Leibniz Legible

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LBr. 57, 1 · Bernoulli, Joh., fol. 86v

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. 81r); this page is its left half.

The machine reads it as

  1. elementa curva in ratione composita ex directa elementorum ordinatae
  2. souplicata, et reciproca pttinum aoscissarum suberplicata. res reduciti
  3. ad quadraturam ci
  4. euron acytoptota, VX. V(dxdx + dydus) ut dydy. Ergo X, dxdx + dydu ut dyt seci fiet
  5. Xdx, dxdx + dydy = b dd seu XdX + X dx dy = dx bdu
  6. seu (X: b) dx = (X: b) dx dy + dyt seu (N: b) dxt + (XX: 4bb) de = (x: abb) ex lx: b) dia
  7. +dt, seu dy = (X: 2b) dX = dx Y(XX + 4bx): 2b seu faet ubi rursus
  8. extrahendo fiet dy = dx Y (2b + CXXFabX) + 2bX): 2b. Ubi primum VCxX + abX)
  9. revocemus ad rationalem, fiet et sit XX + 4bX = XX WB fat: B et LCXX + 4bX) = X V: B
  10. et X = 4bgg:, vv -gg et dx = - 8b g9 dv : qu (vo-93 ergo sit
  11. dy = 490d Subv B) + et X HXX + 4bX) = 4bgv:, vi -gg
  12. et fiet dy = - 4g9 dosiqu, vr-99) Y (2b 4b9v + 2b 4b99 (:, vv - 99)) seu fiet
  13. dy = - 85 dv 2g :, v - g: quov - 93) vel. = - 8b9 dv H29, v - 9) : (v. 93 qu (o v. 35
  14. vel faciamus B _ 2g0 - 2gg = qV W. seu v = 2WW +99, :9 ferifeg, v - g = 2W, et
  15. et v-g = 2WW. g et vp-gg 4W+ 499WWg- g:g9
  16. do = 4 WdW: g. Ergo dy = - 86 uao. ZW: (2WWol: 9) ( 16W = qu wW =ggB). GCE
  17. dy - =2 bg dio: 1 in Eri + 49) - 2bdW. (2WWW +g9) g: W qu (wW +g9)
  18. sit g = - b et fint dy = 2G du. 2iow +b,: W qu (ion +bb)
  19. quae rurcus resoloit
  20. quae summanda resolri potest in duas fucitiores jam 2WW +bb,: W qu (Wot
  21. resolvi potest in duas simpliciores; Rb: ae. qu (W1 +B)) + Rb: ust (_ wio +b0)
  22. + Chiior i b_ bk _ bcct 2bsoio + b5
  23. +bfW + 2BFWW +bF.: WW qu (Won +6) = Zb: wiv. qu(cotrb) p
  24. et scribulur e
  25. et fiet f = 2b et h = (-f =) - 2b et R = (= 2f =) - 4b
  26. + bh W + b3 K WW
  27. - 2bb WW - qb : qua Wo1o +bb
  28. Ergo 2b: Wio qu (Wuo tbb) = 2bb: 10W
  29. = 2bt: igu (101o + bb)
  30. u+ quae (ono +bb)
  31. seu 2b: loco qu uteorbb) = 2bb: WwW = 2bb: w10 + bb
  32. jam ut alteraquoque pars resolvatur fiat
  33. fb W + hB WW + hb. id (101o + bb) = 2b: W2 WW +b6)
  34. itaque 2b: W (uonebi) = - 2bb: WoW
  35. ergotit h = 2b f = (-h =) - 2b K = (- f =) 2b
  36. +2b1: WY + 2bb : W01o + bb
  37. Wu. Ae qu (12 ab 6) . Crob
  38. in unum ambobus fit
  39. Ergo tandem additis his
  40. uodi o
  41. 2b, u exa 2oo + bb
  42. 2b (12 L 2bbW + B (= W
  43. W 99 (1010 +6b)
  44. = 2b dW: qu (110 +b6) Tantum ergo superest
  45. sit t bb = o + 2cob + bb seu 1 sibco toc
  46. W4 qu (101 + bb.)
  47. et W (+ Ado + bd0 seu du = codoW +bdo. W. ergo fiet
  48. et et i = sb
  49. Ergo dy = 21 2ve 2b+ du : W
  50. d et du - bdp. 2W ergo du: qe qu (0ro +sb) bdes 2 A∞ BB Cp +bB
  51. ut quaeratur sduo: qu (101o +bb)
  52. sib i + bb bi + bb fiet wu = b
  53. A Aliter w + bb = sb( + bb) id Elodio= b dv. t (b +bb)
  54. adinatead langente verlcis ducto indistatapt ha
  55. 8 = b5: qu (rto ib) sit
  56. cbb + ZWW = b3. fit 101 = 63- 5bb,:8
  57. Ergo EWd = b 1b2- 55 dF. Ergo res tandem ad
  58. Nempe sed
  59. 5ZW = S 3 do f 2)
  60. ergo A duo: qu (1co +bb) =
  61. hae seu mromentum exaxe, hoc datur
  62. hoc habebitur si cW d de jar
  63. -2b dW: qu (101 +b6) = - 2bdW 8E, Ergo - 2675 d W: qu (wn +b6) = - 2b58 dute
  64. W = b b s(bF-
  65. ergo sEEdio =W ZZ - 2 sio E de
  66. dW: W = = B1: W3. Ergo y = 2b.W + 2
  67. quadraturam Circuli redtu
  68. = 2b1055 + 4bb 4b su 5 di = - 2bW5 + 4bb s Y(b5 - 5C) d = - 2sdv. p. 602
  69. Ergo denique
  70. - 2645dW: qu (1o + bb).
  71. = c - 2b: W - 2u 55. 1. + 4 5 ibB. 35) a : b
  72. fit W8. = b8 et 1otoY = b95 seu WW F P = bb cg WFF = bb 9g: W
  73. 2b - 289W0W0 , 4 (9 d8 = 7
  74. Z= b: ( = bv + 36b5 : 2
  75. sit s(XX + abX) = 4 fiet v = -b p. X et
  76. tam y = 2b 5dW: 104
  77. - 298 + 459d8 :b seu
  78. v= . B (x + abx : X = W = 8 (bv + b6, : 2)
  79. et W00 + bb. bb = p + X, : 2X
  80. 88- b∞ b8- ZY = 2bx 2bX C: +X) n 4Xx (: (x) qu) -2 bbX V 4bb : (quaV
  81. jov : bb = p - X, 32X
  82. = B b3 : (W1 + bb.) et 8 = 1bE- EE)
  83. WWW = g -bv -sib, : 2 = bb 1 - bbX, : 2X
  84. ergo E: b = 2X 2, ∞ +X
  85. HH- Obx. De 1 25 1bZ- 53
  86. so subo nttm sen eo cas quo nes omtus nt e fint re et
  87. hy= b2+ 591 8 ex i 2s
  88. u +bb, quaeritur SPhao
  89. = 13.
  90. Hrc Calculus est
  91. non pertineat
  92. ad potam lachisti
  93. rou nov-aboo tnge
  94. XX Vrrgg = ab PX + XX
  95. ((XX + 4bX) vocetur 4
  96. vu = 06 i - 99X: 2X
  97. Wo10 + bb, : bb = ( + X, : 2X

Cite

LBr. 57, 1 · Bernoulli, Joh., fol. 86v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-958803:0174?run=74