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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 60v

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. 59r); this page is its left half.

The machine reads it as

  1. Hac metrodo optime habetitur, utrum posibule sit vet ab in eotae equare quatrato, nam quantumunque
  2. alsurgal valor rationalis ipsius , facile deterumpr potest modo, generpla
  3. crev + ac = quadrato
  4. X. X+D, X += quadrato. reducitur ad pab
  5. si nempeponatur ax = vV. Esto _ =R sXF + agF + aah, :, ZZ +q E + Inn
  6. si retab, verac- ssut naGgZ+ raafh Z24
  7. votab=
  8. fiet vv + ab =
  9. Haagusquee r 2 a g
  10. qu (Szt etc) + ab qu (32 + Zd ma)
  11. qu (ZZ + mq + mn)
  12. ab qu (77+ m Z + mi) L
  13. +pZZ + a92+ aarq.
  14. +f. +ag.. + dah 5
  15. fit aquerrn) a t p1 3 + aqr anri
  16. 2+f.. ag. F nahi L
  17. qu (pZZ + a9 2+ aar)B
  18. qu (22. + n Z + mn)
  19. (4pZZ + agZue + aar
  20. - f. = aqu = aah
  21. Ae s+pZZ + a9Z + aar
  22. al45. qagu + aah
  23. et posterius ob raeq.3 erit (5
  24. faq faati bZZ + 2bnZ+ bun = tepi ep Z3 +ae92 ta et
  25. Oo purus fiat eZZ + 2C m Z + emm Etpgue + agZ + aar
  26. aequ. 2 eut,
  27. _ def. facg. qu’et
  28. f 4e=p. aF (4 f = e-p = ep -abie +ag = rem -a9 = aeq- 2 abaje +an tenu s a
  29. ob rem coincitentiationes 61to 2
  30. Hinc e tabp L eetab,: 2e aq = reem + rabm,: 20 Haar = eemm Fabun, : 2C
  31. Similiter vet ac-
  32. qu (f22+ en) tac quC2ZF +m
  33. qu (Z2+ m Z + mn)
  34. +5Z2+ a tZ + aacZ in
  35. aC qu (22+ m q + mn) = +f.. ag aat
  36. qu(52 tatz +aaes
  37. qu (ZZ + in Z+ mn)
  38. +522+ atZ + aa 8
  39. a 5.. (4) ag. (4) aah
  40. a H522 + atqe t aac et uiqu n) L
  41. ob piem coincidentiam (Il mo) erit (+)5 = i -5. = is - aC,: i (+ ag = _. IM - aF =ait - ZCn, : 1 (+) dhx ip d aig.
  42. a2 +am m
  43. Unde oi et qu (Z tm)
  44. H) fu () ag. f)aah
  45. Hure ((2m) fit Saii tac,:2isat= imtracnc: 2i et aa = limm tacnn, : 2i
  46. B ex S,t 7 fit (13t0) f = + ee 4 ab, : 2C ag = 4 2eem f rabn, :2e aah = + eemm L abnn,: 2C
  47. et ex 11 a c2fl 14h) f - (4) ii (4) ac, 321 ag = (4) eiim H) racn: 2i aah = (4) iimm ) acnns: 2i
  48. Ex binis valoribus ipsius ag. fit m: n = tabi () Y ace,: e fecip Deii, unde
  49. Habunu min Z mm: an Erjo Mn ta et paatet V anrando
  50. trmratibatm
  51. aabb +a’arce
  52. ar s n cugo
  53. . SeE.B ant nran
  54. )adbCeieii t ce it +(+) 2013 = nm: nn
  55. pursus ex binis valoribus ipsius aah fit mm. nn = F abi(fce i + eer (4) eii, quas duos ipsius
  56. mra: nn valores aaequando fit qu ( abi () ace) = + abi (+) ace, Feei (4) eii. seu tandem
  57. tabi F) ac fabi (4) ace = + eei (7) eii seu fabi Z eei. = (4) ace (7.) eii
  58. Sed ex binis valoribus ipsius f, sit ilidem +abi + eej = (+ ace (4) e ii. Ergo quod mirum
  59. res succedit hactenus, et fit ji. sit 4 1: (4)1 = L 1 et fint ii A
  60. ii + ZeC + ab
  61. + e- 2ecab + a abb + C- 2eeab + aabb + 4acee
  62. itaque hustrantsit hic catcslas nec hac via ad extractionem blaiA.
  63. et i
  64. side quia t pro actitiai
  65. itit
  66. abee
  67. 44 ac ee
  68. pars radicalis fiul extrativilius
  69. licet, nam seqe
  70. 1 t a
  71. it nam isa
  72. aine adc c
  73. et fiet aa bb -2be zabee + e = a a cC- 2ac ee + e
  74. par et
  75. =mm
  76. returhim
  77. EErgo vel in =1
  78. vel n =0
  79. elsicirtu
  80. sid M =1
  81. olist
  82. si divelsi vatrrs ipsius
  83. esset _= tab
  84. fret i = fac
  85. vul se ceset
  86. H e fouet 12 bt a
  87. seu ab nec = act ee, et 2ee = abtac
  88. Sed generalius tentemus aa bb -2abec + + 4ac e = e + 2 ceAaa coco
  89. et firt aabb- 2abee + 4ac es =+ 2 eeaco + aacoeo Sorao = eV + ab - tab pe r. s ent, n ralit
  90. adac
  91. et siet aabbrabee fgacee = 42eV +2ee ab + eevo +Revab + aabb
  92. sin ace -2abec 20 f.et
  93. et firt habeF tace= = reco + 2e ab + eu + 2vab. Divellatur haec aequatio in duas, e q
  94. et brerioris calculi causa fint ~ - fiet 2a 4 ace = - 2geb et evV +20 ab =0
  95. fi etque et= -2aC sed ita siet etiam e = -2 ab quod non licet. Ergo reliaquamus ambiguitatem +rab
  96. ipsins +. Et fiat e evit 20 ab =0 seu ev = -2ab ut -2 ab + 4 ac = + 2ev +2ab,
  97. ubi pra sed ita pro eo substimendo valorem fiit rab + gac aab + 2ab
  98. et foret et foret b queb b + 2ab b L 2b = Z ac. sed talem deter-
  99. Ex aeg. X fiat - 2 abe + gace L a adv= a1v Freev + 2eab + evc + 2vab
  100. minationem inter datas nolume
  101. aliter ua bb = rabee + + 4ac et = aaboA rabeco + recoco fit rabe te +4ac e = rab etoco
  102. Haec aequatio divelatur in duas = 2abe
  103. Alter, aa bb - abee + et
  104. gacee
  105. qu ( + 228) = _ac + e 88 + hace
  106. et fiet ab = ee = ad 8 a. + et
  107. si in vabre ipsius

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 60v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0120?run=74