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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. 825

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: 0.87.

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  1. PrOv. XLI. De Calculo Centri Ccravitatis.
  2. ee Pyramis ejusdem Friens,) alcicudini ceneri Prismatis addicis duabus quintis Fiy. 166.
  3. ditterentia alticudinum, hoc est Z X E b = oB, habetur Ongula Frapezii y 5Ep 168, 170.
  4. (ex utrisque constantis) alcicudo Cenrri sraricatis, leu diltantia d 7a, ZB + 35h
  5. = 2oh. Adeoque ejusdem ab A a distanca, bB + SBV = a + 135.
  6. Cum itaque Cnorila Prapezii cujusque Y sSp, ad respectivam Prianguli Y a D
  7. Ongulam sic, magnicudine, ic 5 ad 2, (ur ad d A. ostentum est:) Sicque illius
  8. Diltancia Ceneri gravitaris ab Aa, ad hujus distantiam, ut a F 135 ad 3 s; exit
  9. Vnsulae Fraperii cujusque y sEp momencum ad momencum correspondenis Vn
  10. sulae Prignouli Pa P, respectu ejuldem Aa, ut 5 a = Z5, ad, 25.
  11. Cumque hoc ubique obrineat; (licque eadem ubique magnicmdinis, Ungule
  12. Prapesii ad magnicudinem Ongula Friansuli ratio, uc 15 ad 2:) Fric momen-
  13. cum Onigulae Porius Semiereloidis, ejulre porcionis, AbBa aut BBd d, aut bB7
  14. ecc. (nam in parcibus perinde procedie demonstratio acque in toris,) ad corre
  15. spondens Momencum Onsula Semicireuli, ejutre. Sectoris Ba A, aut Ba D, aut
  16. a Da Termenti, scc: (quacum deies Cino roy) respectu recta A a: UL omnes illa
  17. Frianguli Ongula, Pyramidetre, eo speclances, in distancias respectire 5a. + 35
  18. ad caldem in 3s, ductas; seu ui omnia quadrata V a (quibus, proprer X P ubi
  19. que aequales, proportionales lunc illa prramides) in 59 = 35, ad eadem qua
  20. drata Va in 3s: HIOc C, ut Omnia 5 a B f 2 sh eo spectancia, ad Omnia 3.5 h
  21. respectira; Teu, ut Omnia 10 a B + 75 B2, ad Omnia 3 5B, eo spectancia: HIoc
  22. eltus We 7 ad 3, acque insuper ut Omnia 20 a B, ad Omnia 3 sB, eo spectancia;
  23. Cumpeis a arcubus arichmetice proportionalibus.
  24. Sune aurem (PrO ABBa Portione) Ommia a s (Tumptis a ariitimerice pro.
  25. Dorcionalibus;) hoc elt, Omnes a arcus arichmetice proportionales, in quadrata
  26. Sinuum. vertorum, areuum ad Semicireutum residuorum; idem acque Duptum
  27. Momenti correlpondencis Ongula ABBa EB. 77 aciem habencis ra, respectu
  28. recta A∞; (propier Triangula sinrulis BB rectis ibidem insiltentia, = B; e0
  29. runque ab Aa distantiam, a; adeoque momenta = a B:) HHoc cA, Duptum ip
  30. TiuS 3a R 2 = Za5 RZ= = aSVR = V R3- =s R=; PeF S F. DEOB. 1O. Adeoque
  31. corundem Decuplum, Icu Omn. 20 aB: CA hujus Momenci Visecuplum; hoc
  32. Clt 3 a R2 f 25 a5 R= = 5 a5VR -= 20V R3 + Z5 R
  33. Suntque Omnia sB2, eo spectantia; hoc ct, corundem arcuum arictimetiće
  34. proporcionalium Sinus recti, in Sinuum vertorum, arcuum ad lemicireulum reli-
  35. duorums quadrata: Idem acque Duxtum Momenei Solidi, quadrilineo ABB ∞
  36. fg. 270. incumbencis, ex duetu rectarum BB, in B0 facti, respectu rectae ra:
  37. Hoc cA, Duplum ipHuS, 32 R3 f Zs RZ = 5S2V R per S F. prOP. 18. Adeoque
  38. corundem Criplum, lcu Omn. 35b7; ct, hujus momenri ledcuptum, hoc ett
  39. 4V R3 + 45 R = 5V R.
  40. Preo Omn. 20 a B2: ad Omn. 3 sB2: (portionem ABBa spectancia;) Tunc.
  41. vc 3 a = kZ + 25 as R2 = 5a5VR = 20. VR - 3 52 R, act 4V R3 f 4 52 R
  42. =s V R. Cui li adjunsaeur, prius memorara, ratio 7 ad 3; (en 232 R3 +. 28, 52. R3
  43. ZSVR, adt 4V R3. = 45 RZ = SV R; Hlaberur ratio momenti ungula porrio
  44. nis Semiercloidis AbBa ad momentum Ongulae decloris BaA, lquarum acle
  45. Ta,) respectu ipuS Aa;
  46. a R. + 25 a5 R = 5aSVR = E V R3 + ac s2
  47. 35 d, dd 4. dk + 45 R2 - s V R
  48. Cum icaque momentum illud Ongulae Sectoris B a A fit (consequentis Tubiduo.
  49. decuxlum )Ev 3. - Zs R2 = 2s= V, (Der SL. prOP. 16.) erie, Ungula porrio
  50. nis Semiercloidis ABBa, aciem habencis sa, Momencum selpectu Aa, (lubduo
  51. decuplum ancecedentis,) 3a R = 23 a5 R= Ba 5VR 3V R + 3+ 52 R 2
  52. 36V X
  53. adenique est, Ongulae porcionis Semieyeloidis AbBa aciem habentis A a, mo-
  54. mencum relpectu ra
  55. Ouod quideti Momientum; divisum per Ingulae illius ABBd aciem habentis
  56. Ta, magnicudinem, Z f R2 + 3 sB R = 2a R2 + 235 R2 = B S V R, (per SD
  57. DrOP. Praced.) exhibet Distanciam Cencri graritaris ab A a
  58. 64VR 75 asR 4F s R f 15a5V + 14 5V
  59. 90 ak 15OSR-- 305V
  60. 45 a. +640 4 25 R + 14 5
  61. 90aR. = 1505R 3050
  62. Idemque Momencum. diritum per Ongula ejusdem ABBa portionis Se
  63. micycte aet TIabenTS Aa, magnicudinem Z a R + 3a5 R = Z V R
  64. F2S, , per 8 I. prop. praced. exhibet hujus Diltanciam Ceniri stavila
  65. Mt in n m

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. 825. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0845?run=74