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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.
TA momentum, = 50 R3 + 5 aV R2 = 3 5V R2 = 3 a S. R - 3 s R -  a 5V; _ rC
spectu Ta = ZCR3 = Z aV R = - Z a s R = y 5 R + Z a s v.
Illud autem, ejusdem Onoulx, crilineo bB A insistentis aciem habentis Y A,
momentum, respectu ipsius TA, ex momento Ongulae quadrilineo bBa A insilten-
tis aelem icem habencis T A, respectu ejusdem Y A, Tubduetum; Hoc clt, ex
SFR3 = ZsBR 2 = 3 5 R = 3 a R3 =35 R3 = Z5V R 2 = 3 sR, (Der SC.) re
linquie Ongulae parallelogrammo BBa B insistenris, aciem habentis Y A, momen.
cum respectu T A, 3a R3 = 3 a V R = = 3 a 5 R = 3 a S V = 3 a R3 = = a V.
Idem habetur, si ex Ongula paralleloprammi R Ba A, aciem habentis Y A,
momento respectu TA, 3 a R3; Subducacur paralleloorammi RBB A, (aciem
item habentis Y A,) momentum respectu TA, Z a v: Cuippe quod restat, elt
Ongula Parallelosrammi bBa B, aciem habenris T A, momencum respectu F A,
a R 2 = = aV; UE PriuS.
Adeoque, (propiex magnicudinem, 2 ab R = = a H = 2 a R2 - = a V2, Ber
SF. PrOP. 17.), Distantia Centri Braricatis d F A, 26 R3 = 22
X
16R3 = 2V 8R3 - 6V R + 22
12 R2 - 3V
T2 R2 - 3 221 acque d 7 ay
22 R= = 3V; ejuque respectu ra momentum,
3a R3 = a v R F 5 a v = 3 a R3 - 3 a v R + 5 a 5 R = ; a 5 v = a B R - = a B;
ut eriam prius ostentum est.
Rut eriam ejusdem Ongulae Parallelogrammo bB a B intiltentis, aciem habentis
Ta, maxnicudo, momenta, et Cencrum praricaris, per se tacile decerminantur;
est utique Polidum ex Prismate, eique suxer impolico Cuneo constante; cidem
BBaB super eminencibus: Ouorum ueriusque separarim magnicudines, e Centra
pravicaris, adeoque et momenta, lacile dererminanur; adeoque de axprexat ex
utoque conttaii.
Rccedimus ad Ongularum Prilinei A ra, ejutque partium, aciem habentium + a
aut huic parallelam, momenta respectu A a: Acienique habenrium A a, momenta
respectu ra aut parallelarum huic; quaeque hinc dependent.
Si Trilineo restituto Leu Fieura Sinuum versorum, A ra insictat Semiguadran.
ralis Ongula aciem habens ra: Oux rectis bB, planum complentibus, insiltune
plana Ongulam complentia, Cunc. (propter angulum semiquadrantalem) Frian-
sula Rectangula Tloscelia; ipsarum bB, seu B, Pemiquadrara: Adeoque ipsa Vn-
gula, (sire qua cori ara, sire qua iplius porcioni ABBa intiltit,) aggresacum
omnium =h2 eo spectancium. Forumque ab A a distancia est BB (= a) relpe
etire: Adeoque simut omnium, hoc est iphius Onsula momencum, respectu Acy
CM Aoerepatum omnium =a B=, eo spectancium, Cumpris a arichmetiee proporeio-
nalibus: Hloc est, Arcuum Arichmerice proporcionalium in Semiquacrata Sinuum
verlorum, arcuum ad Semicirculum reliduorum.
Oux aurem rectis bB, xqualicer ab inricem distancibus, planum similicer com
plencibus, insiltunc plana Ongulam complentia, coridem crunc parallelogramma
quorum bases b B = a et alcicudines (proprer angulum Semiquadrancalem) aequa-
les eorum d ra distanciis respectiris, hoc clt iplis V a = B respectire: Adeoque
Onxula, live quae toci A r a Frilinco intiltit, sire qua iptius Porrioni ABB; est
Aporexatum omnium aB, eo spectantium; sumptis AB, seu AV, hoc ettV, aricti-
merice proportionalibus. Forumque ab A a distantia, EbB = = a relpectire, (per
prOp. 2. hujus.) Adeoque simul omnium, hoc est iplius Ongula, momentum re-
spectu Aa; Aexcexatum omnium =a= B: FToc est, Semiquadratorum arcuum sini-
bus versis aristimerice proporrionalibus respondentium, in sinus versos arcuum
ad semicirculum reliduorum.
Hujusque Ongulae aeiem habentis , a momentum respectu Aa idem est acque
Onouitae aciem habentis Ra momencum respectu ra; propter magnicudines et di-
Ttancias reciprocatas. OradSFI. prop. 16. ostensum elt.
Nempe, si eidem Fritineo Restito A r a, Ongula insiltat semiguadrantalis,
aciem habens Aa: Dux rectis bB intistunc plana, Ongulam complenria, crunE
(propres angutum adt A e temiquaccancalem) iplacum bB Semiguacraca, seu z a
adcoque