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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 722, page id 851387705:0742
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De Calculo Centri Cravitatis. Cap. V.
=1 5 RP + ; 5uP-
A aC P P + isvP + : Re, cilea F A convet
sione integra; Za R D = = h5 R D = ZSVF - - = = C R F + 35
convertione dimidia, a RP = 3sAP + 1 52F.
6+
= de X F +
trem ejusdem Semilegmenei BV A, respectu rectae B V, momentum, rel Semi-
quadrantalis Ongula, cAb. (per S L.) = ZC R2 + 3 a V R - 653. tirso Solidi
illius circa BV, conversione inceera, deseciprum, est - : c X P + : av2 =  ; e
convertione dimidia, - Le R P + = a2∞ 53Z
12X
Ouodque hic de Semitolidis, (inceltiee, quae conversione dimidia describuneur,)
oltensum elt; quae lunc Incesrorum dimidia: Similiter de aliis, quae conversio.
nibus aliis impertectis, (Duca Ouacrancali, _c.) deseribuntur; lerrata prOpOF-
tione, judicandum erit. Ouod et in sequencibus paricet incellisendum exie.
Ouodque de Solidis, Planorum horum convertione circa rectas ran FA, BV
ostentum est; similirer ad alia, mutacis murandis, accommodabitur, quae corundem
planorum, cirea aliam quamris in eodem plano rectam illis paralletam (qua pla-
nC
in convercendum non scce) in quacunque ab illis diltancia, intra luprare, Po.
ficatum convertione describuntur.
Rcque jam quidem, quod ad Sectores incegros BCBA, Ba BA, _ inceorum
Sermencum B B A, ecc. quorum non modo Conrri graritaris alcitudo, (puta quan-
cum distat d ra F A, BV, vel C D, _c.) Sed ipla Centra jam determinantur (ut
quae sinc, in alcicudine designata, in IpPO AXC, PuTA A a Fecta, per s hujus: ) IIIO
rum Momenta, Ingulae, e Solida convertione facta, Patis déterminantur; non
modo respeetu recta qua sic iplis ra, PA, ecc. Parallela, sed respectu rectae cujus-
vis expoluae ureunque in illo plano sitae (lalrem quae converrenda Plana, leu
Ongulae Basin, non secet.) Nam, propcer datum iplum srariraris Centrum, datur
etiam ejusdem distancia a quaris lic expolita recta. Onde reliqua conlequun.
tUII.
Ouod eriam, de Sectore BCA, Segmentis ABA, a Ba, Friangulis BV C,
BCa, _c. similicer intelligendum elt: uepore quorum ipsa Centra graritatis non
minus determinantur, quam iptorum BC B A, BBC; guippe in illorum axe pO.
lita.
Sed Semiscetoris Ba A, e Semilermenti BV A; quorum Centra Crraritatis
nondum ipta decerminantur, sed iptorum tantum a ra, T A, vel quae hisce Da-
rallelae Cunc rectis, Diltancia: Momenta, Ongula, de Solida convertione tacta, non-
dum decerminaneur, nili respectu iplarum ra, T A, rectarum, auc hisce paralle
drum. Ouum rero eorum irem Centrorum distancia ab A a decerminata fuerit
(quod jam Facturi Tumus;) adeoque illorum Cenrra ipsa decerminata; cadem
eriam ad rectas ipti A as parallelas, aur eriam alias in eodem plano rectas, similicer
transterentur.
Ocisiur, de his etiam, eadem univerlaliter decermineucur: eorum ipta Gravica
tis Centra jam decerminabimus, (per 26 Cap. praeced.) extibita eorum etiam ab
A a diltancia, quae iptis ra, P A, dc. Parallela non est.
Nempe; Cenri eravicaris Sectoris B C. A, d recta A n diltancia, est = - 20R
Duod sic ostendicur. Disectis B A, BA, arcubus in s, S; erit (proxter areum d S,
aequalem areui BA = a, ) Chorda SS = BA = c; ejusque SemiltISS , = = 6. Trem
Sectoris B C. A, Cenrum pravicaris G, in recta C8; ejusque d Cenrro distantia
C.C = = R; (pec hujuo B A.) Arque (propier similia Trangula) ut Cs = R,
ad 81 = 3C; Si C. C =  B, ad C. e- , diltantiam Centei praricatis ab A a;
ve