Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 49r

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: 0.80.

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. 50v); this page is its right half.

The machine reads it as

  1. pro quad raturis
  2. Qvaeritur resolutio irectionels Radicts ex altiore in partes quae sint radices
  3. solvendaquantitas
  4. ex inferiore. lab lil Cum nempe consiturate dEbetur
  5. dque A(Z + abzZ + ac). Ha okonem ponatur Z = C + +C. Et sit
  6. O = Sod (tnaa) D =, L(2a t21aa) et e = s(30a+ 31a). C
  7. ponatur porrosqu (Z + abzZ + ac) = aV = i OD + 130Q + 23 DG + ar
  8. Et quia Z + ab ZZ + aC = aa WV, ideo explicatis Z et v, prodibit
  9. 2+ abzzt aeC = 9 + 6003 +40007 + 1980D + ab + 2ab05
  10. + ab (30
  11. +ac
  12. et
  13. 12OCW +2ar OD +2. 13,13696
  14. Ee
  15. ete
  16. X = a +b+C
  17. XA = aa + 2ab
  18. x= a + 42b + aaabe
  19. Caublb 4.2. aab
  20. terminos
  21. quos duos valores concidentios A et quidem ita ut primusm tollumus conseramus ubi irrationales
  22. et
  23. l 80arra n
  24. +ab6.d+
  25. qualis O) faciamus (2ar (4 (0C) + DD + QG) +3ab
  26. et 8 = 2. 13 23 2. 13. 23 =8 seu 13. 23 = 4 sed pari jure 12. 13 = 4, = 12. 23.. Ttaque
  27. 23 = 4: 13 = 4: 12. Ergo 12 = 13 et pari jure = 23. Quia ergo 12. 13 = 12. 12 = 4. Crit ACg 2- 12-13-
  28. Ad Conferendos tesminos rationiles pro vat in valore ipsius aaur pro aarr substituauus valore
  29. inventur fint ac = 3C +500D + 3 ab 00 Seu ( + 200DD X abO + - dabb-
  30. se) extratendo ntrobique 10 + s ab u aabb a rea 00 + i ab = 4 H(9bb + nac)
  31. Seu 04 + 100 + ab 9 + aabb = = ac - aabb. Et extiaibnt 0O + ab a (12ac - 3bb)
  32. esmion matou
  33. Ergo ut res sit possibilis sine imaginariis oportet c esse affirmativam et gac non esse minorem quame
  34. porro in valore curvae conicae, qui huc prodest, et abi C est affirmativa
  35. due dy+ dzdZ) = dz N(2 - 24+ 19 22 + g (9: rr4)) erit ab = (g1r, ., r44) q9 et ac - 4 (9. rq
  36. 4dc =(4: rr4) aque aabb =(9: 1+ 9) (249+ 44r + rY) (M
  37. 22- 94, s(9:, r+4)
  38. et go q non oldetest mind quam ot riet seu eli t d aen db et es Esempe
  39. ergo 4q non soctesse minor quam +9q+ q psterius Excedit per tit ritaque is ita positis valot ipsius ad e temper est imagnatum
  40. Atque hoc quidem nos nun moratur; sed videndum tamen esset an non evitari possit
  41. Sed hoc est absurdum quia semper est minor, nam
  42. Ponamus Q esse 0 et 13 et 23 esse 0. Manebit 12. 12 quantitas ad huc indeterminata, et
  43. fiet 02 3 _ ac = 3O + (12. 12 +2) 0O DD + 3ab 00 + aa bb
  44. Sed hinc si extractionem molimur eodem ducimur, ut 1212 sit 4 seu ut 1212 +2 sit b.
  45. verum videamus an non liceat invenire divisorem alium (quan adicem) aequationis hujus, nempe
  46. 1 + + 12. 1+ 003B + ab 1C + aabb - ac =0 Divita affumitus sit ∞ t ap e cujus quadratum
