Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 705 · Overbeck, fol. 115r

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. Calculus Surdorum
  2. Donamus 2 + Y3 =m.
  3. Aequatio 1.
  4. Multipl. utrinque per Z- YZ
  5. fit 4+ 2(3 -33 3 = (2- Y3)m
  6. id est d = (Z - Y3)m.
  7. Seu 1: m = 2 - Y3
  8. Horu quadrata 1: n1 2 = 7 - 4Y3
  9. Divisis E. e X per m
  10. fit 1: m = (2 - 13): m
  11. MiM =I: M = (2 + YZ): M2
  12. 5 Suma 1: m + 1: m = A: m
  13. addontrinque AWZ. um
  14. a 1 1
  15. Aequ. y -b +213) 2 + 20 +6 +2r3) a
  16. (2+ r3) n.
  17. + a a X
  18. Aequ.
  19. (3
  20. X -(4 +2V) Z +v + (4 1213) a
  21. Pono 2 + r, =m vid. Liter~. Iem 2+ a = W.
  22. fit y -(Em +1) WV +2V
  23. mn
  24. X = 2M W + B
  25. Ergo per Aequ. 1.
  26. fit (Em +B) e +2V) 23
  27. Dfit aW: vm +1:m B. m = 4: m. + 4N: vm
  28. ME vE
  29. a
  30. fit ((2m +1) W +20) 2
  31. (2 +r3)v.
  32. mi seu y = (Em + 1) W +2B,
  33. a
  34. (Em + V)3 3
  35. m313
  36. mv
  37. X = ZmW +V
  38. moa. Et omisso communi Multiplicate a3
  39. = (2mW + D 2m u +v Et Involvendo Explicite
  40. MEvE
  41. md v3
  42. MD
  43. Mn.
  44. Multipl V utrinque per Zm: D fit am + amWer, +W+emtqu + qu = 8m = 12 m H +6mHo qV L 2mW+ V
  45. _ fit 2: m D +2: D = B: mv.
  46. Addo utrinque 4: m v.
  47. a fit 6: m v +2: B Z8: mv +4: m v.
  48. Multipl. V utrinque per(2m)
  49. D fit 2: m +Z = 8: m 3
  50. Ex 8
  51. 4r3-5 p
  52. m2v2
  53. a a
  54. a + 4: m. quae ad Literam Dvalent 4Wm +I: m + 1: m
  55. fit 4N: DE L WE: m v + 8W: mo + 4W: m B = 8WV3: v + BW: om +6N: mn +2WV: B
  56. Divido utrinque per W. fit 4W: v L W: m B= + B: mv + 4: m B = 8W 2 v +8W: v m + 6: m v +2: p
  57. ((2 + Y3) 8W): 413- 5. perr. fit
  58. Multiplicetur
  59. explicite 2+Y3
  60. AV3 -5
  61. 3Y3+4, 3
  62. = 10 - 513
  63. 16+8, 3
  64. d per X3
  65. fit X - 10V3+15
  66. 16 + 8r3
  67. et 13) +4. (4r3, - 5)
  68. facit 4V3 - 5 = 8N: D
  69. sit 4vr3, - 50 = 81
  70. fit v = 8W Hic Valo
  71. Hoc abbreviatum
  72. C8+ 43): (r3, -5)
  73. -
  74. 4Y3, -5.
  75. a
  76. Itaque in Valoribus 8, 4,
  77. Abbrevia dop 5. &t fit 15. -for3
  78. satisfactum est Problemati quo exigebatur
  79. inveniendus Valor v. ration aliter per 7.
  80. B + 413,
  81. et per 43
  82. a
  83. = 5V
  84. qui V’alor vocetur
  85. X
  86. 8 + 4r3= a
  87. X
  88. a
  89. Hoc abbreviatum per 33 - 2, vel 8 - 413
  90. 16Y3 +20
  91. vel X - 1613 -20
  92. a
  93. 16.
  94. Posterius abtireviando per 4
  95. Hem X et y. pure rationaliter per a
  96. excepto irrationali 13
  97. 40Y3
  98. Ergo y = 15 vel y
  99. a 8V3
  100. fit 313 +2
  101. Vael a = 2d
  102. quod hirc non estimatur.
  103. facit 75
  104. per 10r3- 15 vel per 16- 8r3
  105. X
  106. Abbreviado p multiplicans (4V3. - 5) fit +r3), (a 3, - 5) +4
  107. Fac. 313, -2 qui Valor s
  108. nom W est a +Z.
  109. 2 + (2: m) 8: m ad Literam C
  110. sit 2-(1: m) = 8W: v
  111. Item per Multiplicatem (413, - 5) abbreviando, prodit (5+213, 413 -5) +1b
  112. Facit 10V3, -n. qui Valor sit
  113. tertia ex e restituta
  114. 4Y3- 5. Abbreviando (
  115. B
  116. 1 6: mB + 2: v.
  117. Restiant AW: v= + N: mv = 8N E v + 8W: vm,
  118. Aufero utrunque
  119. C
  120. Sumo alore 1: m ad Liter. T. fit 2, - 7 + 4r3 = 8W: 1
  121. (16 + 813): (413-5)
  122. 20r3 +83-23 - 10r3
  123. Pro Aequatione
  124. (4 +213) W. + 8i
  125. .
  126. y
  127. Divido totum per W: v2) fit 4. + (1. m) = 8W: v + 8: m
  128. Altrreviando pW. fit ya = 5+213, + 16: (43 -5)
  129. Maltiplicetur, 5+253
  130. explicite 413 -5
  131. mv
  132. fit 4W? V 4 4W: vn +N: m D + BW: mv + AW: m p + 4: m =B w J. v. + 12W. Nm +6W. mB + 1. m + ZWI: v + 1: M
  133. e
  134. Aufero utrinque aequalia ad Litera 4. 8: mv + A: mv=
  135. 1br +8B3ro Aequatione 2.
  136. 1V2- 5
  137. de
  138. 2. Et eximendo quaedam ex V.
  139. Aufero qu2. vm
  140. Restituantur Aequatio 2. d3
  141. fit y = (5+213) N. + 16N
  142. fit X = 413-5
  143. a
  144. qui Valor voc
  145. =13, - =Y
  146. 4013
  147. 64 a
  148. 5
  149. a
  150. Br3

Cite

LBr. 705 · Overbeck, fol. 115r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-861255:0229?run=74