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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 240r

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: 0.82.

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. 241v); this page is its right half.

The machine reads it as

  1. Quaeritur Sydx posito y = LaXtL, XEm, Xn) per quadraturam rationalem
  2. Hoc tentavi assequi si possem quod sub bliaculo est reddere quadratice extrahibile.
  3. sid est sint tres quantitates A, B, C; earumque biniones AB, AC, BC
  4. Manifestum tres biniones invicem ductas facere quadratum est enim AB. AC. BC = AABBCC
  5. sit A = t + 11SOD + 1210 + 13SQ in omitto coefficientes, quia ab ipsis O, D, 4 alsorberis pos
  6. B = 2 + 10D + 1OG + 1D9 sitax + L = AB, a, x + m = AC
  7. qXin= BC
  8. Fietat Caixtl x+m, Xtn) _ = AB
  9. C= + 3, 10D +32 10G + 33 1D9 Ergo Xet ax = AB- al = AC = am = BC - an
  10. +∞. ∞h2
  11. 100.00ti8
  12. H1. 31 (3D
  13. 12. 3200
  14. 13. 33DG
  15. -0000 am
  16. 000 26
  17. +00t 10D +00t 109 + 0ot 1D coincidentientur AB- al ~ AC- am
  18. +112 ... 1224 -.
  19. + 16 .
  20. 118....
  21. 41319.... 13..
  22. +45. 31t 0D 00zetu Vee
  23. 00. 11 .... 00. 128 ..
  24. 12. 338 in. 1.337).
  25. 13. 329 1,1. 13.319 11
  26. 00f... 0051.1.
  27. 318F 324 11.
  28. 326 ..
  29. 315)..
  30. 33 . 11. 33D...
  31. 137.-.
  32. 11C...
  33. 00dt DE
  34. 00.138.
  35. H1. 326.
  36. 13.316..
  37. BC- an ~ AC - am
  38. in irrationalibus ex priore
  39. G(L. 12 +ca 1
  40. -12. 3)-13. 52
  41. 9- 00 700t +112
  42. -31 l = 118
  43. +6232 80D. 12
  44. 14135Z - 00. 13
  45. = 00, 40o C +314, : +12. 33 -0032
  46. -31G +13,32 =00.33
  47. D - 00, tootq + 12E9:, +11. 33 -00. W
  48. 00b.... er n a 32
  49. es
  50. = 126. + 13.31 - 00. 13
  51. 0 +008 +327 :, +11.33. = 09. 31
  52. permutande oletor 12 - 314
  53. +13,3) =00. 33
  54. C = 00, +00 + 1343:, + 11. 32 - 00. 11
  55. S2d.... Ex Daise e 3)
  56. 136 + 12. 31 - 0V. 132
  57. (1 = 00, +006 43347:1 +11. 32 - ov. 31
  58. petuntuli ers
  59. 13 =31H +12. 31 - 00. 32
  60. I 0c 37( Denominatores valorum exprimantur compendiose et apte ad permutationes
  61. 4 = L 1391 00. 33)
  62. Zprioris (23
  63. posterioris 223
  64. +00723t - 11. 223 B
  65. 131. 123.. 713,. y: 123 223
  66. -12. 213 6,: 113, 213
  67. F13L1B.
  68. - 13. 2128,: 112. 212
  69. Derioris 113 Oprioris 112. ubi Ultima et penul
  70. posterioris 213
  71. dextras bilicium
  72. coincidentientur hi ipsius 2 valores,
  73. primus secundo, et tertius secundo
  74. coesscientes ipsius inter se 3 aequando
  75. ... 8...
  76. ita orientur qualuor aequationes pro determina
  77. tionibus ipsarum 11, 12, 13; 31, 32, 33
  78. 130Z213) 123 23 vel F 00. 113. 213. 24, -31 19 p1G 215 Y31. 13. N _5
  79. in se latet d periuntant. 1 et 02. + 00. 123. 213. 223 - 32. 123, 23, 23 +32. 113. 123. 213
  80. + vo. 12. 213, 212-32. 112. 213, 22+ 32. 113. 112. 212
  81. fit exsi Haec aequatio sitp praecedente petntundo el 3 permulando ∞) et 3
  82. it latera permutant 02 et . 3
  83. a (125 (. 113. 23 = +4517
  84. 5
  85. 23p3 _el +00. 113. 113. 217 - 11. 113, 1a3. 23 L 11. 13. 23. 213 1 2
  86. s
  87. 400. 113. 123.2, = 12 13. 123. 213, H2. 123. 23. 2231
  88. C fit ex V permutando, 10 et 30, item, 100 et 200
  89. in B lapera permutant, 1 et 02
  90. u 13. 2B = Le 18) m. 22 vel tev. 112. 13. 213 1 pui y 213 7 3. 1 3et2 213)-
  91. 400. 117. 113, 212 - 12. 12. 113. ER. +12. 112. 212. 2131
  92. Y fit ex 3 permutando , l et. 3
  93. 7 fit ex 4 permutando 10 et 3., item, 1.. et 200
  94. in Y latera permutant, 2 et 13
  95. ita omnia sunt palchre harmonica, et pleraque sine calcs et legem justitiae sevant
  96. Posteriora ex prioribus sine calculo per descriptionem parum utartem fieri possunt
  97. Examen comprobutorium habetur, dum idem ex alio et ad huc ex alio formari potest
  98. daa inquationa et pars una aequationis formari potest ex altera
  99. eos =e cxi t Or
  100. Vidudon en cortetu ilou daritidiper tedeles cn eandi causa, qua bolies rarius dentent quam balites in aopi. ta s als i10
  101. Ex aquatis valoribus
  102. ipsius et fiet:
  103. Ex aequatigs. duolus
  104. valonibus ippos +
  105. Ex aequatistuobus
  106. vatoribus ipsius))
  107. termutando ut e n
  108. Ex aequatis duobus
  109. valoribus ipsius 0
  110. ex proxi
  111. ermutando 02 et
  112. Ex prima aequatione coeffi–
  113. cientium ipsius
  114. difsrut hatera periu
  115. Ex secunda
  116. 400ru3h
  117. +32. 113.
  118. ex praecendente ipsins valore permut andu ut n2
  119. e = +00)212E
  120. +00223) 113, 213=
  121. Exprima aequatione coessi
  122. cientium ipsius C
  123. Ex secunda
  124. Notae bilices
  125. ut 12, 21 lexprimunt
  126. Notae rcilis...
  127. 1bv 12124)
  128. +33. 112 115
  129. er constaptibus
  130. Res omnis pq ex irrationalibus reducta est ad 499. 1, 2, 3, 4. Vel 5, 6, 7, 8
  131. idem vnlor vel qui aptessimus, substitatur in valoteta ipsoum D, C, prout aptissimum. Et habebur vatores novi horum per
  132. praeterea loco Z in Rationalibus substimatur medius valor ipsius 2.
  133. Solas altimas t et
  134. ita jam bis u
  135. antinu
  136. + (5 =)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 240r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0475?run=74