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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 110r

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: 0.82.

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. 111v); this page is its right half.

The machine reads it as

  1. Sit aequalio data dy: dx = r0 +n9+ ny etc et
  2. assumatur quaesita: dus: dx =- 30 +3 y: et fiet, aequando et per craccem nultiplcando
  3. dro + du y duy d13.5 dx
  4. +10 +1g+ 12g = 13 y + 14y 415y + 1b 7 etc cujus isse () dgo. d3
  5. +30 +31)
  6. argey t nsog eabgo ete Untiis o=
  7. C
  8. +203tYt 1 nsty +23.31V 125 3t y etc
  9. erit
  10. +.1. y + 3. 3y ragy du
  11. Et pantet Gules. in aequ. 4 pro dus. ax substituendo valorem ex aequ. 1. fiet ri. 5.) 10, 1, 12 etc datae per X
  12. +d10 + du y + d12y + d13 9+ d14 9+ d1s y + di6 y
  13. +d307 d31
  14. F10. R. 11 102 12 10. 3.B
  15. 11. 1. 1 11. 2. 12,
  16. 10. 4.4 10515 10.6.1b 10. 7. 17.
  17. 1B. 3. B 114.14 11. 5.15 H. 6. 16
  18. eederi
  19. 12. 1. H 12. 2. 12 1P. 3. B3
  20. 10. 31 + 1. 31 12. 34
  21. (6) (4. 10
  22. O=
  23. 30
  24. aequ.
  25. no
  26. 13. 1. 11 1,. 2. 12 B.3. 13 1. 4. 14.
  27. 13. 31
  28. 14. 1.1I 14 2. 12 14. 3. 13
  29. 14. 31
  30. 15. 1. 11 tG. 2.12
  31. 16. l. 1
  32. 1.31 16. 31
  33. si L 30, 31 quaesitae per X
  34. si indatis non assurgatur ultra 11
  35. n fit suffecerit
  36. aequ. 2 mu laplicari per 40
  37. et habemus duas aegu.
  38. dio + d30 + l. 10. 11 + 1031 = 10.40 +30. 40
  39. et di1 + d31 + 1. 11. 11 + 11.31 ~1140+ 31.40
  40. sie 408
  41. dior d30 + 1. 10.11, 11Y3IC
  42. aequ. q
  43. du + d31 + L. II I F 113I, 10+30
  44. it y + 12y 41313 + 1G L SV L. b in 4 + 41y etc. Ex 093.)
  45. a
  46. 3y
  47. d
  48. si in datis non assurgatur ultra 12, potest
  49. quo tunc fietidio Ld30 F 1. 10, 114 103, = d 1r dy1 + 2. 10. 12 + 1. M I + 11. 31yran etrE S1) 12. M. sY)
  50. lu
  51. et exag. 3 fit 10 ruy r 129 quae multiplicanda per formulam nuius gradus, seu per 40+ a e, ut productum
  52. possit conferri cum org. _ 10
  53. Et ila porro in altioribus semperque eit litera aliqua supernumeraria
  54. 30 31.
  55. quando ad possibile est
  56. Dro Tangentialibus resolvendis in lineis ordinariis hac mihi videtur
  57. extia ethodus : sit e dy: di 10 + ny + 129 etc: 20+ ugrus et
  58. etiam haec pt aduiberi,
  59. Rlian he Asumatur = 30 + 31e +32 e etc,: 40+ 11 e+ 42e ete el pro e
  60. incognita
  61. substituatur in aeq. _ valor ejus ex datis aeq sis sit per compendium 10+1y + 127 etc = m
  62. et 20+21 9+22y etc _ firi e m. n et ex aeg. 3 fiet utique
  63. Co 90 edo
  64. (6) 825) 30 n = 31 ne m. + 32 n m ete usque ad SCBH. I
  65. _H 40p +41n m + 42 n m etc usque ad. 30 p m
  66. co
  67. M
  68. ubi est y sine e se
  69. E Porro dm= A10 + du. y + dir y ete B + 2. 12 98 + 3. 13ye ete
  70. et du =deo + duiy +d21.y etc + 1.21 C +2 2ye +3. 23yC ete
  71. ed02
  72. ris ita temperanda
  73. 1
  74. assurgat in halaeq
  75. quam erate
  76. co-
  77. et ex aq. 6( disfeantundo fit C = 40n + etc 4 30n dn + n d30 t stn dM + n am
  78. sit per compend GC ex aeq. 6 y2) O: D fiet de D AO- OdD, : D. ubi explicando
  79. per 6, 7, 8, 9. et tollendo e per 5 seu 1. habetur rursus y sine c. quae duae aequationes
  80. debent coincinere nempe W e 11 et 6
  81. Conferamus pranc methodum cum mea ordianter iltee aequa
  82. ut
  83. ante e= m: n ubi m et n, dantur per y onfervenientibus numeris quer dantur
  84. sit s 9 ubi q eodem modo per x datur. fit o at a da + dGC dg+ dg. C
  85. unde ex 1 et 3 fit n d4 + m dqu0 sit g 30 + 31y B2y + 33y et c =0. et fiet
  86. dg = d3o + d31. y + d32. 9 + d93. y etc. et +q = 31b, + 32. 2y+ 3335+ 39 4y etc
  87. Et ex 4 per (B6 et + Cit n denique sit mF 10 + 1y + 129 +13y etc. et h= retuy + y et
  88. Ergo 4 explicando fit 20. a30 + 2. d30 y(52r. d30 y + 23. d30y3+ 24430y + 25d30y + 26130y ek
  89. ubi possumus vel coparare
  90. g. 11 et 12.
  91. (11)
  92. 20 d31 y + 2 d31 y22 d31 yr23d31 y +24d31 95 + 25 d3l y
  93. 20432 21 431 22 d3 23432
  94. et
  95. te
  96. 24 d32
  97. etc
  98. int ope aeque sobit O = 7 10. 31. + 11 1. 31. y + (14F3t y (+ 13, L y + 14131 y +15. 131y5 + 161.31
  99. tollendo y secluere
  100. relinua habebimus aeq.
  101. op erit copair
  102. (12)
  103. dentjica.
  104. 10232 y + 11232y +12. 2. 32y 4 132.32y 414.232 y + 19 232 y
  105. 1. 9. 10, et 4q5 tollamus y se
  106. liabitis oe divi et, et
  107. 8= 50+ 51r ) et in abeu, altis asiendat quam gli. s
  108. 30
  109. ek
  110. et
  111. eu
  112. etc
  113. et
  114. etc
  115. et Ia ea
  116. +31Y + 32 y 4 33. 9t + 34y +359 4+ 36 y
  117. ex

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 110r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0217?run=74