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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.
CapV.
Fis. 166, Similiter; Ongulx Frianguli Ba V, aeiem habencis PA: Momencum respe
Atura (idem acque aciem habentis r e, respectu F A, ) 3 S B= R = = 5B3 = 35 R
350R2 + 55 R = 2532; relpcetu Y A, 2 sB R2 = 3 sB R = + 5B3 = = sBR
+353R - a 53B = 3s R3 = 35~ RZ + 553R f 5 3V; DEx S N. PrOP. 26. Vn.
sulaeque correspondentis Parallelosrammi bBa B, geiem habencis. L’A, moivencum
respectu r0. (idem acque aciem habentis ra respectu, Y A,) ab3 R = 5 ab =
SaR. = 3 4uR + 5as R - 3 a s2V; respectu T A, Za R3 = 5 aV3 = 3 a B R2
+3aSR = 5 a F2B = 5a R3 =5 a V RF +, 3a57 R + 5452V; per GE. PFCP. 19.
Erso Ongula Praperii bBaVp aeiem habentis, PA, momeucm respectu ra
(idem acque acieni, habentis r a, respectu P A,) g, B R + 3 sB2 R = 5 a, B3 =  5h.
=3a R3 + 35 R3 = 3 a v R
respectu TA, 3 a P3 + 2sB A L. 3  R A d a s  C + 3 s R - 5 a 5 v. - ; 52 v; ee
35B R = = av + + sB3 =  a B RZ + 3s BR 2
+3a5=R + 853 R = 3 a s B = = 53 B = 4a BR  2 5 b R - 2. c b R - 3 s H R
= 3a B3 + 4 5B3 = 3 a R3 + 35R3 - 2 a v R2
55VR= = 345E R F 353R +
5a52 v. + 253V. Adeoque (Proprer maenicudinem 2 a b R F SB R - = aB2 -
35b2 = 2 a R = F35 R2 = a v R - 3 52 R + 5 a 52 + 5 53; Der BC, PrOB. Pra
ced.) Diltancia Cencri Gravicaris d r a
25R sB
12 a R F 8 5 X = 4 a B = 3 5 B
24 a R + 125R = 6ab = 4 5B
25R fBh
B Y 24ase F 12SR 6ab = 45B  d A, 2R b 2 aR f125R 6ab 5
Fademque Momenca, ex respectivis Momentis correlpondencis Onsulae porrio.
nis bBaV A, 33a R3  385 R3 F 25V R 21. F 353R, c 3 a R3 + 35 R3 L 1252 R2
=2753R, (SC. praditis,) Subdueta; Relinguime Ongulae Segmenti b V A, aciem
trabencis F A, momencum respectu Ta)=  a R3 f (2 s R3 (= - 76 R3 ) = ZaVX
+85VR2 = 5a52R  3853 R + 3a 5 V = +53V; d respectu T A, = 2 a R3 F
25R (= = =C R3) + 3 aV R2 + 85V R = 3a 5 R - 18S R = 3a 5 v 5v:
Oc Tupra SF. Unde reliqua deducentur ut prius.
Accedimus ad considerationem Momenti Ongularum Semieycloidis, ejulque
Fig. 166, parcium, aciem habencium r a vel huic parallelam, respectu rectie A a aut paral.
168, 170. lelae huic: Adeoque et (proprer diltantias es alcitudines reciprocatas,) aclem ha-
73, 174. bencium A a duc huic parallelam, momenci respectu re, auc parallelae huic: FO.
rumque quae hine dependent
Diltribiuis inaquie (Et ad S L. prop. praeced. e alibis ) cum Semicireulo in sua
minura Priangula aB, Peu Y aP; cun Semiercloide in respectira Traperia Bb,
(eu ysEP, tig. 168. quae respectire aequalià linc iplis L a P Priansulis, et paral-
lelosrammis y dEp Fe. Y70. Tunit Tumpris: L rISI intellisaneur, ac prius, On
sulae Semiquadrantales aciem habenues ra; quas compleane uldem Priansulis
Praveriisque minuris, intiltences minutae Onsilla. Oux itaque Frapeziorum
Ongulae, aequales crune respectiris Friansulorum de Pacallelosrammorum, Onsulis
limul Cumpeis: Or ad SC. jam ostentum est.
Ongulae Prianguli Y a P (Pyramis cum sic) adeoque de huic aequales similiter.
que policxe Prianguli (in Praperio incermedii) vBr, Cencrum gravicatis (illic
in aB, hic in BB, potiris, ) a ra distabit Dodrance alcicuclinis, (Per PEOP. 6.
hujus,) hoc cst, 3 Va = Z B. Adeoque iptius YaP prramidis (sed non et
iplius vB =) distancia ab A a, ZBV -
s
Ongulaeque parallelosrammi Y sE p H3. 270. (urpore Prismacis, duabus baFI.
bus Friangularibus incerjecti,) centrum craricaris d ra diltat, alcicudinis Belle.
(guancum scilicet inde diltat TriansuLI CenErUNI,) Der PrOP. 5, 6. hujus; HOc
elt, 3Y a = 3h. Acque cancundem inde diltac bipareicae Onsula, parallelogram.
miS vS, 2E, (utrinque Z DB aqualiter remotis,) Hg. 208. Centrum GravITaTIS, in
ipsa bB policum. L jusque Cencri, a Cenrro Onsulae vB modo indicati in ca
in quod spectat, seu dictanciam a 7 cs,) c(t 2 h- 2B
dem bB, distancia, (alticudinet
=:. Adeoque, propter Prismaris magnicudinem ad magnicudinem PytariciS,
Uc = ad 5, seu 3 ad 2, (est urique Prisma dimiclium correspondenris Paralle lepipeci,
824
70.