  47. enjus quadratum OA + 2aM OO aamm unde fiet (V (1 2t 2y 1) n +2 geam 5+ + 2005 + nam 0 t aamm
  48. +( 1B. 5) (r 43. 5)OODD. sed prius du explicari debent 0b et D)) ut omma
  49. a reducantur ad unam variabltem 1. Et fiet
  50. S+p = 10 1 + 2. 10. na V + 11. 1. a a)
  51. 20. 21
  52. 21. 21
  53. A- 15 MCD = mocol + n. 10 2 a + n. 1 2jaa
  54. al (d0 +2)
  55. am - bb 2ac am =
  56. 1. 2
  57. 10 bi + 1. ab
  58. 20 b 21 ab
  59. am
  60. 10. 10 + n. 10. 20 = Ann. 268. 20 = ( nn = 1) 20. 20
  61. biH est
  62. seu fit 10 = Ln. 20 = 420 LInn - 4)
  63. quaesita aequatio hanc dividens esto f1 + ag =
  64. ubi f et 9 sunt 0, haec exaltata dabit quadrata
  65. dabit fWV + 2f 2afqV + aagg = b iquae multiplices
  66. per 10428 + n. 20 et Aeq. D per H, et alte
  67. una ab altera subtrahatur, fietue
  68. +2. 10. 11 a ff2 + 11. 11 a45f
  69. + n. 10. 21 ... - +n. 11. 21..
  70. = 1. 10. 102fg1 - . 1. 10 aagu
  71. Seu 10: 20 = 2 V (nn - 4) = = n nn - 4 = 12 49. 12 + 8. , (V. 10 20
  72. eti o.o
  73. plaestat sumere oripore
  74. seu 1124 +4. 12 - 32, : 9 Z nn - 4. ubi si 12 = 2 sit un fit nn-4 = Travicem in
  75. Rursus Exa est f10: 20 = -, 2. 21 + n. 11 + b, :, 2. 11at n. 21 + b = 2 s(nn - 4)-
  76. et eodem modo
  77. si esst nn _ nN - 16 - 9 seu AH = 2 fiet n = 5 = 12 +c. seu 1 =
  78. g et nn = 2 et n = = 4
  79. 48. 4 100 10. 4 = 576. 4. seu nn = 676. 4 et n = 26. 2 = 1 +2
  80. nN = nu 16
  81. 60
  82. dd ergo 12 26] - 2 = 26 - 10 = 16 et 12 = 4: 15.
  83. 10
  84. 100
  85. 4. 3b = 64. 4. finn = 336+64, + et n = 10. 2 = 5 = 12 + 2 nond
  86. 10c
  87. HM -
  88. 113
  89. nn - 4. 64 = 225. 4. seu nn = 4. 287 et n = 2. 17 = 12 + 2 firt 13 = -
  90. Et 12 =B quod succedit rationalitar, et fit fa L(nn - 4) -
  91. un-
  92. ide haec quia dnusi 12+2 dividi per, 3 ut fial n
  93. =
  94. X = - 2 fit -B = e2 +
  95. ctante ootdinatarm
  96. pro ibypeibola aegulisera ad Asemploton relala t positis otentia A fit du i
  97. si
  98. X DIff13 = 10a1+ uda iett
  99. ear
  100. 125
  101. 2d - 2
  102. 10 1 fit 20 = 1 sit 1 2 1 sit a = f
  103. 29 119
  104. 239
  105. Ergo b =0 et ac = f et 30+ DD = Y A12aC =
  106. ili 66 eso asis quo ae a ed as tea idenua
  107. 10=, 2 20 = -10 et 21aa = f13 - 11aa
  108. u ulcami quantibas BC et 3 sit alti sed tom anat i d feun pro cndes porito
  109. qui non sit ipse aequam
  110. atque adeo sum
  111. adtes
  112. pt
  113. acilo
  114. orc aloru
  115. ve sed sum
  116. est di
  117. id
  118. mionem
  119. it
  120. 1d
  121. 55 vc
  122. mumur 1
  123. deprtendi2
  124. us
  125. ut
  126. X. yy2
  127. ZyX
  128. 24∞10
  129. 57b X
  130. 00
  131. 76
  132. i
  133. 150
  134. n
  135. aavo=
  136. 13

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 49r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0097?run=74