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Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 172r

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: 0.67.

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The machine reads it as

  1. Ec.
  2. pprotentis
  3. perg
  4. surit
  5. iscedasaparata
  6. pisi dier
  7. 18 splemg
  8. Hc Bes
  9. mit zusanm grae
  10. Methodus Tangentium dinversa pentata, simplicissime
  11. eculi hujusclntrli
  12. s
  13. per assumlam s quationem generalem. r dy: ax sumendo
  14. u
  15. ete et procendo ad l
  16. Hic certuapparet exitu, vel absilula
  17. cum resfieri pe, vel pos suppositis quadratum. Sed galont admidu prolixa
  18. sit vB = du: do Et sit aegnalio proposita D 2 10 + 1 Y 4 129 + 135 2, 4) ere
  19. 20+ ∞ 11y + 2t 15 + 23y 1247
  20. ubi tet 20 2t edc exprimuntur ratio 20L 2ise b etclum d uo Eidys ~y dm M Vag rgyaZ p. 13. Gaye fHCK
  21. upliter a ceju differentialis cunt aq seu per compendium ve ( O: Y
  22. integre per X
  23. E
  24. (et d= 5d0 - OdD: D
  25. Quam explicando, et pro du ponendo QV, et dx tanquam pro constante sumtam dissimulando, pe
  26. 1
  27. 5) 202y ete in V. d10+ Y du ry dnesc = 5. 11V42 2Y ∞ + 3, 13. 5V et0 = 10 + nyeue in y d2ory ert 1y 2104 2y i
  28. du
  29. 1 20+ 2y etc.
  30. Ex Assumatur jam hV= Ler 30+ y C325 193y etc quae eqtatae semperen. quo ponendo
  31. E, sit 30 31 9, 33. dari ser x, quuae fom aequatio rationaliter et integre
  32. A sumatur jam. V= 20421G +. 329 433 ( etc =
  33. et habebitur dus
  34. 40+ 41y +427 143q el
  35. 8+6. 64 eadem modo ut in 5y5, tantum pero 10, 11, etc. 20, 21 ex sl
  36. seu ere
  37. sceribendo 30, 31 iic 40,81
  38. et duos valores . 21 et 5 vel 4 0quanto fit D de 049 = 846 D - 618.)
  39. sed res ad hic distinctius explicari pt sit Are nam dO omponitur ex duabus partibus
  40. lu
  41. a +3V seu a1 = a6 + ((X et l 3 d9. + d5V et 465 e d5 V
  42. et 162 3B quos valores substituendo, in aeq. 8. fiet:
  43. 1280 + D94 d1V - O∞4 ah - 0g 43 v = 9. 5 + dv BMSe -B,B
  44. fit , +2D a 5 - 59Dde - D92d + 099 d D,
  45. v =. - 830d5 + 630tG + 384+0- 094 +3
  46. 1 (15
  47. quae aequatio 15 debet esse, ide
  48. ed
  49. et
  50. stasse
  51. rem Bevius assequi licet sine du, les modo:
  52. assemitas
  53. d: Dpoust et v= 6: 4 Cerquo 9 = 36 et Cd1 3dC = ∞46 + 6 +3
  54. jam d0= do+ 0 et similiter in caeseris nitaque explicande aequationem e se
  55. os+ Cdde + 8+- D -6 3 e (2t 0 ergo deiz a quldo
  56. - 0 d - Q+o = D 45 +8+
  57. cede
  58. Ergo demque fiet + OD 0 + 38+3 - DD (5- 59. (3 = 0D 5 +06 1 (B- 3b de
  59. adquae aequatio suam suum esiamen secum fert nempe unum latus fat
  60. ilx alio mulando a et O et b in D et e etv
  61. mutando. D, 5 D
  62. munando
  63. t t ns
  64. et At
  65. i rcanot
  66. ponantur GeD) data 6 et
  67. + sorturitio nesi pube e
  68. vasito Nota
  69. Et Quelqu hoc es
  70. otan quin sim
  71. E Est autem 3 = 10 + _X + 12X + B X 1t 14 X en dC = G dio 5 + diy + d. siu
  72. 8
  73. 5
  74. stantem - 10r11y + 2y+ 13 2 4y ete fiet dO = dio Y + ai 1 + Si. y ecc. B dC = 1II. y +2. 121) f3. 13y a y etc
  75. D - 20+y +2 199 1245 eu 3 = dro y + du y + de2 y en L7 = 1. 21y + 2 127 43. 2 14245 erc
  76. 5 = 30+319+328+ 3337325 eu (6 = d. 3y+ d3.y du y en d5 =1 n9 + 2 319 + 3. 45 4 3r y et c
  77. conlo 9 = 40+ 4yt4 g2) +445 et S0 = daop Lda y + dorY et d - 1 2sqg ere
  78. Hqus. 2S Hinc jam calculum actu ipso qua hicet perficiamus.
  79. et 40 410
  80. SH cooo
  81. (20. 40. d10
  82. 20. 20. 30
  83. 1 20.30 420
  84. 10.1. 1,3F
  85. 12o. 1O. 190
  86. ab. 1b d+o
  87. t
  88. 20+
  89. Ex hoc colculo initio pater semper fieri
  90. 2o c10. dar + 20. 12. d 40 + 22. 10. dao omnes possibiles cobinatio nepisuo cer vit factat
  91. Nempa iquatio factu
  92. G20, 11. d4c. + 29. 10. da1 + 21. 11. 440 nihilo constat. ex duubus par
  93. A20. 90. d12 + 20. 42. deo + 2. 40 deo i
  94. 1 tao 41 du 421. 40. d 1 + 21. 41. de0 deprarum iaciis. fero termino
  95. 22020d32 -20, 42. d30- 2820 d30 pro penantepet
  96. 20.31. 38 - 21, 20. d 31 - 71. 2), 47 continat Cil, 10 vit 10
  97. = 20- 30. dn - 20 32. d. V - 22. 30. d30
  98. =30 31. 12. -2]. 30 d21 - 21. 31 42 Codh. et aliom
  99. +10. 20. 33 410, 22. 13b +12 8 3
  100. 10. 31 X
  101. +12. 2043C +11. 4143
  102. e
  103. a
  104. C
  105. 140 dio
  106. nantem potentaae extecniae
  107. rc
  108. istum
  109. ues
  110. Eollendo
  111. pliibet ta
  112. sini
  113. 3
  114. iiiusuca
  115. vel et
  116. cononten
  117. in affectum namero ve es dgtineus let
  118. ho ete 3. tite. ig
  119. Acoullari arem, quud qui to d ererti at
  120. i delpo
  121. u
  122. 1
  123. (410. 301. 21
  124. 1010.191
  125. 10. go. 1. 11
  126. ae
  127. c
  128. F

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 1, fol. 172r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068194:0343?run=74