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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 168r

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: 0.85.

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The machine reads it as

  1. Absolvatur
  2. ut in fine
  3. 10 VV + 17
  4. et 2000+ 12 ita sunt explicanda, ut factum ex ipsis in se invicem
  5. ductis fiat aequale quadrato, s idque scilicet ita ut
  6. ii
  7. e
  8. sitera v 50C+51e+52,: 160e46i e+62 (itu deni expksi
  9. ic o
  10. n inventa rationemoas quadrata aque
  11. jam quod in viatulo lat
  12. adhibetur in explicatione iphius v, vinculum nen
  13. ita
  14. 1c aequ
  15. + 10. 51.5] +2.10. 51. 52C +. 52.52 : 608+612+62
  16. oYBH12 aequ. 10.50 e+ +, 10.50. 51 e2 + 2. 10. 50.52 C
  17. Hinc si 20vv + 22 explices e
  18. modo solum ex in aeq. 3
  19. pri. 10 et 12 ponendo 20 et
  20. +12. 61 + 12. 62d
  21. et in se invicem duos valbres ducas, hominator
  22. producti fit utique quadratus, quia in utroque valore moncintr producente nominator est idem. Tautum ergo superest ut
  23. ex producto i Numeratorum fiat quodratus. Itaque unus numerator scilicet in valore 3 conparetur cum
  24. + 12. 60
  25. A 20. 70 C +2. 70. 71C + 71. 31, in, 80C + B1C + 32; alter scil. in valore + comparetur cum 90. 90e + 2. 90.91 8+ 91.91, in, 30C + 81P + 82
  26. aeque
  27. et 1080C1 +702. 81C +70. 82C
  28. Hic 100 (Supponit +2. 70.71.98,. + 2.70. 7181.. + 2.70. 71. 82C
  29. 10 etc)
  30. pro3 literis,
  31. et 600ek
  32. pro duabus
  33. ad ser.
  34. vandam
  35. legem
  36. sd moge
  37. neorum
  38. materia
  39. em
  40. EX1ZCt 13,
  41. +
  42. + 71. 71.90. +71.71. 81. +71. 2182
  43. aq. (9) compendio
  44. 100e+ 101 23 +102e +103 C +104
  45. aequ. (M)
  46. 105o + 3. 105053 +2. v sost e .
  47. + 10. 51. 55. 4 2. 100st. s1 C 4 10. 52. 52
  48. +17. 60. 4 12.6] . 12. 62
  49. Ex aeg. 9. fit 80 = 100: 78 8 = 1: 71
  50. per ( fit 703. 81+ 2(10. 80)15 70. 101
  51. 3
  52. rere fit 13. 81 + 2. (71. 82)70 = 71. 103
  53. 4(5
  54. n. 103 -2.70. 104, - 71
  55. seu fit 70. 713. 101 + 2. 70 18- 793. 71. 103 +2. 71, 100
  56. Ex e. multiplicando 70. 7(2. 82 +2,713. 7(. 81 4 78. 7(80= 70. 71. 102
  57. per 20. 7 fit
  58. 104
  59. vi
  60. f= 7. 70. 104
  61. 100
  62. (15)
  63. a416
  64. eodem modo ut in aeq. 7. pro 70, 71, ponemio q0
  65. et faciendo
  66. (1)P 200C+291 C t2orC + 2032+ 204
  67. seu ex 17 per 15 fil(70. 109 ≠ 2. 78. 11. 103+ 7 p2. 100 = 20. 71. 102 +4,10.109
  68. prodit 70. 104 +715 100 + 78.71.102 2703.71. 103+ 70.713101
  69. inveniri pure imo tolli. Sed quia id prolixius, rem potios praestemus
  70. per adjectum calculum DO ope duarum radicum aequalium.
  71. 2030 2905051 ( 4 2. 7050. 52e
  72. 422. 60 1 + 22.61.. +32. 62
  73. obae q. g. patet forumlam 100C 410 B etc. habere duas
  74. et ex 17 perch fit 703. 104 +270. 71. 101 (713 109 2 70. 71. 102 + (4 117. 100
  75. si aeq. 19 et 19 invicem subtrahas redit aeque 16. siu sibi addus,
  76. itaque ope Aeqq. 1b et 20 tolli poterr 71: 70
  77. 4q
  78. 1
  79. +40. 51. 51 n +2 30 51. 51 C18a. 52. 5L
