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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 742, page id 851387705:0762
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De Calculo Centri Cravitatis.
Fi8. 159,que tae distanciae in magnicudines ductae, (nempe Ongulae, JV R; e Semi-
Tolidi SDRP, Per SO. PrOP. Praeced.) exhibent semiquadrancalis Ongulae luper
BC A Sectore, aciem habentis A a momentum respectu iplius Aa, SC R3 F 85V R2
Semilolidique correspondentis, Le R2 f EsV R. Ec specinrim, pro Onsula Se.
micirculi, de Flemisphaerio; ib R3 P, e 3 R32
(Alque hic obirer notare non erie imporcunum, momentum Semilolidi respectu
tui axis conrertionis, duplum esse momenti correspondentis Ongula Semiguadran-
talis respectu aciei sux seu Plani per illam perpendicularis; quod in hujulmodi ca.
sibus semper obrinet, quod semel moneo: Cum enim magnieudo ad magnicudi
nem sic ut Z P ad R; Cencrique distantia, propter conversionem dimidiam, ut
2 R ad L P; erit quae ex uritque componitur, momencorum ratio
Deinde, quae Friansulo B V C intistic semiguadrantalis Ungula, aciem habens
Aa Pyramis est; verticem habens C. Cenirum; Basemque Priangularem rectae
BV insistencem; cujus quidem Prianguli Cenrrum gravicacis ab A a plano, distat
EBV =35; Centrumque graricaris Pgramidis (urpoce in recta, a batIS Centro
ad C prramidis verticem ducta, qua cs Pyramidis axis, tres quadrantes vertus C
abscindens; per S hujus;) diltabit ab Aa plano, Z x 35 = 35. Oux quidem di.
stancia, dueta in Onsulae maenicudinem 3s x, (per S R. PrOD. Praeced.) extribet
ejuldem momencum respectu Aa SN: Et Semitolidi correlpondenns (eujus
magnicudo ad magnicudinem Onsulae ese ut 2 ∞ ad R; Cenuique graricaris distan.
cia, ad distantiam hujus, ue 2 R ad Z P;) moimentum Z 5 X.
Acque haec Ongulae, Semicolidique momenca; momentis Ongula Schmisolidique
Sectoris BC A (S P. reperris;) Ablata, si supra Centrum; vel Addica, si intra
Cenirum; exhibent Cngula Semiseemenio BV a insistentis, aciem habenris A0
nomentum respectu A a, se R3 F 85V R F 2S N: HIOC CA, (PFGpteF N= X
supra Centrum, auterendum; et x =- R FV, intra Cenirum, addendum;
SCR + 55V R = 2S R F 1 S V: FL lemitolidi, = e R. + Z5V R27
N=e R
F25VR= = 5s R F 5SV. Adeoque (proprer Onsula magniudinem, vR
=ESR f SsV, Der S R. propolitionis PracCdentis) diltancia ceneri gravitaiis
Oneula ab Aa 3C R3 + 350R7 = 25 + 250
80R2 - 4s R F A 52V 101
3C A3 + 35VR +25 
4V R + 4 s 2
Cencrique semisolidi inde distantia, ad hanc ut 2 P ad 5 P, teu 4 R. ad P.
Porest aurem hoc momentum Oneulae. de Semisolidi, Semisegmento BV A Con-
renientium, sic alirer concipi. Nempe, E omnes ordinacim applicata BVI etc
aequalibus incerralsis sumpiae, (complentes BV A Spatium,) ducancur primum in
sui semistes, uc habeantur Trianpula eidem intiltentia (Ongulam complentia,
quae lune (ut supra ostensum est) Ordinarim applicatarum Semiquadrata: AIque
ac demum Priangula. (semiquacratis aequalia ) in rectarum duos Friences, (pro
diltancia Ceneri graritatis a verrice in Friangulo:) Ouod prodic, BV X = BVX
BV = SBV C, exhibebit momentum Friansuli rectae B V insistentis. Ouod clin
ubique tiac: Frit Onsula Semiquadrantalis, super B V A insistentis, aciem haben.
eis Aa momentum respectu iplius Aa; Tummx Cuborum ordinatim axplicatarum
Lriens; Pura, :Omn. 8 (Quod perinde rerum est, si pro Semilesmenio BV A
in verrice terminato, sumeretur B V CD, vel quaevis alia Semicirculi vorcio, dua
bus ordinacim applicalis incerjecta. Quippe, e ties; Omn. s monenium Onsulae
Timilirer exhibebic.
Sed e idem momentum jam modo repertum est, se P 3 F s5V R ELL +53R Y
253V. Flujus icaque Priplum, 3e R  F 3SV R  = 4 53 R + L53V, aequatur Omni-
bus o; hoc eu lumma cuborum ordinarim applicatarum, quae seimisesmencum
circulare BV A, in verrice terminatum, complent. 
(Si vero haec ad summam Cuborum ordinatim axplicatarum in alia pOrTONC
puta BV CD, non ad verticem a cerminaca, accommodare liber; id Fer, ut alH
modis, sic hac falrem Faeili rarione; nempe, si, modo jam tradiio, habeatuE PIF
num simmma omnium o qux Eorum A D C Semilesmentum spectant; acque deinde
summa omnium  quae spectane Semilesmentum AB V, acque demum haec summa,
ab illa subducatux; quod reltat, erit omnium o porrione BV CD spectancium
fumman
 WWAS Verun
Cap. V