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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. 761

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: 0.84.

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The machine reads it as

  1. PTOP. XVII. DeCalculo Centri Cravitatis
  2. Fst A R = ASR minus, Z A R F ~ R2: HoC Cst, Z A R + AS R = v R; l
  3. vel (relticuro valore minuscularum a, 5y) Za R + a sK - VR
  4. Adeoque (momentis per magnicdinem dirilis) Portionis bBa A, distantia cen.
  5. eri gravitatis a bB,
  6. a +=
  7. R = a5
  8. 2a = 25
  9. F 2V k
  10. 2a. + 25i e ab Aa
  11. ; ec. ab A a = a -
  12. e - a-
  13. 2. a 2 5
  14. 25
  15. Vel d
  16. Fodem modo ostendetur (proxter bxB = a R = s R,) momentum portionis
  17. bBx respectu bB, (ungulamre correspondentem cujus acies BB,) este = a R = B R2
  18. e respectu rT, za R = as R F B R2: Et Cencri praricanis distanciam a bB,
  19. = 2 BR
  20. a -= 25
  21. _, 2 7 Y _ = 2 4 5 2. B R
  22. Auceriam (propter ABK = a R = 5 R,) momentum porrionis ABV relpectu
  23. BK (ungulamre, correspondentem,) este : a R - v R2; d relpectu A ay L a R
  24. =as R F 2 R =: Centrique graricaris distantiam d B R,
  25. a = 2. a 5. + 2V R
  26. a = 2
  27. EvR. et ab AC
  28. 2a = 25
  29. Si vero, ex Portionis bBa A, momenis respectu bB, et Aa; anteratur Paralle.
  30. logrammi BbBa momentum respectu ucriurris (proxter cencrum gravicatis aqua-
  31. liter ab utraque distans:) ITOC eAt, (propter bB = V a = B, ee BB = a, hujus
  32. que semissem ZbB = Z a) E a B = a R - = a v: Tlabetur Seementi ABB, mo-
  33. mentum respectu BB, -Za R F V R= L = a V: de resrectu Aa, == a R a5 R
  34. =VR2 F = a V: HIoc eAt, Semisumma quadracorum arcuum nibus versis arith.
  35. metice proporcionalibus convenientium, porrionem b B A complentium: Adeoque
  36. hujus duplum, corundem quadratorum Summa. P.F (momenta per magnicudinem
  37. dividendo, hoc es, per = a R + s _ F a 2, ut SB.) Distancia cencer pravicacis
  38. d BB, 3 a -
  39. 2V R - a5
  40. 2eR + 2a
  41. 2VR a5
  42. R; de ab A a, Z a = = 2C R f 2a2
  43. Eu speciatim, Segmenti A d C momentum respectu ds, (proprex v = R), est
  44. R3. Centrique praricatis a ds distantia est R.
  45. Y78.
  46. Solidaque de Semitolicta convertione facta; sune ad respeclivas Vngulas, (ut P
  47. Expius dictum eAt,) ut P, e ZP, ad R. Puta
  48. Solidtum Frilinei Ar a convertione circa + Y tactum, est d P3 + 2 R2 P; de
  49. Circa A a, 5∞3 - 2 R = Y
  50. Solidum Porcionis bBa A convertione cirea BB Factum, clt. 3 a P F v R P; &
  51. circa Aa, = a P = a 5P = v RF
  52. Solidum Porcionis bB, convertione cirea bB tactum, ell. = ae P = B RP; de
  53. Circa FF, Z02 P = a5P F BRZ
  54. Solidum Porcionis A BK convertione circa B K tactum, elt : a P - v R Z:
  55. _ CirCa Aa = a P = a5 P = VRF
  56. Solidumque Segmenti A b B convertione circa Bb K factum, cst. - 3 a P f. v RP
  57. 2i e eirea Aa = = a P + a5P = v RP +
  58. 2.k
  59. 2 DE
  60. Et Semisolida, horum semistes.
  61. Si vero libeat haec Ouadrilineorum, et Sectotu corsespondencium, momenta L
  62. respectu Aa incer se comparare; (praeterquam quod illud jam Factum ests dum
  63. VETOrumquE MOmenta danEUE;) Dicendum est, Momencum Ouacrilinoi bBa A
  64. respectu sibi adjacentis Aa ad momencum Sectoris B a A respectu A. a adjacenns
  65. sibi; else uc, omnes BB (illud complentes) in respectiras BC (complentes a BiC
  66. Friangutum;) ad casdem bB in respectirarum B. (complentium a po Frilineum)
  67. Triencem. Hoc est, ue Omnia rectangula bB6 (eo spectantia) ad PrienLCM
  68. omnium bBv. HIoc est, ve Omnia ab, ad Omnia Z sB.
  69. Ouippe Priangula sinouta ut a B (Sectorem complentia) sunt (quoact magni-
  70. iudinem) ad correspondeniia Parallelozramma bB (Quacrilineum complentia)
  71. D dddd

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. 761. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0781?run=74