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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)
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PFOD.XXVII. DeCalculo Centri Ceravitatis.
Finc = Er (sumpris cum Fcumr arictumetice proportionalibus; LInEquC CenEOTUI Fi5. 199
Gravicacis ab M distantiae R M = Zr; adeoque corundem a PM F diltancia (uc. 200.
Docc ad RM, ut Sinus Rectus anguli P M R ad RactiuM, Leu uC S ad R, ) RS =
Xi adeoque corum respectu PM momenta LIY X q R
3X (cumpriscum
t, Tumr, arithmerice proportionalibus, ipsilque spro linubus rectis arcuum arirs.
metice proportionalium ad Radium R; ) adeoque (ut prius etiam, oltensum est
in ratione iptorum a3S: Si, pro Omnibus a s, = 60 A1 = 6aV R3 = a R 1
3a 25 R~ = a 3 VR, Substicuaneur Focidem  
6C+r2R3 = 6aV+r 2 P 2 = a3 tr 2 R = 3a = 5Tr 2 R = a3 v17
xe Spiralis, quoulque libet concinuatae, (cujus Raclius ulcimus MI Y = 1,) momen-
cum respectu recta PM F, (tories compucata parce qualibet quocies iceraio deleri-
bicur,) e quidem vel ad parces E, ret ad partes C; Prour signum  auc = PEX
valeat. Aut etiam, (PrOPter + = ∞,
6er2 R3 (= 6a2 P - 6st R) - Cavr  = a re R + 3a s12 R + a vr Y: Vet
3a24
(Propier eandem ubique rationem rad a, quae est R ad P; ulpote in cadem ra-
tione semper crescentibusr et a donec perreniatur illic ad R, hic ad P, in termino
primi cireuti;) 6a R - 65 R. = bav N - a P + 3 a s R + a v R 7: Vel (nectecto
T: quipue dum P Donitur pro ∞ P, intinicelima parte ip(ius Z, e P pro carun-
dem in  linea parcium numero; tancundem eric DF, acque ipla ~ Linca;)
6a R3 = 65 R3 = 6a V R 2 = a 3 R23 = 3 a 2 5 R3 + a 3 ∞ R2
Sune aurem, ut ex praedictis patet, singulorum sectorum exisuorum maeni-
2∞ ileu 3∞, , (propter r =  R.) Adeoque omni.
Eudines, Etr; hoc eltus
R2
um summa = ∞ : ret  Curpore ad maximum coties sumprum, ut L ad 3:
PeT BrOP. F. hujus.). Nempe in ca ratione ad 3 R ~ Z vet (neslecto Y) ad 5 R~
erienrem circuli primi, seu tiguram spiralem primae circulationis,) ut a3, 2d ∞3
seu utr 3 ad R3; hoc eltu ut Cubus Radii terminalis MT, ae Cubum M A radii
circuli primi.
Per hanc ilaque Magnicudinem, si diricamus Momentum modo craditum; ha-
Debitur
Ceneri graricatis Fi.
surxe Spiralis (quousque libet concinuacae) M P T (cocies compuais sinoulis
parcibus quories iterato describuntur) distancia a recta PM P; ec quidem vel ad
partes F. vel ad partes Cin (sire Momenta spectemus, lire diltantiam Cencri grari-
tatis,) prout signum F vel = pravaluerit.
Nocandum interim (ne haec perperam incelligantur) in semicirculationibus se-
cunda quarta, sexta, (reliquisque in locis paribus,) pro Momencis his acque Di-
stantiis restimandis, linum snegacire incerpretandum esse; urpote, in his lemicir-
culis, ad concrarias Diametri parces polium: Adeoque ita exponendum, acque si
concrario ubique ligno afticeretur. Quod et ante intinuatum est.
Et quidem, pro integris Circulationibus absolutis, (propter cum s=0, cum F
v = 0, in sine cujusque cicculacionis, ) Magnicudines crunc,  ; Momen.
Ia retpectu PM F (nexlecto T, ob caulam modto dictam) 5a P. - a’ P (corieo
repecicis omnibus quories iceraco deteribuntur;) dictancixe cencrorum gravicais a
PEEEES
PMF