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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 71r

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: 0.76.

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. 72v); this page is its right half.

The machine reads it as

  1. 28 Fel. 1691
  2. in Hyperbola primoria est D y = aa: x e dy = - aadx: XX et dx + aus = dx a + X B. X
  3. sid x - +bB et X a b =+ h3 + 46b a + 6hb n + 4 hb 3 = b 2
  4. +qu+6dce 4+ a
  5. = quadrato ab stgatma =se f + 2fgn + 2f m H
  6. fiet. S: Sk ta e et m - b + a
  7. et
  8. + gy n + 2gmN + n
  9. g- 4 2h +2aeC,: (h4 at - hbt ace,: t
  10. 2th +aC (b+ + 4h+ 8ha ce + 4ace: D a 6kb 6a c
  11. quibus propribus aequationibus duabus solatis utcunque, problema est etiam in irrationalibus
  12. habetur quaesitum, adsunt autem literae tres in effectu in determinatae
  13. faciendo Dh2+ la Ce = o-gn fiet C = - h: 2C et b = (a ch: ac =) h: àc
  14. 40
  15. ex 44
  16. it.
  17. 16 12 20
  18. ax
  19. 224
  20. 40 1121224
  21. e +364h: ac
  22. +ah PK + h a K + = gh + 9a + 18a 23
  23. x= h + bn et X+ = h + 4h Bn + 6FbAN + 4h bN + Pn (XX = vaet axdx- ava
  24. ce t en
  25. 444 set dx = ava: 2 tra
  26. ac44 ent6ac en +4aen + a en
  27. et Xra aequand. quidut ab fupn - f 4+ + 2fsn + 25. R + 29m N + m n av+ va = vr coco
  28. sit f= h + a c
  29. et m = N + q eF
  30. 42
  31. 12 18
  32. et hb = + aC t b: a c8
  33. 18)
  34. 17,6
  35. postremo 3h + 3h
  36. X: a
  37. +9m
  38. et C = - n b: at 6 posito g- d
  39. +R 3sd.
  40. ad seu R: C = a
  41. seu 3h + 3 l Th + h2 + h2 + f2 = 0
  42. faxco
  43. quod non procedit Ergo non licet facere
  44. fb=h + aC
  45. 120
  46. 1618
  47. seu 6+2 K =0
  48. M = ,b+ a. ~ 2h b + 2aC 2hb f2aC
  49. 6h = +ba 256m 10
  50. quod sufficit ad solutionem
  51. h + a
  52. b + at
  53. quae duae resoloi possunt in numeris
  54. rantur edy. Ergo dutu et xyix set ssa ex
  55. lur Extdus
  56. ergo datui et sxhya = SX a +X da monilsumesra
  57. faciamus _da +x a: X = y habebitur syda ex datis sydx jam a txa = x y
  58. fiet X = a: y- a et X = a aVa. Y a. Tantum opus est ut ex
  59. a possit extrchi radix quadnato quadratica
  60. rydus = av alia et Y - a = = l + 21 n B + 2l’ n v2
  61. Sar a = 5). 5y - = 5 .V du: p sx +1
  62. y- t . (+ m B+ nV
  63. PEAB+ v
  64. con a ida pe ae sax iX
  65. + mt V + 2m n V + n vF
  66. ao v. sit penient ex - a p - ga V - 6a p v - 4a pv - a Y
  67. aequani quto ab AF + EB =
  68. 2aqV - a v
  69. ar +4+ 8v +6YSV + 4rSV + st V
  70. r5 = l. Znt m- a
  71. Pr = 2Vm: a - 44p,: 25:
  72. Ss-a 24 mn - 4a p : 2 (n, ete
  73. ergo 2l m - 4 aap. 2m n - 4a p = + 3, (n + m - a p (
  74. ta - pata et Wlat B 2Vm - a p a = 4 5 Pn + Dm - a p 1 - a p
  75. Suk. a 10
  76. et
  77. F 2amn - 48 p = 4 5, (3n 7 m - a p an - at
  78. Hae tres aequationes si solvantur a numeris rationalibus vel
  79. ircationatibus habebitur quaesitum
  80. X+a) = (X + a 2aX + 2X coa + 2 Co u co fiet X = + 22c0 - ac0
  81. 2aco 420
  82. cov fiel
  83. +2a2 = a c0 = 2C00V + 2acov usi datur quidem divulsio sed no ex hibet solutione
  84. indetermnatam Y- B bm + Ca. et Xa=
  85. dia ra 0- 3b+ DC sa Bnd a 1. 6 be 6 a p a anve fit nt i n- na 0.a
  86. M
  87. a bm
  88. y- a = v: a
  89. se invile un
  90. vr a
  91. qaeato
  92. a -da a
  93. s 2ha h. aep
  94. adct a5c6
  95. S. Va+X x:X fut
  96. lata dx:x-a tdo
  97. qel avtra d
  98. con
  99. a + v= co
  100. quod non procet
  101. p FV + V
  102. debu quib
  103. ebma
  104. sit - a gytus
  105. amb-e fiet
  106. C = p = qui
  107. ergo c-42
  108. i quare gato eo
  109. reduxcinus,
  110. oportent
  111. - naae quare
  112. conto

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 71r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0141?run=73