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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. 829

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: 0.88.

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  1. PFOD. XXI. DeCalculo Contri Cravitatis.
  2. =a 2 V = 5 a5V = 552v: (Tumpris v arichmetice proportionalibus; ) complent Fis. 166.
  3. ejusdem A b V Ongula, aciem habentis bV, momencum respectu A a; leu (prop.
  4. ter alcicudines et diltantias reciprocataS) aciem habencis A a, momencum respe.
  5. ctu bV.
  6. Sunemcem, Omnia = a2 eo spectancia, (sumpris v avichmeriee proporcionali
  7. buS;) hoc est, momencum ipsius AbB tig. 170. Plani, respeciu Aa; (per 8F.
  8. DFOD. 17.) = 3 a 2 R F a 5 R = ~ R 2 F Z a 2 V. AdeOque, Omn. = = a R: =
  9. a 2 R2 = Z a5 R 2 + ZV R3 = = a 2 V R.
  10. Trem, Omnia as, eo spectancia; hoc est Solidum A B Bfig. 170. ex ductu re-
  11. ctarum bB, in BV (H8. 269.) respectire; (Per SL. prOP. 18.) + a 2 R +
  12. 2sR = = a5 R = Za5V. Adeoque Omn. 2 a s R: = 542 R + 3 52 R
  13. +a5R 2 = = a5 V R.
  14. Trem Omnia Z52, eo spectantia; hoc ell, Momeneum Scomenci Semicireuli
  15. ABV A8. 269. respectu A a; (per SR. prOP. 15.) 32 R2 = 5S2 R + 35 V. A.
  16. deoque Omn. 752 R2: = bV R3 - - 52 R2 + - 1 52V R.
  17. Tiem, Omn. 2 (arichmetice proportionales,) Zv, (Der proB. T. hujus.) Adeo.
  18. que Omn. - 3v R2: = - 5v R2 = - 3V R3 + 352 R2
  19. Trem, Omn. L a 2V; hoc elt, Momencum Ongulae ABB fig. 270. aciem haben-
  20. tis Aa respectu Y A; (per S L. PrOP. 29.) = 3a R2 + 2a5 R3- v R3 + Es p2
  21. + a5VR = 3 a 2 V R = = a 25
  22. Irem, Omn. = a 5u; hoc est, Semimomentum, respectu F A, Solidi AbB fig
  23. 270. ex ductu rectarum bB, in b V tig. 169. (Der SM. PCOP. 18.) 5 a 2R2-
  24. 245R + , 25 R 2 + 3VR = = a 5V R + 13s= V R - 5 a53.
  25. Trem, Omn. Zs=V: hoc est, Momentum Ongula A B V A5. 169. aciem ha-
  26. benris A a respectu Y A: (per SF. PEOP. 16. ) 30R3 = 55 R2 + 6s2 V R-
  27. 552. Adeoque Omn. 652V: = 5V R 3 = 18S2 RZ + 1b 5 2 V R 2 5 a.
  28. ErgO, Omn. = = a2 R F Za s R = Es = R = 3V R2 + 3 a 2 V + 3 a 5~ + 552v:
  29. Hoc elt, Ongulx AB V, aciem habentis B V, momentum respectu A a; aciemre
  30. tabentis Aa, momencum respectu bV; Sa2 R 2 = + as R + 9= 52 R2 - 3 V R3 +
  31. 2a2 vR + 3a50 R + , 35 = V R - = a 25 2 - 3 a 53 - 452. Idem quod priuS.
  32. Acque hoc momencum diritum per Onsula aciem habentis b V magnicudinem:
  33. Exhibec distanciam cencri sraricaris ab A a
  34. Idemque per Ungula aciem habencis A a magnicudinem divisum; exhibet hujus
  35. distanciam Ceneri graricatis d b V; e consequener, d TA, et ra; ejulque prop.
  36. terea momencum respectu TA, et ra: Dua eadem etiam lunc Momenta, relpectu
  37. Aa, aciem habentium F A, _ r a: Oua per magnicudines divita, extribebune
  38. et harum diltancias ceneri graritatis ab A a. Eadem quae prius.
  39. Acque, his demum Momencis, si addantur relpectira Ongularum DB a B mo.
  40. menta: Hlabencur Ongularum Ab B a momenta respectira; cadem quae superius
  41. alia mechodo invenca LunC. Acque hinc, distanLIA CCNHOTUIM GTAVIIALIS; U pruIS.
  42. Superest candem, uc Vneularum aciem habencium A a, momenca respectu ejus. us
  43. dem A a, investisemus; ee quae hinc dependent.
  44. Distriburis igitur, uc prius, cum semicirculo in minuta Priangula P a P, tum Fio. 166.
  45. Semicyeloide in Minura Prapezia y sEP: Semiquacrancalem Ongulam, Semies. 168, 1737
  46. cloidi insistencem, aciem habentem A an complebunt Solida his Minuris FraperiIS 174.
  47. insistentia; sicuc ee Ongulam Semicireulo intiltentem, eandem aciem habentem,
  48. complene Solida Friangulis illis insiltentia.
  49. Friangulo Y a P intistens solidum, Pyramis est, cujus centrum gravicatis in a B
  50. positum, abscindit inde, versus a 2 a B, (per proP. 6. hujus;) adeoque ipsius ab
  51. A a diltancia exit ZBV:
  52. Traperioy s E p intiltens solidum; Componitur ex Fruncato Cuneo, seu Pril
  53. mare duobus similibus Fraperiis y dEP incerjecto, alcicudinem habence ip (i a B = a
  54. aequalem: AIque, ex Cuneo ei superimpoliro alcicudinem habence, in B, nullam;
  55. sed, in b, ipli B V = s aequalem; cancam seilicet quanco altius est Colidum illud
  56. in bus quam in B, hoC ett, quanto tonsiOr ell b l, quam Ba.
  57. MMMM I 3
  58. (Nec

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. 829. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0849?run=74