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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. XXI. DeCalculo Centri Cravitatis.
Ouaque Semiquadrantalem Ongulam eidem insistencem, aciem habentem A a, COm. Fiif. 166.
plenc plana, eildem rectis insiltentia; sunt Priangula Plolcelia, carundem recta- 168.
rum lemiguadrara: hoc est, Omn. Za 2  a 5 + Z52: eo spectantia. ITorumque
Friangulorum centra graricaris, ab Aa diltant carundem rectarum B V beste, hoc
elt ZbV = 2 a- f25. Adeoque Priangulorum illorum Momenca, (duetis magnicu
dinibus in relpectiras distancias,) Tunt Omn. = 43 + a2 5 = a55 + 553: (seu Fri-
ens cuborum omnium b V,) Cumpris varichmecice proporcionalibus.
Sunt autem, Omn. 3 a3: (lumpris v arutimetice proporcionalibus,) hoc ett, Vn-
Sulae AbB Hi8. 170. aciem habencis Aa momencum respectu Ae (per S M. prOP.
20.) 2C R3 = 2 aVR= 3 a3 R + a 2 5R +  a 3 ~.
FxOmm. a= S: (eo spectantia,) hoc eltu Duplum Momenci relpectu Aa Solidi
ABB f8. 170. ex ductu rectarum bB in B V respectire, (per 8N. Prop. 18.
==C R3 = 2 5V R2 + 3a3 R = = a  5 R + 3 4 5 R + Z a 2 5  1113IC
lip
TremOmn. a 5: (eo spectantia,) hoc est, Duplum Momenti, ejusdem AbB
Solidis respectu plani A ra, (per GO. pr OB. 18.) =3C R ̸ 3 av R
+353R = 5a 5= v.
a 5 R
ECOmn. 355; (eo spectantia,) hoc est, Momencum Ongula AB V aciem ha-
benuis A a, respectu A a; de R + 5sv R = ns R + : 5v: per 8C
DrOD. 26.
LrGO, Omn. 3a3 = a 2 5 = a52 + 353: = 3Z e R3 - Z aVR 2 = 85VR - 52 R
= 3a25R + 5aS=R = 36s R + 3a3V  5 a2 50 f3a52 V + 353v. Quod igi-
cur CAMomentum Onsula segmenti semiescloidis AB V, aciem habentis A a re.
spectu iptius A a. (Idem quod prius invencum erat. ) Ouod iEaque PEF MaGNI-
cudinem diritum, exhibebir diltantiam centri gravitacis ab A a: UE priuIS.
Atque huic quidem Momento, Si addatur Momentum Lnoula BBa V, (modo
cradicum,) habebitur Ongulae ab Ba, aciem habencis Aa, Momencum respectu
AC: UE PriuS.
Fxhibuimus ipicur in expositis Ongulis Semicrcloidis, ejusque partium, tum
Maonicudines, E Nomenta; cum Ceneri graricaris in Lingulis distancias a duobus
Talcem planis non libi inricem parallelis; acque in quo certio per aciem plano
constiturum sIC, CxS G. PFOD. X2. constai (eo nempe quod Onsulae alticudinem
bisecat;) AdCOGUC (PEr PTOP. 26. cap. PracCd.) ipsa sravicaris centra determina.
rimus.
Ouaque de Ongulis dicta sunc; eadem ad Colida conrettione tacta Pacile trats.
FCrUNtIE, ODC PTOD. 72. ec 24. uc suis locis Capius ostensiim.
Ouaeque de expoliris dicta sunc; ad alia, calculo rire adminiltrato, facile avoli.
cantur: Or ad pracedences aliquor propoliciones admonuimu s. 1) iI Clas CIIPCIEseS
Ouaque de Onoulis Solidisque Semicfeloidem Primariam (hactenus cradicam)
R
dicta tunc; eadem omnia ad Ongulas, Solicaque, Sccundarias (sive Prorractas FIB. 175,
sive Concractas) similicer spectancia, tacile cranstereneur. Nempe, quocies rectae 176.
b B in calculum veniunt; pro an substicuenda erit alia quanciras, quae, ad illam.
eam habet rationem, quam habet recta r a, ad Z P, semiperipheriam circuli gene.
TantIS. Ex similiter, mutacis murandis, de carundem Ouadraris, Cubis, Cxeterisque
pocellacibus; ut ad caleem propolicionis pracedencis ottentum eM.
Innnn 2