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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 39r

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: 0.73.

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. 38v); this page is its right half.

The machine reads it as

  1. ruae sunt aequationes 2ak + aX -
  2. C apax + d (t +) y, = y, (+ ()) (+ +)X quarum
  3. interset locus prioiis est sectio conica, locus posterioris
  4. quaritur, ut ais pe solvi possit problema horum duorum
  5. locorum intersectione. a quatio posterior digesta dabit:
  6. (+ =) VX (1+) fV + 2 X - daque = 0)
  7. +(+ +). (+ +)aq
  8. Convertatur aequatio in proportionem, utroque ejus, ut initio
  9. expressa est membro, tum per y, tum per a F X,
  10. diviso, fiet:
  11. d(+ +) v.1
  12. f+ f) f (+ +) X
  13. a + ZX
  14. Ut rem numeris probemus, ponamus. a- 1..
  15. fier 1(3 (t )4 (. n
  16. = f. = 2 - 12
  17. es- - f E 2 - 19 2
  18. 104e3 -51-6152
  19. - 14
  20. 34 36.
  21. 2 X = - Z -a
  22. a- 9t Say osae s - (1 et
  23. in (irulo po Z = 2, fiet: a - X - 47-
  24. (11) fot1F) XV cplicetur
  25. X u circulo = g- ta y
  26. fet - 4+ 5a s = cy - ad r 4d
  27. Ergo add = cs = 2 cy ad 4 2Cyqd
  28. Ergo ad- cy, seu a d = cy +39
  29. seu adr
  30. Sa( 4(1) 4 ras, +a
  31. =2 19 16
  32. B - - 12 - - 3.
  33. (1X) 1 (+ +) +
  34. d = =
  35. (+4) f. (3. +) =4 .. .. (+ +)
  36. M
  37. a
  38. murim
  39. +DFC + Fa d
  40. 2 A m- vd
  41. . et
  42. et 7= cy su es posite V de p
  43. d+ βy
  44. erit Z et y = d fict Z= cY - cd ad
  45. + (++) s. C
  46. d +23
  47. vel + Eg + 9+ X - = a
  48. sit Hypertola cuus rectingulu
  49. ACE= F cdq
  50. abscissa FA = EC sit Cd- 3+ - y
  51. Applicata FE = s AC sit AB- + c4 +4, + BCX
  52. Sectio lonica GC, cujus abscissa X = GD, = BC
  53. applicata DC- y est DC, erir
  54. t quaesita, puncto intersectioniss
  55. Hyperbolae, et sectionis Conicae hatae
  56. de terminata,
  57. + (es (+ f da (+ f) 15) syA rayi (t +) olt +)da Substibunu p (3
  58. e
  59. = cdga
  60. +Y- -1 + 4 si +(1 +) cg +91 X - q
  61. (+ +) da X y
  62. (+Fda + y
  63. X =+C d.
  64. (Guadutum de +4 + X, est -
  65. +1 44) Sa 13Y ad a ( ) adays t
  66. mnliplicetur utaque aequa troni pars per L( +) da +yV, D +9+X
  67. fiet = c0
  68. d- 2day) + da
  69. aqu +ya f - aq +74 23 a (+ +) 2da) +7)
  70. 3a (++) adayY + y)
  71. 2t Ctda
  72. =, D + A (+ X) + s a
  73. (1) cqda = cqty + cqda
  74. et Cq C etc = aqu F v etc = S (20). (+ +) das 9 = r9V 4) da
  75. eu altogda da i
  76. er pra tlpsir e
  77. 144 - 95 = 49)
  78. 122 243
  79. yx (( () foda
  80. dit
  81. ++) 1=
  82. fiat a + x
  83. .. . . . . .
  84. 4K4
  85. . X = 3. 1 =4
  86. +fi + (+)t
  87. - 3524 - 35 2
  88. Edle 20
  89. v = 5 - 12. = - 7.
  90. Y = = 7 - 5 - - b - 4 1 = 5
  91. B5 a2 12 +5-
  92. 70 + 120 3 + 41=7
  93. 324 = 24
  94. (s)- 5 - 2
  95. 35-60
  96. + 2= 3
  97. 85 156
  98. (+)(+ +) 4 4
  99. et habebimus: X.
  100. ----.-
  101. B....... -- r - ∞
  102. (+ +) a ( +) +
  103. ABLIEEHEE
  104. BV
  105. 12 5-2+
  106. 5412 7
  107. 1+2 - 7
  108. 3535 9 - 5b + 120 + 95 = 14 5, 24 - 16, 2 49
  109. 62q
  110. 25 235 - 1225, -
  111. c 49 diffi - et 1
  112. 6549 24
  113. 35(X4357 134 136
  114. +5- 3C2, +92 ~4 4533, + 933
  115. f 18 + 30
  116. st
  117. a

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 39r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0077?run=74