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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 119v

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: 0.77.

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The machine reads it as

  1. La trax 1-
  2. Datae curvae aliam parallelam nvenire. Honfante Hoc fier si
  3. X
  4. d. quaerenda:
  5. P, aZ
  6. vi
  7. v + du v
  8. dqre vds+
  9. dir
  10. f
  11. g Sipta
  12. dugri
  13. 19
  14. prpendi culari DC addamus CE constantem nam
  15. datur CE, datur et ratio CF ad FE (eadem quae ratio
  16. PD ad DC.) ergo datur triangulum rectangulum CFE
  17. ergo recta AB, sid est AD + FC.) abscissa, et
  18. recta BE, (id est DC(+) FE) ordinata
  19. Experiamur saltem in parabola.
  20. (E F) latus rectum ejus 2a Ergo Dera ADF X.
  21. DCH Trax. FE, Yrax. Ergo FEF FC.
  22. FC + FC
  23. b’ar
  24. b ab, utxa
  25. aetrax1
  26. FEp
  27. ag. sim raro Y u qe
  28. buar
  29. v. fici
  30. r
  31. atixa
  32. a. CErib
  33. 1 _
  34. Lae + 2aX
  35. ergo BFB Vrax + b sEra C
  36. 2 + x - 1ZX.. Eigo X
  37. atixa
  38. ab Y2xa bb Frxa. Ergo BF Tax p
  39. a Z- X
  40. Tax
  41. =ra co srax
  42. rax
  43. atrax
  44. vuar
  45. aetrax
  46. dque auferatur fiet curvae
  47. Elementum a- 4a 1 a 8.
  48. vae. vi vta-
  49. quod si esset quadrabile omnes parlere
  50. Vineae quae parabolae sunt parulletae
  51. endenai possentus mensurari possent
  52. V. Ergo ba av + 2XV2
  53. et ba = av X
  54. nusus trax +) traxst pco. se
  55. Unde foi deque ae+ B trav cors
  56. 1 B
  57. ZX
  58. p. 1ZX + x + b + 27b + 2xbV
  59. co. Ergo re Brar
  60. ato-atrax
  61. lax
  62. a +raxI
  63. ae
  64. Saetrax HZ
  65. sae trax
  66. X II tax
  67. Z-X p)
  68. a +rax 2aX
  69. Va +2ax
  70. se
  71. a
  72. Ergo 6 2- x + b
  73. Ergo ba +b
  74. b2aV
  75. a trax
  76. braV
  77. aa
  78. p
  79. u
  80. trax
  81. F b2. Ergo FCF. ba
  82. et AB, x+ FCH X + ba
  83. FEFI
  84. ba
  85. pea- li 2 e rax
  86. p2
  87. C
  88. Sae +2ax Ergo
  89. seu si +5 +. x
  90. co
  91. actorax
  92. a Y a H raxp ba a
  93. Ego fier aequatio: a + v, a +v, b + v, b - v p cov, cov. Ergo Egobpo
  94. et erit quantitis V addenda ipsi Prax hobebitur seu ipsi eoa habebiturue Z.
  95. v
  96. nimirum y+ v+ coa. sn Z ∞+ asato, at b b. abi posto
  97. cat
  98. Idem calculus institui potuisset pro curvis omnibus, hoc modo:
  99. pc
  100. DP
  101. ADAX. DCHy. CEpib.
  102. ABrI Z BE Fjco. BDrd FEB f. CB B ∞. Ergo F 1
  103. Fp b
  104. Ergo des bc. Jam ZI =x = d. Ergo ZF, =x = bc. nisus co+Py (=) (4)f
  105. by
  106. et co Sp - yt. Ergo pZ 5 = xp _ = b sp. go et pcop (=) pus Zby
  107. ex natura curvae
  108. ces
  109. d
  110. ubi explicatis p et y per X. ac sublato denique X resbit per unau aequationem restabit
  111. in altera tantum et co. Sed hinc intelligitur non semper per ordinatas daturam curvarum
  112. i commodet explicari, sunt euim quae melius per perpendiculares declarantur.
  113. +
  114. aerrax Y. Zb a trax f 2nba qrabx
  115. est
  116. e
  117. rax
  118. sabiprosito apib
  119. fiet:
  120. 21I∞+ =Ya-v
  121. cujus differentia. . aequalio ad
  122. langentor dG erit:
  123. 2ax
  124. quae est parallela parabolae
  125. posita du constante quadralo ipsius
  126. sa
  127. 1)- E0a
  128. aco = 2a co vrax + 2ax
  129. sit ba
  130. Mhevius

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 119v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0236?run=74