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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 125v

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: 0.72.

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. 124r); this page is its left half.

The machine reads it as

  1. y = + (_, X+L, XIm, Xtn). quaeritur extractio. productum est a X 1XX +m X + lma a quandum quadrato
  2. sit x = ( 100 ( + 112 (O. erit XX = H1OB.vo GG + 2. 100. 12 BD a N -100 + 12 OD, ac
  3. +II2. 112 BD
  4. compendio rmen vocetur p, imtinama vocetur aque
  5. 310o. l +3L 18R..
  6. Quabratum, lum quo aequatio institui debet, sit excitatum a at 2O ta ZD, nempe aa BO + 28 1OD q
  7. +(WE
  8. px 11 1agu + lmn = = aa aequ (Grs
  9. troa W0op
  10. l+ 3 100.in9BB ∞
  11. os
  12. 400
  13. P0VZPOY
  14. A qui
  15. Eoosntg
  16. + 05. 100a9
  17. 00
  18. 1.122OD) _F 1b ag
  19. -
  20. C
  21. a
  22. + cc8dua
  23. aa
  24. Q
  25. 20 a8 1()
  26. P. tatos
  27. Ex irrationalibus
  28. aa2
  29. Fiat 9 = 102 +ua
  30. 007 = 308131a
  31. O5 = 10. 30 2 9. 10. 3 (e 8 1979
  32. 11.30
  33. 004-204+4a
  34. 300. B0100. 100. 112 ZC + 20 u s ev. 12 p C2 +00. 80. 0002 OVaq ~ _2. 0020 + 2. 00. 1aa
  35. 1. 10.30. 12. 112. 112 Q 1. 10HI J. 1. 112 a Q + 11. 31. H12. 12. 12 aa
  36. fit 3. 00. 170 + 10. 30. 115 =0 vel 100 = 112 1(- 10. 30: 3): a f20 = 2. 00. 100. 112P 208.4 = 00 aq
  37. 200
  38. 11. 30
  39. in Rationalibus ot evanes cat e3 fit ve 00. 100 43. 12. 10 30. et 100 = 1 (3 0 ) . Wu. 31G ,112 a
  40. Ia 1131. 113 aa
  41. quos duos valoras aequano fit absundam, ha3 Ex Btionalibus Talisergo Hypothesis non succedit,
  42. 184058 + 0op 4 + 0. 100 age + eo lmn fat x= A +4 +On
  43. 3. 1V0. MIGOD -15. 100ul 10 to Y + J. 1 3L vort a GQ + 3. u3 s 1B 12 aaq in p halebimus 8 et 3 0 tor
  44. 1. 02 M2 8
  45. sicesit in tat Aa latus t + l2 Y(D tytu +2t4 SOD
  46. X = 85 + AVOD asentit ad 56 . 1 ti D sCD
  47. 2401
  48. si Latus SVZZ + 7h+OD, ascendil ad 513 775B, (t Y 1GG0D et Si B131OD.
  49. ut ita demum institui potest comparatio
  50. sitonditur ad sextum gradum explirando omnes por eandem; Euso opus in parte rationari 7
  51. 7. Cgq. in irrationali ryque 6. summa 13, ad literae autem sunt 1 20, ob 10 variantes simplire
  52. caetem prom et ino liteae ob 66 sunt tres, ob 7Ihes, ob 0D, tres sunt 9, sb 5.73, 4.
  53. ob 73, sunt 3, in tumma 16 ex quibus etiam binae videntur superfluae
  54. deberent. +46 +GVOD, et 46 + +D habere divisorem communem
  55. s
  56. N7 = +95 + qYOD sZ = 4 + t (OD
  57. +m
  58. 5 =. 103 + +07Q. 192 7 - . 107+ . sDE 3 -. 109 +. +94
  59. 517 in S 3 in 23 = sst 7733, 517 = X I 5Z = X + m 7B = X + n
  60. debent aequai. S - l NZ -m 23 - n Hoc maxiinc succedere, debere videatur
  61. et tamen non successit: ine si N = NZ -mtl hit _ 7 = Z +
  63. et p et pari jure S Z = =B +H- m fiit s = Y +H m
  64. S - 7 = (it addendo s0 -3 - l- +
  65. m. L
  66. et pari jure 6 +3 = s B = n -m et 2 -5 = n m Ergo FC s - X = lam _n - m - 3F
  67. = lm
  68. Z
  69. 108+ ADQ in a1 +OO + 12. 15Q debet esse, 11 = 31 - 21 et 12 = 2. 32
  70. XL+ IaKA CaX + CNNEX+N =21 +C. 2 194 ita productum fit rationale. Sid hoc fieri deber adhuc semel
  71. DO constans et si O = 10X +M a ut D = 20X +2 a feret 11. 1 - 12. 20 = 0
  72. X taLLI ax FM2a X + AnEXXL (Q ax HL B. . 32a 3(31. 35. 10 = 31. 20 Ergo 10 : 20 = 12: 11 = 31: 31
  73. 10X + a f - 1
  74. sed pari pne ficot etium
  75. fiet H 12: 11 = + 31: 32
  76. 30Xtta, 20X + 2 a, 30 X131 10X - a f- 1
  77. c
  78. aXX 12210.
  79. I1. 2
  80. 10XFIA 20X +21a IOX tUa, 30X +31a
  81. 10.2DXX + Z 1WX L L 10 sXa t 1N, 1dXa =na 10 exa +na -10 tx a + 11a
  82. 10, 10XX F2, 10. 1a X + 11. 1a4 20 20 Xx +2. 20. 2 ax + 21. 2 a 2 0. 31. y. ( X = + 2. 1511 253IX 411. 4. 3
  83. to Lax La 10X 10. 10- 2040. 30. 30 X 2.10. L1
  84. 110. 2021 3. HX + ~191I. et H p 2. X +2.
  85. deona, XX + 2. 2 ax + _ d. aa, _ Ax + 231 ax + g1 21 ai test et 3
  86. u
  87. 2010
  88. Or 2. HiloaX+
  89. 1.3
  90. 3
  91. 10.10. 20. 20. 3030 X + 2 1 +2-10 1 21
  92. ex
  93. a
  94. XX+ uax + 12aa
  95. XX+ 2laxtmaa
  96. I1. 2 auX

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 125v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0250?run=74