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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 328r

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: 0.81.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

One image of two folio pages side by side, registered by the library under both labels (also fol. 327v); this page is its right half.

The machine reads it as

  1. a nax - L = X vay fiet 2as = aXy. seu y et txady
  2. seu Xt = 2aa: ary et ex = raadu 3: atus et X dx = Aa: atque Ergo
  3. du circuliser pit
  4. posito aera 2. pendeti ex quadratura sorculi a saa- aZ: 23 summanda
  5. - - Aiter 2ax =x = XX 9y, fiet ZL x = xyyfiet X= 2a: aa tyu
  6. Iea on e (H Bet dx = 4Gdy, (aargu) et 2aX - aaXX X
  7. =3aydy. β)(aa + yy)
  8. 2_C. DC B 10 (eu 1). De(ser2
  9. AB X BC, yu. AT, + X AK radius a, seu CK AT =TC
  10. Xi LTC: AD = CK: BC seu +: X = a: y. seu
  11. srax - XX) =aX seu at b - HtX =X aaX + adeoque t = ax : E ax - XX)
  12. Net X = 2 +), ad + H , se (A dx se ABBA = bis ACA
  13. Et. siX dt = B D = bis AOAS= XF - bs ACA = La)
  14. Ergo bis ACA= X + - 2a ((tt dF: (aa + H)) + Ergo
  15. ACA= tianqu. B
  16. sia AC- G hilin. AIBA
  17. lineo AYOA
  18. re drc BA T+ trianu B AKC = a sIt d. (aet 1B
  19. ata) aquatur din
  20. seu an ACA La et sector AKCA = trianus
  21. 9r
  22. erit
  23. ua
  24. seu sector AKCA = triangs. BAT + trianque. AKC - triliu ATDA
  25. sed trianus BA T = tinanus ATC
  26. . Ergo fiet
  27. dector AKCA = quadrilat. KA TCF L trilin. ATDA
  28. Ergo rit scob ax est quadallat HATC. sect AKCA = = tritin. AFBA
  29. jam quadrilaterum KATC = rectanus. K AT et fiet sect AHCA= at t sin
  30. seu Trilineum circulare cavum ATCA L trilin AFBA
  31. fect AKCA = a. AT - L hiliu AFDA. f= at - Ra saat: (aa + H) t
  32. diffea seu sector ACA est summa omnesm A seu F demta summa omnum
  33. F seu AK, seu A applic ordinatarum ad A
  34. et dimidium trilin. est summa omnimmatt. (aa + H) ordinatarum ad AT, ergo
  35. jam fa a. AT, est summa omnium
  36. est summa residuorum, si sumum
  37. a prioribus summandis respective detrahandur posteriora, seu summa omnium
  38. residuum prioris summae detractae ex pnore
  39. a dt, a ( a - aH( aatH) =
  40. sect AK CA
  41. dt, a+ aH- a lD n aa + H seu (d t a: (aa t H) = puo AF, a, et AF C
  42. q
  43. a
  44. F na udo Fde La sdydy dudx = sector, y = S (ax - XX) et
  45. Htam conclusionem brevius sic consequi licuisset:
  46. dy = (2 2X) 2 (a - X) dx Eax -XX et dydu = aa - 2aX + XX Adx;, 2aX = X X
  47. it depdus + dxdx = dx dx aa = 2a Xdxx + XX dodx + 2 afdxdx - xx dudx
  48. 2aX = XX. sei sector = L aa (dx a C: YhaX-XX) = + aa fix L aa sx t. X
  49. X = 2aH:, aar tt dx = 4 tat (:, aat HC) 2F dt 13(a at t1) seu
  50. ax 2+((44++ 11at 3C ut): ( (it aa + FI
  51. aattt = at. zaa -+tt
  52. aa + +t
  53. et dX l. X dt. H, raa - 4
  54. ax lx = 2aH+ 2aut ratd = ae 2aH + a+ 2abdt- 3at. 24 ta n) t
  55. _ (aa +H)
  56. nat H.
  57. B1) aat et
  58. aa +1t+ 2lt
  59. Ergo dx = +2at dt 11 tdX =
  60. (Cat) t arcus
  61. +2aUdt: (2 (a t H) a + adt.
  62. Breviter fector iaaflx: teaxn
  63. 2aH: (aa +H) 1em n 44 + H eencus
  64. dx: Max -XV) fiat X - alt
  65. at. posito Al esse arium
  66. et erit sector Za dare et arcus = aas.
  67. aatu
  68. AB, X; AK, vel RC esse a; et AT vel CT esse t
  69. b 2
  70. 32 1aB1 6 sit

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 328r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0651?run=74