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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 24v

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. 25r); this page is its left half.

The machine reads it as

  1. Aequando duos valores ipsius 30, et ordinando secundum 4O et 41, fiet
  2. Compendio 720. 41. 41 + 211. 41. 40 + 202. 40 40,- 0 fet 2C
  3. 101. 40. DC
  4. 210. 41. 00
  5. ) = 4 qu (. . . . . .) - 302. 320. 4040
  6. 200. 00. 00
  7. O1. 220. 40
  8. 200. 820 - 00. 00
  9. et (ur 320. 41 = Y 311. 311. 40.40 + 210. 319. 00. 80, + 4. 31F. 310. 40. 1 - 4. 302. 310. 40. 40 - et. 301 920 4o
  10. =g.302. 32040. 40) . 311.40
  11. 00 1: 2
  12. 220 = 144, (11300 + 123. 20) 8 3H1= =. 2. 123. 144. 21 (113. 00- f123. 20) 310 = = 123. 144. 21 (113, 10+1 2 3. 20)
  13. 1+311: 40
  14. 220. 4 =
  15. 202 = 123. 123144, 21. 21 301 = 123. 123. 114. 21. 21
  16. ergo ubi ad explicationem aequationis venerimus
  17. 300. 60 == 123. 123, 21. 21 (111. 00 = 112. 20) - 123. 144. 21. 21 (17 00 +123. 20)
  18. apparebet dividi omnia posse per 113.004 123.20,
  19. et siet 3. 144. (113. 00 + 123. 20) 41 = A4. 1232 144. 214 123214424200 +4. 123. 144. 21. 40. 00.
  20. (ACCSt. qu. +. 144 (123. 2121 (123. 141.00 +123. 113. 20= 144. 11300 = 144. 123. 20)001) 1.3. 111. 4. 10
  21. CC3. 40 que 12. 14. 4 00 - 4. 15. 141. 14. 21. 40. 00
  22. Pn 2. 144 (13. 10. + 123. 20) 4 = x o v)-
  23. Et habetur 22 =
  24. copendi enuntiata
  25. 123. 114t (2.∞ +00) + V (4 1s etc
  26. ubi evenescit 40 in irrationali si fiat (44- 114 =0
  27. et evanescet 20 in irration ali si fiat 14 -12 = 0
  28. Eodem Modo ex aq. 3. compendio enuotiata, pro; 123, 144, etc. porendo 223, 249.
  29. 2. 144. (113.00+123. 20)
  30. 223,. 244 (2. 40 +00) + V(4
  31. . 223 etc .. .. . .)
  32. 2. 244 (213.00 + 223. 20)
  33. ubi rursus ut evanescat 40 in irrationalifiet 244-314 20
  34. vel ut evanescat 20 in irrationali siet 244 -212 =0
  35. prout scilicet postremo volumus quarere 40, vel 20
  36. nex valorum ipsius comparationem, ne opus
  37. sit irrationalibus sublatis id quod quaeritur, v. g. 40 (vel 26)
  38. rursus altolli ad quadratum.
  39. vocutum v
  40. praestitisset fortasse ad calculi uniformitatem non ipsas Z 18, C) explicare per D, sed omnes
  41. , O, Q, D explicare per V, ubi fiet 3 = 10V+ uh, etsi in praesenti Casu, fieri posset 10 = 1 et 11= 0
  42. ita calculus erit paulo prolixior quam opus sit, sed major erit regularitas. Si suppleantur
  43. mea quiae
  44. desunt 00, 0d 80,
  45. 3d 4 11208 + 12390 = 0
  46. 114D4 1346
  47. _) DB = 111 . eBP + 2. M. 10. 1 LV + 101. 11. 11 lih
  48. 0 = D) +
  49. 122. 2n. 203V + Z. 122. 30. 21 hH + 122.21. D1 1
  50. + 133. 31
  51. 133,30.30. + 2. 133-3031
  52. 141. 40. 40 ) 2.99. 70, 41
  53. 113. 10-20 7 152. 1021
  54. 113 Jars q 11.20
  55. 3 D. X0t ,(er 10
  56. = ∞ v+ h
  57. . 20v + un
  58. (2.344. 4142 + 319. 42. 44)G + (2. 344. 4. 43 + 314. 43. 44)0
  59. 31I. 44. 44 + 344. 41. 41 + 314. 41. 41
  60. cu DB + am P Fhar
  61. sit e + Y( e fh
  62. sed hoc juste pro lixioras
  63. res detenurhatur expagm.
  64. + 9900) + 2 f99 =
  65. 2a. g2. N. 98 +344. γ1300 + (2314. 4. +525. 11. 4) 04 seu ex a4. 7 t 8 fiet t ( b. h (b - a) (H +hib. 1), g9 (g9. + h (b.c)) = h (b - c) (99 + b - c) h) f. f (5f ilb. - a) h)
  66. Si1. 44. 44+ et
  67. (∞8 + nD + hit tiat LLN + Chm) FThan.
  68. m = f4 +90 hhn = p4+
  69. velsi 1. + 16 llpr _ - alrsf. alpgg = (Hggt allrr = 45 glv. seu Alpr + Fgr = Gr Fgyp xlrr
  70. Hinc haum A = lus
  71. Vedd extrahibile, sead
  72. intentionem notum, unsi fiat f Ale L(2, H- al p, 199- alq) = 2f9- 4lX cut alo, gu - plr- (g fiet 311. 44
  73. V =-mh H (= Brum - CH) sed
  74. jam si sit Gy + CD
  75. sequenti
  76. = 30v+311
  77. = 40M
  78. G2
  79. 06+ r08
  80. quod non potest
  81. fet qn taic summntur novissimo tensum
  82. non ut ante
  83. +. 1. . 41..
  84. 1121 11. 21
  85. 148 - 14471, 00 = 17 04
  86. 4. 102. 112. 10. 20. 21. 2
  87. 4. 120. (2
  88. seu tiet. 2L 2((2v. 1 2, 120. 104
  89. Deu Yl2. 120. 702)
  90. 4. 102. 102. 20.
  91. du 122 1b. 2
  92. torter
  93. R(4) 112. 112. 10. 11. 2021
  94. A. 120. 102. H. 11, 20.20
  95. 4. 20n2. 10 11. l1. 20
  96. (4. 120. 112 10. 10. 1121
  97. 4. 12. 102 11. 20. 20. 21
  98. 4. 102 112, 10. 20. 4,213
  99. qu (N. 27 811. 20) = 112. 12- 11. 11. 20. 20 + 10. 10. 21. 21 -2. 112. 112. 10. 11. 20. 2
  100. vel 10. 21 - 1(. 20 = 0 Sed si hoc verum Z et V
  101. si te pur asus set
  102. plicatio stpit
  103. in ratione constante, contra hypostesin
  104. 4. 150117
  105. (A uIoZ. 11
  106. 4. 120. 120. 11. II. 10. 10
  107. 4 . 102. 102. 21. 21. 20. 28
  108. I. 12. 112C. I1. H. 20. 2
  109. 11 112. 112. FB FD. 2. 2
  110. 2. 112. 112. 10.1. 20. 21
  111. 8. 120. 102. 10. 11. 202]
  112. 4. 120. 112. 10. I1. H. 20
  113. 8. Iv. 11. 21

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 24v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0048?run=74