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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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De Calculo Centri Cravitatis.
Ciap. V.
Sc
170.
Fig. 269, Grariratis Scholat Manera a convertionis axe, ad lat ua ab acie lua 2
Ut 2 A del = f. Semoridique momentum respectu axis lui, ad illud Ongula re
spectu aciei lux, (in ratione quae ex magnicudinum es distantiarum rationibus com.
Ouxeque de expoliris Onoulis (sire quae tiguram sinmis reltorum, live qux
figuram Simuum Rectorum spectant, corumre partes,) dicta sunt: cadem ad alias
(calculo rite adhibiro) tacile accommodantur.
Si autem pro figuris jam exposicis A T~, arV; Prorractae Contractaere conside.
randae veniane: Onocies rectae b B in Calentum veniune; proa, substimenda erie
alia quanciras quae ad illam liu UE ra; ad JP; ut ad Propoliciones praecedentes
monitum elt.
Ouxque de Colidis figuram Sinuum Rectorum Onius Ouadrantis craduneur; ca-
dem eriam ad Solida tiguram Chordarum in Semicirculo Spectantia cransferentur;
uni ad propoliciones praecedentes monirunt elt.
Donitur,) ut 2 ad r. Uc in luis locis paltim oltentum elt.
L LC F. a X.
Semierclois, elt, correspondentis Semicirculi Generantis, Tripla: PL
Partes, Partium (respectire sumptarum,) Triplae. Puta A= a = 3ADa;
e BBa A = 3 Ba A. FE RC ubique.
C. Ilorum vero Momenta, ad Momenta horum, respectu ejusdem ra
B.
Fansentis, ut 5 2d 2; seu Dupla sesquialtera.
Atque hinc eadem respectire determinantur, tum quod ad Magnitu-
dines, tum quod ad Momenta, e Centra gravitatis, in Semier-
cloide; quae supra in Semicireulo (PrOP. 25.) et in Fixura Si-
nuum verlorum, (PrOP. 27.) determinantur.
Nempo (recentis Symbolis ut in proposicionibus praecedentibus)
Semicrcloidis Ara; magnieudo, 3 R P: Momentum respectu ra,
8P2 P; respectu TA, 8 P D; dictancia Centri grariratis a r a, 8R;
a TA, 3R: Nomentum relrectu Aa RP2 = Z R3; respectu T
 PP. +; R; distanria Centri er avicatis ab A a + P - 10 .
8.
16 P2
0∞ ia Y7
Complementi Semieycloidis, A T Y; Magnitudo, L R P: Momentum
resrectu ra 3P2∞: respectu TA, S R. P; dictancia Centri BraVIEaTIS
2 ra, ER; d TA=R: Momentum respectu Aa s A D2 + Z R; respectu Y,
Es RP2 - 3 R; distantia Cemeri eravicatis ab Aa, + P +
16P
16R
∞i aY.
Portionis Semiereloidis BBa A, magnitudo 2fR: Momentum respe.
Au ran FR F EsbR; respectu F A, 2FR = Esb R; dittantia
Centri gravicatis a r a ER F = B f; 2 TA, ER-
18F: Momen
tm respeCtu Aa, 2 a R F 3aSR = 3v R~ + ZsR; dittancia Ceneri
Pravicatis ab Ao  a  25 -40 R + 25
Oa L95
f 4v R + 2s
Segmenti Semicreloidis bBF, NIaBnitndOZ a R = Z5 R: Momentim re.
spectu ra Za R = 3oR= i sbR; e respectu FA 2 a R. = 75 R
=B sBR.
a.
206.
3.