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Leibniz-Handschriften zur Mathematik LH 35, 7, 14, fol. 1r

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: 0.77.

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. 4v); this page is its right half.

The machine reads it as

  1. de inoestigandis figurarum quadraturis e
  2. ordinariis, quando sunt possibiles.
  3. aequatio (11. y + 10 20
  4. ubi coordinatarum minus ascendens y, endats
  5. subsistat in primo gradu: sd lituae coefficientes 10 et u involvent alteram
  6. coordinatarum X. Et 10 = 30 + 31A3IX eu et nL qurqequ etc. sit dy: dx e
  7. ifferentiando jum aequationem 1. Ht dd10 + du. y 80 unde tollendo y.
  8. fiet 10. 21 - 11.20 =0, et in ea 20 = dio +ne et 21 d1. et fiet: 110d11 = 11. 11e = 0
  9. Naut interpetenur per aequ. 2 et 3. est protera a pono dio - 1. 314 2. G2X + 3. BX 14 34X e et
  10. d11 = 1. 41 + 2. 42X + 3,44 X + 4. 44 X et. Ergo ex ∞q. 9 explicando fiit:
  11. + 1. 30. 41 + 2. 30. 42X + 3, 3093R + 4. 30. 4aX et ino = 40. 40 + 2. 40. 41X + 2. 40. 4 2X + 2. 40. 43. + 2. 4044
  12. E1. 31. 41 +2. 31. 12. +9. 3. 43.
  13. =1. 32. 41. + 2. 32. 42
  14. - 1. 31. 40 ∞ 2. 32 40 13. 35, 40 - 4. 19. 40
  15. fit + 41. 41 +2. 41. 42 42. 41 13
  16. etrs eseu 2 + t=Oe
  17. 4a it datr aequatio:
  18. 1aora oL 1EX ex = not MIXrBX e
  19. cgo 4B+hD=
  20. fiet 28 + hD ODe et 40= 0gC Ergo
  21. =1. 30, 41. 110 +2. ZC AENoX + 3,30. 43. 1OX +4. 30. 44 110X + 5. 30. 45. 110 X 50. 46. 110X Ck
  22. 1. 30. H11 d 2. 30. 2. 11 0 + 3. 10. 42 1. 0 +g. 1
  23. +1. Se ALI a+2. q aune. 2o f q. M. ta o. eu. e
  24. 41. 10 a. 113. f2. 1
  25. 1. 31. 1
  26. = 1. 31 40110 = 2 BE. gonco X. 3, 31. 40 (OX - 9 14. 90110YX - 5. 35. 0 110 X - 6. 16 o11B. X
  27. iplicau L , 3L. A. 1 = 2. 3 40 poX
  28. pb. 3o0.g1i 40. H sil e 3. R. H:, 4dta r mt = l. 51. 48. 11 0 - 2, 31. 40. 111 a 3. pp. qu 1(1 1 = 4. 34. 4e llic
  29. 1 H ag2+ t214
  30. etto reoqu
  31. =151. 72. 12. - 5. . qus2. - 3. 37. 4 12.
  32. ne
  33. equ (16)
  34. + 40. 40. 100 + 2. 40. 11. 1or ft 2. 40 92 BX + 3. qu. 43. loB + 2. g0. 4 4 o X +2. 40. 45 1VX
  35. 4 40. 40. 1010 (2. 40. 41. 101 , +2. 40. 2. 101. +, 40. 13 101. 42. 90. 44 101.
  36. = 40. 40102. + 2. 40. 41. 102. +2 40. q2102 + 2. qu. 3 102
  37. + 40.40. 103, +2. 40 4 103 +2. 40. 42. 163.
  38. comparando, fiet ponendor gu et co esse datas aequales umilutiu
  39. 312 -30 1oS, 130. 16 31 1 = 100 +10G 21O seu 41 = u0 3t . 100. 30. jem ipsas 100, 11, 112
  40. Sed hic eundium per gravus primum enim nonamus extare 30; 40, _, non ultra, et fiet 116 = 40. 40. 100, 30. 41- 40. 31
  41. comparando inveniamus
  42. 100, + 101, 102, et
