa;
Adeoque Omn. a2S.R, =  a R3 = 2a5 R3 + a 2 V RZ - 2V Ra01 +S
FFO, Chorum neprepatum) Omn. 2. a R - 2. s R2 = 2aV R, + aZ sR, =
 4a5 R3 F a dk 2 - 6V R
Hoc iraque subducto, ex 227 R 3 = 2a5. R3 = 2a 2 v R + a sR; habetur,
6vR  + 3a R3 = 6aSR3 - 3a  v R = = a sR, = Omn. a N
Arque ad eandem Formam, (eadem quoties opus erit repetendo restigia) proce
dendum esset, E POrro Omnia a +, Omnia a3X, (aut etiam ulera) inquirenda el.
sent: Vel etiam, Si loco iplorum x, alia quaelibet quantitates ponerentur, Ouod
nic obicex n etLB. 193. CssAE cALB
Clsa ntaque ( uc jam anee ostensum eAt S P.) singulorum Sectorum exiguorum MaB: Fix. 193.
nicudimes, timc t 11. Z
28
a RL
22
;distanciaeqi, ab P NC, R X =
vuunu
e
a X
383 (Po. 200.
Fto
PFOP. XXVII. DeCalculo Centri Cravitatis.