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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, 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: 0.71.

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The machine reads it as

  1. nquisitio in aequationes Tangentiales reducibiles
  2. ad ordinarias, per Homoeeptotas
  3. sit equalio generali; Honoeop loto.
  4. (40 = 1007 iox +UA By + 12X, + 121 Fg, + 1X + M XyF 13, XyF 11 4 1329. + 14X9 F 15X er
  5. e
  6. est
  7. iffast it ruraus L 2Ax A 212 Xy dx X XAy +g. rkytyt3 Zyar BXdy 14. dp 3 ijax ex re Xy tqu 2. e qu s GA
  8. rs su
  9. yax
  10. Pay ryax xidus p’ax ydue
  11. sit jam aequatio data d ye cornen n
  12. 1 ydx ydu
  13. du
  14. Ex F 3H Zpu gin 32G 55F ux 3
  15. ∞ Hinc ex aeq. 2. tolletun du tam si pro dus ponatur O pro di puonctus D a fidt
  16. o-nso tm
  17. O- 1180 +1. 2t X +11. 4 x9 +.L. p, B. F 1 Sa 15 733.
  18. +I1. 20 vm. 2 H(2 fu 2 A. B
  19. xo
  20. 34 u 322
  21. in
  22. 1i 22
  23. 2
  24. e
  25. 2733
  26. or 2 ra ta par gniso 2v 2u
  27. qula
  28. 3
  29. 24
  30. srru 2p. huus 2
  31. o 111. 22
  32. 2121 28 t 3t. 31
  33. 13
  34. 1ut. 22. M. 2
  35. 3
  36. 4
  37. yd
  38. 32t
  39. +SEC Xydy + 23X dx. + 35 X dus etc. Dertendo hanc aqua- fec. Yay 4t 3 tau vy + 2u + G
  40. Analoga
  41. pus ax vamerit in fictiti prasime, sut 2A Nepupe iissepa est
  42. tionem
  43. 33
  44. yi
  45. 23
  46. 227 24 X 25y
  47. et ductur, mqua sud d romoentota restituit homoeoptosius.
  48. sequitut s
  49. pay
  50. B1 Xy 34
  51. 23xyh 2tZ
  52. in valore tali esse homoeoptotas et si valor ex aquation
  53. 34
  54. uiu . e.
  55. homoeopeotae; lex tamen certa est permutationis, quae substituto
  56. potandum non posser. i
  57. 121. 22 121 2d e1. 23 ca. 1
  58. Sit jam aequatio ata differentialis generalis semplex homoeoptota O= H ay hau vag
  59. de
  60. s
  61. at Ergo aliq aequalio
  62. secundum do et dx e etiam generalis simplex homoeoptota, ea per omnia similis erit
  63. ipsi 3 nisi quod pro 20 vel 21, et c. substituemus 60 vel 61, etc et per 31, 32, CM substituemus 71, 72 etc.
  64. xt FSsrara gelys a rys tan treitus abuegerern in dy it stitus e r aboar nta 16, 2 X ay
  65. hay
  66. xuac iaque ydx
  67. abqua aequatione 5 potent intellgi decude aequatio 2. Hinefic aty (86 bi Keayrb sun iabe eup v +6ax et
  68. 51 X0
  69. aque srbemus o2 b
  70. uide aquando valores 6 et 4, instolutul muliplitatione per crucem fist
  71. ruru
  72. 1.se + 1X + 10.61 X9 + 2012 X + 209 atxy 4 10.73X, + 20062t ∞9 + 2673IXy + 2034X
  73. BIXy 74e
  74. 0b2
  75. B3
  76. ama es
  77. Defficientibus seu n
  78. o o+ vibu 2o LXy + 2061, i t 2oCu. 34. + 10.63 5 t, o. bu Xitro. 631 Xy, 1 ~ 64 5, +206) 1 410 6H Xy +2065 L, et
  79. 73
  80. tat
  81. o itiraoli comsina
  82. 20n
  83. 2371
  84. 2160 . 21 61 21. 7 4. ba
  85. 31. 60 L31. 7 3
  86. Ager. Boet 4eii1u r
  87. 10ge
  88. +2b
  89. 400 80) quo 810- 7 + 310310
  90. 314. 80
  91. 3IB1
  92. 191. 908
  93. Ix hoc asequatione 6 mitabile
  94. 2162
  95. 31. 7
  96. +40826)
  97. L2uiio
  98. + 2000
  99. 40obio
  100. 32. 40
  101. 74
  102. 731 X
  103. 732 fy 2H Y9
  104. institata jam multiplicatione per crucem
  105. ib prodibit aequontio:
  106. +42 72)
  107. 21911
  108. + 3072
  109. qV. 7101
  110. +4030) (+48 G2
  111. +26120
  112. 13
  113. 20. 10 +X
  114. +2162
  115. +3b121
  116. 1411. 81
  117. + 2sV
  118. 1320
  119. 12
  120. +12. 61
  121. +321. 71
  122. 330. 6 + grr. 800
  123. +Xy +411. no
  124. XV 2C.8I
  125. est X et y pari quidem
  126. in hac aequatione 6 ducta ex duabus in =. 610 quabus X et y simul pEF - a. 6d
  127. ntur patet. 321. 800 X et y quidem pari jure 320. 81
  128. tantitu
  129. tractari itaque opqus 20. o
  130. uti sed posito
  131. esse transpositione
  132. seu duobus laferibus ut eodem modo exprimantur. verum quod memorabi 32 eoo lissimum est aequatio
  133. equationem fieri nihilo aequalem non eodem modo ex
  134. ista hoc modo nata dividi potest per x-y. Et sic mutatur it homoeoplotam, in qua oimnib
  135. positis intulo aequalibus x et y eodem modo tractam. Notantum etiam in aequatione b evanescere combinatus
  136. ones in quibus X et y pari jure atuntur, seu quae sunt potentiae ab xy. divisione facta res sic stabit
  137. C ry- etc 13 4400.44
  138. a
  139. 4003
  140. 27 Xy Xy
  141. VdxtBy
  142. d
  143. ist
  144. B
  145. 440.731
  146. 12
  147. 3
  148. ain
  149. 23161
  150. F231. 100
  151. 400. 83
  152. 62
  153. 400.740
  154. 4210.730
  155. +220720
  156. +230710
  157. +240. 900 (.Y
  158. 400640
  159. 10. 630
  160. Xy -32o.b2
  161. 330.610
  162. 390. 8a
  163. jure utuntur, et
  164. + recter
  165. x221.90( - 210610
  166. que62
  167. ne
  168. 63
  169. (6)
  170. t
  171. esr
  172. a 22b
  173. + ex = 0

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 110r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0219?run=74