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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 322r

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: 0.82.

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The machine reads it as

  1. X, XYb, XC aequ. Oto. fiat X quadratus, OV, eriet vv Dab, et XXBac quadratio quadrati multiplicat
  2. per communem seu vobab = O0, et Wdac = ED) Ergo VaYab, v- tab 008. Ergo
  3. An. vv- ab et vo ac possunt habere communem divisorem in indefinitis.
  4. m Ce v= 12 Hlm + 113 In + 13 Imn = 100a vv - 12tm + 2. 112. 13l Hun + 2. 100 2
  5. O- 210 fl+ 220 +m + 230 Lan O0 = 21ia F am 8= 412 Ulm + +13 Iln + 423 imnt quod
  6. Et
  7. ana namsm
  8. O0g = 210: 412 al Hm + 230, 412 an AImt 2. 210220. qu0 a Vm
  9. ona
  10. visvot
  11. D = 3 10 val + 320 Jam +330 tan
  12. + 2. 24d. 30413. an sIm +2. 210. 230a 423 an IIm 12. 210. 220 atm H2. alm + 210. 400 aa l
  13. ita OO Z fit homogeneum ipsi ve +ab
  14. = (avv + aab =) 112 alm + aab + a 12 1 al u 2. 113. 112n Hlm
  15. Sed aliter brevius aa, v - ab, vo- ac = Dto. = O0Y. 4N
  16. vo = 12 lm + 2. 11. 1 m Sn
  17. X = 2p + 212 SIn
  18. 8= 2t ala + 2. 31. 3 a sin OY -alp 20 3jal P + 212 3 al YIn
  19. v= idlm + 1 Ymn
  20. O = 31 Yal + 22 Van
  21. D= 41 val + 42 tan
  22. n
  23. 20ge anp
  24. 212.Ean..
  25. 2. 313222alM 2. 20. 31 3rap..
  26. p=4 al +2. 41. 42a n 95 = 20. 4+ al +212. 4 al sen
  27. 42 an
  28. 20.qu’ aup
  29. 22. qu an
  30. cums ob OB8 ∞ avv = ab, fiat ualm + 1ann -2a b = 20. 3i a lr22. valu 2. 11. 92. 12 alni 2. 20. 41. 4ap..
  31. (2, 203r anse
  32. Iius ob YD) ∞ arv -aac firt ualon +CEamn - aac = 20 4i alp + 2. 31. 42 21 2aln
  33. 20. 4 anp.
  34. et firt 2 (131. 32. 212 -9. 41. g2. 212) aln + aal,:, 20a (a- 3P)B + 20 (42-3 n
  35. et m2 20a 7 3)Ip + 2442+35) np + a (2. 22 a (H. 42 + 3132) t aab taac s:, 2a 2a ( + 12 n)
  36. Exirratios ob OC) X ∞ avv- aab fiet 2a 2. 11. 12 a m = 212. 35 al + 212. 32 dn + 2. 20. 31.32 Ap
  37. aulibus ob 00Y ∞x app -aab fint 2. 11. 12 m = 213. 4( l + 212. 45 n + 2. 20. 4 42 p
  38. unde fit p 212 (4 2 2() l + 212(42 32)n, :, 2. 20. (31. 32- 41. 42). Mosque ipsius P valores aequando inter
  39. se fit 212a(i - 31)1 +(~. 32)1)= 4. 212 (1.32 - 41. 43. aln +, 31. 32 - 41 42) aalb- c) unde + et a interventa onstantium ex se invicem
  40. habentur. Aursus ex Locu valoris ipsius in prolixioris sed homoeoptati id aeq. 4, potest ex aequ. 1. dici duci talis ME 2 20. 3i alp +20. 32 anp + 2. 3(. 32. 212. alnt aabs:
  41. Nal. +12 an, et pro p subsis substituendo valorem ex 17. fit, 20. 2F 35 203( a l212 (4127 L+25. 3( a l 212 (426) n +. 25. 35 an 212 C39) 1 a1sti 31) n
  42. m.
  43. Rarsus et 6 et 7 fit
  44. +2. 25 (31. 3e 41. 42) 2. 31. 32. 212aln + 2. 36 (31B2. 41. 42) dab, :, 220(31. 32-41. 92) 11’ al + 2. 70. 31. 32 414)’an
  45. 226 (3L. 31 -41. 42) 2. 11. 12 m= 20 (31. 32(9142) 212. 41l + 20(31. 31 (41. 92) 212. 42n + 20. 41. 42. 212 (45 3() l +20. 4. 42. 2n () 31)n. Ergu ex
  46. ei seu 50 (31. 32=91. 42) 2. 1. 12m = 212 (31. 32. 41 -41.42. 31)l + 212 (31. 32. 42- 41.92. 35)n. Et ex aequ. 10 fit m = 42. 3(453 ) All 1