  43. si extaret tantum 4 30, 31; 4D ghecet e = 430. 41 + H, :, 40 + 2. 40. AX + H. 91 X
  44. i extucent tantum 30, 31, 3; 40, 11, 12. ficet C = 139 -2. 3
  45. sit jam ( C = a:, 20 +21X +22 X, fi et 20; 2, 1 40 45. 1 3
  46. rt 2t 12 a2F
  47. -2.3. 4 adeoqe e = a 40 + a 41X + at2X:, _10 r 10 9 X
  48. 30= a 4 + 2. 3240, : 2. 42 fit 24 40. 42 +231 40. 92= au p2n. teg
  49. a 412 (+2. 32. 40. 41) -= 2a40. 42 = 2. a40. 42 +240 (2. 32. 40. 4D seu fit 41 = 4. 40. 42. seu 21 - 4 6.
  50. 31 = a 412 + 2. 3240. 41 = 2a40. 42,: 2.40. 42 31 = a42 L 71 41 +32. 41, :, 42.
  51. et dantur 40, 41, 42. restant 30, 31, 32. X 30 = a 40+ 3140: 41
  52. Ergo e = a:, 20 + 2. 190. 49X + 22X. sed ita rursus nominator est quadratus.
  53. comparemus cum e = 21 +22X + 23X + 24X + 2GX,:, ( 40r 4, HX = 3E fit 30. = 2 +31 40,: 4 et hoc 121. F2. 31. 40. 12 - 2. 32. 40. 41
  54. (+2. 30. 42 X 1 + 3.50. 43X 333
  55. -2. 3
  56. Se ex laret tantum 30, 3133 33; et 4. 4142, 43 fieret e - +3
  57. = 22. 41 seu 31 = +22. 41 + 2. 32.40. 419: 40. 42
  58. . 40. 40. 41. 42 + 41. 42. 22. 41-2.41. 12. 21. 42 +
  59. 3. 21. 40. 42. 4313 31. 40. ate q0. . hitart
  60. 91. 2 F 40. 41. 42 + 7 33. 49. 40. 41.42,: 40. 41. 42
  61. 31. 40 91. 21. 42 = 40. 41. 42. 23. Ego 3
  62. 2= Em 32 = 4. 21. 42. 43 - 2. 22. 41. 434 29. 40. 425e + A. 33. 40.41. 427: 4. 40. 41. 43
  63. et ex Xt fit 32 = 25 + 33. 42,: 43 et fit 4. 21. 42. 43 - 2. 22. 41. 43 4 24. 40. 42. = 4. 25.40. 41, 5, (1340. 41. 42( 3. 40. 41. 42) =33
  64. +241. 9240. 41 a
  65. Ergo 32= 43. 2 41.
  66. Etrursus +9. 21. 40. g2.43 - 3. 22. 40. 41 453 + 13. 40. 91. 42. 43 - 25. 4041. 42,:, 40. 41. 43 - 3. 40. 41. 42. 43 = 33
  67. 43 - 22. 41. 41. 43
  68. 14. 21. 41 4113 - 2 u. 41. g2 4 + 24. 70 M 5 -4. 25 a0 31 32.
  69. q0e aytars. 1 nalt3. 3 aeid.
  70. 21. 40. N. 45 427 2.40. 1 47 57
  71. +15. 2 avin 15 - 9 12. quaits 1 23 4 4. 42 13 + 24 40 AI. 4Z + 2. 25. 96. 4(. 42 = eA. et aeres
  72. Et 2........
  73. 3. 24. 48. f2. 43 -7.425. 48 41. 4.
  74. iuo
  75. (Ex A. B. 0 ost =, C 10 matm ese 1 . 2 B t qea
  76. 322. B 28. 4o. 1 3+ 291. H. G 3C. 5. Ap. 1
  77. 10, 840
  78. mu ultina melioiem quam
  79. hactenus viam sum ingressus
  80. Hauui, sed circa eam fui bagatus
  81. impatientia prosequem
  82. Nom angpusa eq. 16. suficit oeuir
  83. sen valorim ipsius edatum iu
  84. derivari ex est con fugere
  85. iri us t abaant
  86. ob 30, 31, 32; 40, 41, 42 fue. 31
  87. Ob, 30, 31 N2 33; 40, 41, 42 asto 1 2. 40. M X e. 4
  88. uo isiit i i . uarini
  89. 2243. 2. D- 4. 121. 42
  90. 2.4 3. 4 = 4 40. 4

Cite

Leibniz-Handschriften zur Mathematik LH 35, 7, 14, fol. 1r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068085:0001?run=73