  80. radices aequales (posito 100 = +) adeoque considerari posse ut
  81. aequationem talium radicum. Hinc multiplicari posse progressione
  82. chithmetica salva aequatione et fieri, s. 101 C3+ 2. 102C+ 3103C + 4. 107 -
  83. et 4. 100 C+ 3. 101C+2. 102P + 1. 003=0 unde per ter minos summos
  84. fit. _ L. oB 12. 4. 100. 102. + 3. 4. 100. 103C+ 4. 4. 100. 104
  85. - 1. 3, 101. 101. = 1. 2. 101. 102. = 1. 1. 101. 103
  86. et per terminos imos fit.
  87. 5II
  88. p 102. 103C f 1. 3. 105. 105C F 1. 4. 123 104
  89. L + 1. 1. 101. 103C 4 1. 2. 102. 103C + l. 3. 103. 103=
  90. =4. 4. 100. 104.. - 3. 4. 101. 104.. -2,4, 102. 104
  91. pro ag(+) et (5) scribamus compendio 3oec+ 3) C + 30 et 40C+ aet
  92. Exbeth pet 31. 42 -32. 41 in 31.40-305 = (2) 30. 42- 32.40, ut
  93. itaque si hypothosin
  94. tunc ex p.
  95. alibi calculavimus. est gutem 3249
  96. assumamus Z2 =0 seu 408
  97. fiet 31. 42 in 39, 41 = 302. 42. seu fiet 31. 4f= 30. 42 et ex
  98. +6 vel 7 fit 31: 30 = 42: 41 et explicando aeq. _ ex 4996.7.
  99. 1. 2. 102. 103f2. 4100(32. l.5. 103.
  100. 3. 4. 100. 103. 3. 4. 105. 1642 2. 4. lvetr. 24. 102. 10
  101. 4. 100. 103
  102. = 1. 2. 101. (02. 1. 2. 102. 103 = 1. 3. 101101. 1.3. 14, 107
  103. coparatis cum 4 et 5 fict
  104. (121
  105. = 1.2. 101. 102. 3,4. 101. 104) (113. 101. 107. 7. 7. 102. 11
  106. adeoque destractis destruendis in aequo fit Et in hac
  107. 3.34. novissima aeq. 13 p nova rursus institui potest explicatio
  108. nam quia assumsimus 2 vel 40 =0 et 32 = 44. 100104 - 1. 1. 101. 103.
  109. hins sit 4, 4. 100. 104= 1. 1. 101. 103 quem valorem ipsius 4. jaieq
  110. (15) - 1. 1. 2. 2. 101. 102. 102. 103 NN
  111. suubstituendo in aeg. 13. fiet:
  112. = - 1. 1. 3,3, 101. 101, 103. 103
  113. ∞I. 1. 3. 3 101. 101. 103. 103
  114. quae est aequatio identica, successit ergo hypothesis (10D sube
  115. a P. 1. 2.2. 101, 102. 192.103
  116. seu 14) adeoque non amplius est hypothesis sed necessaria veritas
  117. Hinc quia calutus idem in comparando secundum eq. 9 esse debet
  118. quia qui foret, si aequ (() fictitia esset veritas, et eo casu
  119. 4. 100. 10317 10
  120. 24100. 107 +1.3. 10, 10
  121. Ex ro ( pripriiatali haius pogiun fit 8C- 10017 Et eodem modo fier
  122. fit ergo 71. 703. 4. 100. 103 - 1. 2. 101. 104,:,-2. 4. 100. 102 + 13. Iaod fier
  123. 91. 903. 4. 200. 207. p. 2. 201793:: 2. 4. 200. 202 + 1. 3. 201. 201
  124. et pierndo a et 80 = (00:70 209: 90 82 = 104: 718 seu per (14V
  125. 3= 101. 103: 4. 4. 100. 7(. 201. 203:, 4. 4. 200. 912. senique
  126. 81= 70. 101 -2. 71. 100, : 703290. 20] - 2.91. 200,:90 ((23
  127. itaque absutrant denique ad instur (14)) scribatur 4. 4, 200, 209 = 1. 1. 201. 203
  128. vatu itaque athibiti aeg4. (14D 23D, (191, ((21D, (22), et in is explicatis 7, est
  129. ) per aeg9. 71 et 91 per aegq (17) et (17) et denique explicatis 100, 101, 102, 10) 104
  130. ahselutus et noenientur 10, 51,52, 60, 61, 62di licet
  131. Absol f
  132. i

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 168r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0335?run=74