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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 95r

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: 0.79.

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The machine reads it as

  1. X = YC + SD X erit Xx + ab, XXHac = O+ 1∞ D + B, 9+ 2OD+ C, = O Ft B(B +bc + 0) 1BD. io (ersia
  2. fin = 20 + 22 tabi C )is. Ergo siet
  3. 4
  4. 4t
  5. +20)
  6. +40)
  7. aa ff1O + 6ffOp (b +C) ssB. trabess = f49) + 4aa 0 + 840D. + 44(61) B + qu bt C)
  8. ut prodeat aequitroidentica sed hebet idem
  9. expheculur faciendo 1d = 10Z rua, et D = 20Z+ 2ia, pt 9 = 30213a a
  10. a
  11. pottatet extab, Xx tac aequam qu (10d + 16D)
  12. qui fa vel sic potius 09+ DD = 1024 + uaZ + 12 aa
  13. phamiffici, ex solis C et, D, seu ut ( +D
  14. fiat = 402+ 4la, et hoc valore substitule
  15. prodeat identica cum eodem modo se hateant
  16. in aequatione vel sic OO+ DD-73
  17. et 15 = 2032+ 21aZ + 22 aa fiet 00 +D) + 2D = quadrul = 410ZZ +, 11aZ+, 12aa = quadrato
  18. 1. 12 + 22V = quadrato adeoque l. 12+ 2.222. 204 , l.H f2. 4
  19. seu ZZ +. L. H 12.21 aZ +
  20. 1.10+2.20
  21. 110+2. 20
  22. V 1. 10+2.20 4)1. 10+2. 20.)
  23. et fiet: 4. (1. 12+2. 22) (1. 10 +220) = qu (1. 11+2. 21) seu 1. 112 + 4. 2121, 4. 11. 21 = 4. 10. 1 + 8. 1. 22
  24. sed quia etiam D +FDD- 26D debet esse quadratus fiet rursus
  25. 16. 20. 22 + 8,1220
  26. 113 f4. 21 = 4. H1. 21 = 1410. 12 = 8. 10.22. Et duas aequationes a invicem subtiahendo
  27. fiet
  28. +.16: 20. 22 = 9. 12. 20
  29. 8. I1.21 = - 16. 10.22-16,12. 20, seu 11. 21= 2. 10. 22 +2. 12.20
  30. Et invicem addendo fiet 11 + 4. 21 = 4 10 2 + 16 2. 10. 12 + 9. 20. 22
  31. sit 21 = 2 10. 22 + 2, 12.20,: II et 11. H( + 1618.25+ 12. 26 + 32. 10. 12. 20. 2; 11=
  32. 2. 10. 2E 2. 12. 20. seu W + (2. 10, 22+2. 12. 20)1 + 10. 22+1220+ 2.1012. 20. 22 =
  33. 10. qu (10.22+ 12. 20) 0 (1 - 16 = -8) et siet 11n = 10. 22 + 12. 20, -1 + 2 Y. 2
  34. et 21 . 21 = = 4 (10. 22 + 20): (qu (-1 + 2 f.2)
  35. seu 21 = 2 il (0. 22412. 20). + (- 1 + 2 f- 2) et 11 = 10. 22 +1220, 1 (- 1t 21.2)
  36. n
  37. D= 40Z+ ala, fint
  38. ( +7 = 35(3 + 2. 30. 3143 + 3131aa et OD = 30. 407Z + 30. 41 aZ + 31. 41 a
  39. Aliteret medius
  40. = 30 + 31a.
  41. fiit 44
  42. 40 +2 40. 41 + 91. 4
  43. 30297 + 2. 30. 31 aZ + 31. 31 aa
  44. aaff) 402
  45. 2. 41. 4
  46. 2140. 41
  47. +(494) 30.4073 + 30. 41, aZ + 3. Maa
  48. 6aaHs
  49. 4 d (br9)
  50. =aH(brC)
  51. aaque
  52. n b
  53. + 31. 400
  54. 00. 30 a7
  55. 0040 aZ
  56. +. vo. 31a4
  57. + 00. 41 aa
  58. ia
  59. usb)
  60. +oe
  61. bct
  62. aa
  63. 31. 40 2
  64. An sic O+) = 10Z + ua
  65. aff0
  66. daffsh1onBaf00 + 2.10. 1B. _D + H. 1I. aatsaa
  67. ait siet od
  68. 4 59 94
  69. 00. 10 OO
  70. saaffV
  71. +4WbFC))
  72. aff(brct
  73. aa qu (br
  74. -bc. f5
  75. + 00. 11 a0.
  76. 20000. a1
  77. +00. 10a0
  78. +00. H1 a a
  79. 00 e aa
  80. 0000. aa
  81. et et O - D = 20Z+ u a
  82. seu b-bb+
  83. ita habebimus 9O + 9D + 2OD = 187+210. 1a 2 212
  84. et 9O + DD= 2OD = 20 +220. 2 aZ + 21. 21 aa
  85. 1O +D) = 10 27 +2. 10n ay + I1. Haa
  86. 20C 42. 20. 21 a 2121
  87. 28 = 2. 20.2
  88. = 21.2
  89. sed calculus non fit brevior
  90. sed me sed optime, ut sufficiat
  91. facere D = 100 + ua
  92. =0 hoc est drevissimum
  93. compendio scribatur
  94. 20F1
  95. 2500
  96. 120500.00
  97. 30, 10. 10
  98. 40 00. 10
  99. 140. 00.00
  100. 50. 11. 11
  101. 40. 00. 11
  102. 1C 39. 30. 10.10 4+ 30. ( 00. 10 +20. 30 fint 30. 10 = 00. 5o + )e(53 - 4. 20. 30):2
  103. et eodem 60. H1. = - 00. 80 +00 (8- 4. 40. 60), : 2
  104. ristal 2. 30. 10. 1I +00.50. 11 + 90. 00. 00 + 90.00. 10
  105. 10=- (5229a5) 7 (au (518a - 6aaes) - +4u (4a = auss)) 2 (+ a aats)
  106. bretstaa ) + S (que brcs 4aa. ) L 4 caa quilo vC) - be ss) (4 c aas)) : 2 (4 - naf))
  107. Saaf
  108. Eb) Q rese
  109. M+H.2
  110. -bVree
  111. sit ((= 1
  112. et cc - 2bb
  113. =∞-1, sit
  114. et 2 etb
  115. fiet C = 1: b
  116. et cC 2bb
  117. = - 2bb

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 95r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0189?run=74