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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 187v

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: 0.76.

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. 188r); this page is its left half.

The machine reads it as

  1. (Xx + lmax + lnaa aequanda Eto Ugy. sit X-
  2. 20271214a y
  3. 34 20. 132.30) 42 = 40. 32: 30. fint X = 2030 25130 + 203rea ∞ Et
  4. 32= 31: 4
  5. AlNX = II, 20. 20Z + 2. 20. 21473 + 2. 20. 220a Z7
  6. aa
  7. AlmX = lm, 20. 30.. 4 1. 20. 31
  8. 1 21. 30
  9. +ln =lu, 30. 30 +2. 30.31
  10. illyy = l, -40. 70 - 2. 4v. 4)
  11. cta
  12. 30. 30(2+ 30. 5 az + 30. 3 raa
  13. +1. 21. 21 a4 2 + 2. 21. 22 aZ + 22.22a
  14. +1. 20.32
  15. 1. 21. 31
  16. 1. 22.30
  17. 42. 30.32
  18. 4 1. 31. 31
  19. - 2. 4042
  20. = 1. 41. 41
  21. f1. 21. 32
  22. l. 22.31
  23. + 2. 31. 32
  24. -2. 41, 42
  25. + 22. 32
  26. +32.32
  27. =g2. 42
  28. sumq 40.40 ll = (20. 20U) = 20. 3olm + 30. 30 ln sit = (20. 20l) + 2. 20. 5oll + 50. 5oll. Siet
  29. Extermino
  30. 20 = 5-B 50.50l - 30. 303: 30 2.50 44t +40 = 20 +50
  31. EB G +e Ergo 4 40 = (50. 5∞ = 30. 30n + 30. 50m - (2,50l, :, 30m - 2. 50l
  32. sit 4 242. gll = 22. 22ll + 32. 32lm + 32. 32 ln. ubi 22. et 42 ponendo valores,
  33. ermino imqe
  34. fit 4 40. 40. 32: 30.30)= 20. 20 (32. 32: G0. 30) l(+ 20. 3232: 30) Im + 32. 3El, et omnibus
  35. divisis per. 32, et multiplicatis per 38, fit 40. g0ll = 20. 20l + 20. 3olm + 30. 30 ln, ut ante
  36. Ex termino secundo, 4D. 41d = 2. 20. 214, + 20. 31 M + 21. 30M + 2. 30. 311. compendii
  37. causa sit 2 2∞ Y 2. 20l + 30m = 6 270 et 20m + 2. 3on = , 80l, fietque
  38. 24 40. 41 = 70. 21 + 80. 31 seu 4 41 = 70. 21+80.31,:40. Ete
  39. hEx termino ultimo idem fit quod ex secundo, nam prodit.
  40. 2. 41. 40 (32: 30) I = 20. 52.5 2, 21. 20(32: 39(+ 21. 3 2lm + 20 (32: 39) 31, + 2. 31. 32ln
  41. qvisaque aequbione per 32 et multiplicata per 30. fit 2. 40. 41= 2. 20. 21 + 21 3oM + 20, 31m + Z. 30. 31 R utante
  42. prodit ergo nihil aliud quam 41 = 70. 21 +80. 31, 40. ex dambus termino secundo et penultimo.
  43. ut valor ipsius 40 ex a primo et ultimo superest
  44. 32. 3 = 31: 43, exis.
  45. suphest Terminus medius destimendis ubi ft pro 3rBonendo 31: 4. 30, et 22ququ et 12, et 4) licando
  46. et (70. 2it 2. 70. 80. 21 31 493. 31 + 1 _ (3t. 13B ( = 2. 20. 20 (V. 30 u+ 2iUt2o f1. 4. 30)m +21314 20 3o (l 3 ft 2. 3o( l. 2o (+ 1 1a
  47. 2, 2020(32. 30)D rs. LI 2,0. 80 ∞1. 4t. H 90 31 4040
  48. N fictque = 4. 30. 76. 21U = 2.4. 30,70.80. 21. 31l = 4. 38. 80.312I1 =0
  49. P4. 20. 40 21H + 1. 4. 38. 148. 21. 31lm = 4. 40. 3s I1
  50. aenulus 20 30 40 50 31 32 22 42
  51. quot
  52. 5
  53. 63
  54. 18 27 18
  55. 32: 30 4 2. 20.40 31 I
  56. +Z. 20. 30, 403 lm
  57. L 2013040
  58. 46 30. 40. 3e ln
  59. A. . 30. 40. 3 ta
  60. 32-31: 4 22 = 20.32:30
  61. 22 =20,317430
  62. 24.18. 4. 9. Ergo 22 ∞18
  63. 42= 40. 31 : 4. 5
  64. qy
  65. Quia omnis res reducta ad tus aequationes praestari poterit in numeris
  66. 63 49
  67. pro 20, 3, 40,50, ponendo numeras et pro 31 ponendo tnumerum divisibilem per 6,
  68. sit gn. Ita 31: 9. 30 dabil 66.7. 7.: 4.3 = 399 = 147 pro 32 et 21 30.32= 2 13.197
  69. 2. f3l. 32 = 31 4. 38. 32 = 31. E 32 = 31. 4. 3 31 = 42, 31 = 6. 7. 6.7 = 36 99 Jam
  70. 36-49 4. 3= 3.49 Ergo 31= 2) sed d hoc displiet quia jam habemu, ideo potius fint
  71. +31 = 68, 18 et 31 =95. 4 et 31. 4. 3 = 99. = 99 9. 9. 4: 4. 3 = 9. 3 =27= 32
  72. e
  73. Ergo pro 31 ponamus 18, et pro 32 ponamus 27, et fiet 24. 3. 27 = 2. 9 = 18 132 =9 2.417
  74. pro 40. ponatur 70, ut fiat 40 = 20+70. potro quia praeterea video ipsas l,
  75. m n. non sufficere: ideo sic proesdamus _ a hil + 12m +
  76. 8
  77. 574
  78. ideo pro Ugus scrbamus tagu, sitque p talis, ut fiatioh. l + 12 m + 13n + p =0
  79. eto 2Il + 22m F 23n + 24 p =0 et 31 l + 32m + 33n + =p = 0.
  80. 191
  81. arsu
  82. 252
  83. e
  84. s,
  85. vd
  86. 12. 23, 31 4 11. 23. 32 = 11, 22.33
  87. iC. a 1 412. 1 1. 20. 323:3 413,. 221 = 13, 21 1. 412. 21
  88. (162
  89. ( 228. 22E p
  90. i
  91. 21. 2
  92. i
  93. st
  94. a
  95. is
  96. fit canone
  97. 1t
  98. 2
  99. 6
  100. 38
  101. 23. 104567
  102. Siq
  103. 286si3
  104. 2qe
  105. 33486
  106. 17
  107. 16
  108. D
  109. a
  110. ontcae
  111. 3079+31a 2+ 3aa a 302Z +31a 2+ paa 2.730. 32= 31
  112. P. V( + 30. 41a + 4. 3 2. 90
  113. 30. 2 + 30. 3la Z + 30. 3a
  114. C

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 187v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0374?run=74