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[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, fol. 776

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.85.

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  1. De Calculo Centri Cravitatis. Cap. V.
  2. Fio. 169, plus ZV R2 - 4 52 R: HOC est, à A2 R - = S2 R = = ef R. (Nempe Solidi hu-
  3. jus porcio ABK.
  4. Erso, Omnia OZa, SZ a, _c. Scementa; hoc elt cocidem Semicireuli, dem
  5. Dtis ipliS AZO, AZS, _c. Tunc (propter Semicirculum = ZRZ;) EARF.
  6. minus Z A R - = 5=R; IIOC elt, E ARP = = A R + LS R: leu (reltiuris mi-
  7. nulcularum. valoribus,) a RP = = a R F Z S R = = a RP - = e fR: Ouae eltu
  8. Portionis Solidi quadestineo ABBa incumbentis magnicudo.
  9. Adeoque, torum A dr a Tolidum, (PTOPter a = = P, e 5 =O;) clt 5R2=
  10. 16RP2 = ERY
  11. Sed e eadem corius Solidi magnitudo, sic Facilius colligitur. Sumpris in A a
  12. diametro, duobus punctis quibulvis equaliter a C Ceniro vrrinque remoris, ut
  13. S Z: manifestum est, cum linus rectos 5Z, Z F, tig. 160. invicem aequales esse;
  14. tum rectas 52, 2 C, Seu Z. 2, F C, Fg. 170. hoc est, areus BA, F A, Scu B A, Ba
  15. Fig. 269. Timul aequales Semiperipheria ABa, seu ra rectae. Adeoque duo limul
  16. rectangula, ZT X L, S, CF X F. Z, aequalia uni xaxSZ. HOC clt, Omnes BV 10.
  17. tius Semicirculi, in respectiras bB; cancundem este acque Omnes BV unius qua-
  18. drantis (hoc elt ipse quadrans A DC. = 3 RP,) in 70 = = P, ducta. HOC cAt,
  19. SRDZ; totius Solidi magnitudo; ut prius.
  20. FIinc etiam; Porrionis Solidi bBr magnicudo colligitur. Nam tocum Solicum
  21. sRPZ; dempio scomento AbB4 = = a R~ - = a R = Ls= R: Relinquie
  22. Scomentum i6 R~ Z = = a RP. + + a 2 R L52 R; V el (TUmPIO a == = P - a,
  23. a2R = =52 R. Quod iplum in inguilicione prius rOPCrEUM CraL. OuipDC, Sumpto
  24. AK = 7B, (adeoque relticuro a pro e) cric rBB == A K b, cujus magnieudo si-
  25. pra invenia cA + a = R = = s= R; COU L ef R. Fst enim, es, hoc ett a = sin a Y sy
  26. POrrO; Si ex Solido ABB~ = E a RP - + a R F + 52 R: Auseratur Solidum
  27. bBa B; HOC est, bB = a, in Segmenum Semicirculi V B a = Z a R = = 5 R L =SB
  28. lper GF. prOP. F5. quippe quod, in B V A elt an V, idem in BV a olt a h; et s
  29. uirobique idem;) hoc cst (PrOPtEF a = ZP = a, e B = 2 R (v,) in = RP -
  30. Za R = =5 R - 25V; NempC = a RF - = a R ( = a 5 R = = a 5V, Teu l’a R F-
  31. Zea R - = a 5V; Relinguicur Solidi porrio AbB = : a R - 3 a 5 R f : 52 R +
  32. 2a5V = =CR + =a5v: Seu summa rectansutorum omnium as Colidum illud
  33. complencium; sumpris v arichmetice proportionalibus.
  34. Auretiam; Si ex Semicylindri portione AK BB; hoc elt, ex Semicirculi Ser-
  35. menio ABV = = C R + 35~ (per B F. prOP. 15. ) in DB = a ducto; hoc Cst, CX
  36. SCaR + 3 a5V = 3 a = R - 3 a5R = = a 5V: auteratur Semicylindri portio ABR
  37. = a2 R - 52 R (per BK, ) reltabic Semieytindri porrio ABB, = : a R=
  38. 2a5 R + 3 52 R + Za5V; UE prius.
  39. Similicer de Momenris judicandum erit.
  40. Nempe, Momentum Solidi AbK, respectu T A; idem elt acque Mometira
  41. Omnium A B V Semicirculi Sesmentorum illud complentium respectu iplius (plani
  42. tangentis) Y A: HOc cst, (Dex SL. DTOD. 25.) Omn. Z C R = ZSVR = 353.
  43. seu Omn. Za R - = sR + L SV R 55 553: Sumpris a arichmetice proporciona
  44. libus.
  45. Siine aurem Omn. a Carictmetiee proporcionales ulque ad, a maximum,) 5a:
  46. (DEE PFOB. I. hujus. ) Adeoque Omn. Za R: = a2 R.
  47. Trem, Omnes s(eo spectantes,) Tunc iptum a B0 = v. R, (Per 5O. PrOP. 17.)
  48. Adeoque Omn. = =5 R2. = = = V R3
  49. item, Omnes su, tunc ipsum A bK Solidum ex ductu rectarum, B0 in bR
  50. hoc est (per SI. ) LV= R == V R2 - 352 R. A deoque Omn. L 5V R: = = V R3
  51. TIem, Omm. S3: (PEF S V. prOP. 23.) = Omn: d R. Sun autem Omn. 02
  52. hoc est, quadrata Ordinacim axplicararum, Segmencum ABV complencium, seu
  53. Omn. 52, Tumpris v arictmerice proporeionalibus: Duptum Momenti Segmenit
  54. ABV (Aig. 269.) respectu Aa: HOC est (per 5 V. prOD. 15.) ZV R2 45 2 R - +
  55. 352V: Adeoque Omn. 0 R: (= Omn. 53:) L RV R3 3 52 R2 u 3 sEB R: F. D
  56. proprerea Omm. L 1. 5t: 3d H392 R2-. B3 _ A.
  57. FNBO
  58. 2
  59. st

Cite

[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, fol. 776. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0796?run=74