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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 829, page id 851387705:0849
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PFOD. XXI. DeCalculo Contri Cravitatis.
=a 2 V = 5 a5V = 552v: (Tumpris v arichmetice proportionalibus; ) complent Fis. 166.
ejusdem A b V Ongula, aciem habentis bV, momencum respectu A a; leu (prop.
ter alcicudines et diltantias reciprocataS) aciem habencis A a, momencum respe.
ctu bV.
Sunemcem, Omnia = a2 eo spectancia, (sumpris v avichmeriee proporcionali
buS;) hoc est, momencum ipsius AbB tig. 170. Plani, respeciu Aa; (per 8F.
DFOD. 17.) = 3 a 2 R F a 5 R = ~ R 2 F Z a 2 V. AdeOque, Omn. = = a  R: =
 a 2 R2 = Z a5 R 2 + ZV R3 = = a 2 V R.
Trem, Omnia as, eo spectancia; hoc est Solidum A B Bfig. 170. ex ductu re-
ctarum bB, in BV (H8. 269.) respectire; (Per SL. prOP. 18.) + a 2 R +
2sR = = a5 R = Za5V. Adeoque Omn. 2 a s R: = 542 R + 3 52 R
+a5R 2 = = a5 V R.
Trem Omnia Z52, eo spectantia; hoc ell, Momeneum Scomenci Semicireuli
ABV A8. 269. respectu A a; (per SR. prOP. 15.) 32 R2 = 5S2 R + 35 V. A.
deoque Omn. 752 R2: = bV R3 - -  52 R2 + - 1 52V R.
Tiem, Omn. 2 (arichmetice proportionales,) Zv, (Der proB. T. hujus.) Adeo.
que Omn. - 3v R2: = - 5v R2 = - 3V R3 + 352 R2
Trem, Omn. L a 2V; hoc elt, Momencum Ongulae ABB fig. 270. aciem haben-
tis Aa respectu Y A; (per S L. PrOP. 29.) = 3a R2 + 2a5 R3- v R3 + Es p2
 + a5VR = 3 a 2 V R = = a 25
Irem, Omn. = a 5u; hoc est, Semimomentum, respectu F A, Solidi AbB fig
270. ex ductu rectarum bB, in b V tig. 169. (Der SM. PCOP. 18.) 5 a 2R2-
245R + , 25  R 2 + 3VR = = a 5V R + 13s= V R - 5 a53.
Trem, Omn. Zs=V: hoc est, Momentum Ongula A B V A5. 169. aciem ha-
benris A a respectu Y A: (per SF. PEOP. 16. ) 30R3 = 55 R2 + 6s2 V R-
552. Adeoque Omn. 652V: = 5V R 3 = 18S2 RZ + 1b 5 2 V R 2 5 a.
ErgO, Omn. = = a2 R F Za s R = Es = R = 3V R2 + 3 a 2 V + 3 a 5~ + 552v:
Hoc elt, Ongulx AB V, aciem habentis B V, momentum respectu A a; aciemre
tabentis Aa, momencum respectu bV; Sa2 R 2 = + as R  + 9= 52 R2 - 3 V R3 +
2a2 vR + 3a50 R + , 35 = V R - = a 25 2 - 3 a 53 - 452. Idem quod priuS.
Acque hoc momencum diritum per Onsula aciem habentis b V magnicudinem:
Exhibec distanciam cencri sraricaris ab A a
Idemque per Ungula aciem habencis A a magnicudinem divisum; exhibet hujus
distanciam Ceneri graricatis d b V; e consequener, d TA, et ra; ejulque prop.
terea momencum respectu TA, et ra: Dua eadem etiam lunc Momenta, relpectu
Aa, aciem habentium F A, _ r a: Oua per magnicudines divita, extribebune
et harum diltancias ceneri graritatis ab A a. Eadem quae prius.
Acque, his demum Momencis, si addantur relpectira Ongularum DB a B mo.
menta: Hlabencur Ongularum Ab B a momenta respectira; cadem quae superius
alia mechodo invenca LunC. Acque hinc, distanLIA CCNHOTUIM GTAVIIALIS; U pruIS.
Superest candem, uc Vneularum aciem habencium A a, momenca respectu ejus. us
dem A a, investisemus; ee quae hinc dependent.
Distriburis igitur, uc prius, cum semicirculo in minuta Priangula P a P, tum Fio. 166.
Semicyeloide in Minura Prapezia y sEP: Semiquacrancalem Ongulam, Semies. 168, 1737
cloidi insistencem, aciem habentem A an complebunt Solida his Minuris FraperiIS 174.
insistentia; sicuc ee Ongulam Semicireulo intiltentem, eandem aciem habentem,
complene Solida Friangulis illis insiltentia.
Friangulo Y a P intistens solidum, Pyramis est, cujus centrum gravicatis in a B
positum, abscindit inde, versus a 2 a B, (per proP. 6. hujus;) adeoque ipsius ab
A a diltancia exit ZBV:
Traperioy s E p intiltens solidum; Componitur ex Fruncato Cuneo, seu Pril
mare duobus similibus Fraperiis y dEP incerjecto, alcicudinem habence ip (i a B = a
aequalem: AIque, ex Cuneo ei superimpoliro alcicudinem habence, in B, nullam;
sed, in b, ipli B V = s aequalem; cancam seilicet quanco altius est Colidum illud
in bus quam in B, hoC ett, quanto tonsiOr ell b l, quam Ba.
MMMM I 3
(Nec