  47. 4212. 32 (4- 32) ann + 212 (31. 42 + 35. 45+ 2. 31.35-4. 313241. 42) aln +2(31 30-41.42) fab, :, 2(31. 32. 41. 42) (1r l + 12n). unde
  48. ex aegus. 12 et 13 duos ipsius in valores aequando fit (31.32. 452- 41. 4332 pi Il + (31. 32. 45- 41. 42. 32) 12 nn = 3F (N = 31) 1l. tl + 32 (4 - 3 r) uN nM
  49. in qua rursus est aequatio inter l et n
  50. sed malim post aequo e omnia relumere taistituendo calculum secundum homooptosin, quis comprobationi servit,
  51. +(35. 45432. 41+2. 35. 30-4. 3). 82. 41. 92 Y 1. 12 In + (31. 32-9142) 1n ab
  52. Ex5 et 6 est 4. V1. 12m2 = (9). 212 (31+ 45)1 + 212 (31+ 42)n + 2. 20 (31. 32 + 41. 42)p et pro p ex aequ. 7 in hac sbsti
  53. tuendo valoremfit m = (10) - (31. 32 - 41. 42) 212 (3eta C) ( (31. 32 - 41. 42) 21265 + 42M,:, 4. 11. 12 (31. 32- 4142) seu destrndis destmendis
  54. in CaH3 (g2. 3C) F 31.72. 41 (=41. 42. 45) - 41. 42. 31) ( ((3l 32. 32 2+ 3132. 2 L 91 42 3V (AI 42 a. ) n, , taumeisit
  55. (31. 32 +41. 42) 213 (41 3e) +(31321442) 212 (11 30)
  56. (.31. 32. 3(7 31. 32. 4C + 41. 42. 411) = 41. 42. 312). (. 31.37. 312 31132. 42 = 41. 42. 3r f 41. 42. 4
  57. seu m =12) = 231. 32 (45 31)C 212, 31. 41 (32.41 - 31. 42) l + 212, 32. 42 (31. 42 - 32. 41)n., :, 2. 11. 12 (31. 32-41. 42
  58. seu m (3 212. (32. 41 - 31. 42) ( (31. 41 l - 32. 42n) p: B 2. 11. 12 (31. 32,-41. 42)
  59. sed ex aeq. 4
  60. quaeramus rursus valorem ipsius M, explicando, in e ea p, per aeg. 7. quispl simpliciorem quam 3. sufficitus atturata
  61. alterutia ex ipsis, quia ipsae 3 et 7 jum sunt aequata. Hinc ex aeg. 4 per orqu. 7. fiet:
  62. M = (14) = 20. (41+9,2). 212. (4,= 3,) l + 20. (4143(). 212 (932-3 5) In + dab t9) 2(2(. 52- 41. 42),:, 4 ( l + 1 2n) (3132- 41. 42)
  63. 20 (42435) 212(91- 314) In
  64. 20 (42 4921) 212 (40. 38) nn 4q (31. 32 - 4142) ae B1 3et a 42) b2
  65. +4iqu Ar. 32+3qeL 35. 32
  66. uti coeficirus ibsius in est 4
  67. 4+4. 31 37- 41. 4
  68. Seu m. (15) -20. 212. A 1=- 3) I + 20. 212 (421 -321) nn + (31. 35 -41. 42) In + 2a (brefo1 32. n a2), 1 a (u tri a) (31 gr. X1 42)
  69. vel m = (15) = 20. 21 (2) aPL∞ 42 n +3r l + 32n) + 2a (b7C) (31. 31 - 41 42): 4 (l +ien) (31. 32- 4142)
  70. quos renos
  71. qualores 13 et 16 aequando sit 2. 211 (32. 41- 31. 42) , 11. 31. 2 l = 12. 32. 42 nn +. 122. 3, 41 ln = 20. 22. N. (17) ce qual.
  72. 20. 212, 11012. [2(411 - 421) + 20. 212. 11. 12, (1351 -3En) + 2. 11. 12 (31. 31-41. 42), a (b+C); Haec rursus est
  73. leziarn
  74. aequatio ad l et n quae debet identificari prion nempe aequationi 8, ut saltem habeant unam
  75. hadicem communem, itque idque obtinendum est per arbitrarias, quod si efficiatur habebitur solutio desidenta
  76. dempe ope quatumr collatitiarum aequationum invenimetis
  77. m relationem inter L et n, et deuique
  78. de
  79. aequ. 7. valor m per aequ. 13.
  80. relatiom inter C et n, per aeq. 8 vel 17 quae i ficts et denique re atio dater constantes per
  81. e
  82. alor
  83. quandum relationem inter constantes. Et adeb
  84. ea conidentiationem. Hoc ergo resumendum et absolvendum

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 322r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0639?run=74