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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 67v

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: 0.83.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 70r); this page is its left half.

The machine reads it as

  1. 19) Antequam evolvamus aeqq. 11. 12. B. 14 articuli 18, explicemus aequ. 8 articuli 16. tollendo 512, 323,
  2. 712, 124. Nempe per aegy. 9 et 10 articuli 14, et per aeque 1 et 2 articuli 15 fiet (1mo), 512 = -(15: a) 23512: 123 et 523 15. a) 1eseg: 12
  3. et 712 = BF - B71a) 23712: 323 et ry23 = (7. a) 12G25: 3it. quibus insertis in aequ valoribus in aeq. 8 artic. 16 subistitutis
  4. quae erat 112. 512. 323723 = 137. 523. 312. 712, fief -112. 15. 27612, 323. 37. 127152 - 12g. 1, 12535. 312. 37. 23712. seu fiet
  5. N2. 3237, 235122. 12725= 1232 3122. 12525. 137 12 sen 12. 323;, 123. 312 = + 12523. 23712, :, 2352. 127 25 = 33. Xn:, 512. 729
  6. et 112. 723: 123. 712 = 112. (12723: 312) = - 123. (23712 -323) se uE 129 13 12 = 112. 323. 12723,:, 122. 312. 23712. Unde per 2
  7. 5x3. 312,27512 323. Et Porro u12. 512, -, 123. 523-
  8. S2Z12 23512, =, 1232, 12523 =(mo) 31. 712, :, 323. 723
  9. eris 112. 723, :, 123. 712 = Ato) + 12523. 12723, :, 2351r 63712.
  10. et 17. 512, : 312. 712= -112 (15: a) (23515: 123), : , 312 (37. 4) 23112. 323 = 112. 323. 15. 23512, 5, 123. 512. 3]. 23112. se per 2
  11. (15. 12523. 23512, i,37. 12725,. 23712 = (9n0) 123. 523, :, 323, 723. Et 112. 313;, 623. 712 = 123. 312,: , 512, 72
  12. (20) Ex aequ. 13 articuli 18. At per aequ. 17. articuli 14, fit - 7123. 21 1 4 712 St2. 3C5,:, 1723. 123. 312 - 121 . 143. 5
  13. 23 12523. 23512, 12523 -235127:, 12523 + 23512
  14. itidem quaeri posset, et 112. 723,; 523. 712 =. 123. 312, :, 5.2. 323
  15. -(5, a). _. 12523, 23312, 12523 -2351, :9 112.123, 12523+ 23512 su
  16. L7123, 125232, 123. 312 + 7112. 23518, 112.323,:, 1723. 123312 - 1712. 112323=
  17. 127 2),: 1723-1712 (1i2. 322 seu (+
  18. . 12717do) 1Stosa
  19. vel denique + 7123, 12523, 12723 f 7112. 23512. 23712, 1:, 1723, 23512. 12723 f 1712. 12523. 23712
  20. vel + 1n3. 25 E x a u. (
  21. 13. 712-1712. 512.723,:, - 7123, 123.712 +7112. 112, 723
  22. Unde post destructiones 12523. 2ysI2,:, ~B125 23H23BI2 2, 1723. 123. 312 e 15 27. 23112 - 1712. 17. 13. 2952. 1275, :, 4 7p p. 123. 82. 237122 + 712. 112. 315. 12725
  23. 5: a)12523, 23512, 125C3. 23512, i, d2 423, 11523+ 23SI 15. 12925 72. 22712 15 sp. 22. 127 25
  24. UIB EY aequ. 14 articuli 18 fit per ac
  25. bel Denic 4t) 125a3 - 275125. 1 12523+235I = 1723, 12523. 23712 4 1712. 23512. 12723, :, 7123. 23512. 23712 +7y2. 12523, 12723
  26. iculo coprobavimus
  27. 1723. 12523. 2371241712823512 12123
  28. . . . . . . . . . = 17 2 3. 125 23. 2371 ( - 1712. 429.
  29. (6t) 12723- 23712:, 133t 25t12 = 1723. 23512. 13723 41712. 12523. 23712, :, - 7123. 23512. 234712 7112. 12523112723
  30. erdantando 15, 3,7
  31. 5t) 1272323712; , 12123+23712 ( = - 7123. 12525,12723(L 7112. 23512. 23717
  32. e 1723. 23512. 12723 + 1712. 12523. 23712
  33. Et ex aequ. 12 artic. 18 fit per ∞eg. 6 artic. 15. ad instar aequ.q
  34. tem illius coincdere numertori hyius, Itm et nomina oqu alis
  35. 123, 12523, 12723 47112, 23512. 23712)
  36. Has Utamur jam egg. 2, 4, 5, 6 articuli praecedentis et dividendomultiplicemus aqu02 et 6. nvi-
  37. in labenta deptris n aequ. 4 et 5 numeratorem illius coincidere nominatori hujiu
  38. (200) 12523- 23512,:, 12523 t 235125
  39. Ubi notandum pui aeqq. 2 et 6 no
  40. 1schCZ - 12525. 23712 15 - 23512. 12525 12725 4 235I2 12523. 23712 +2723
  41. Sed nondum hinc aliquid magnopere apparet
  42. 12323. . ZZIIL. HB 4. 125C3. 27SI2. 23712. +23 51. 25712. 12723 +23515. 21712
  43. 12515. 1272524 12523. 23712 127234 23512. 13523. 12723
  44. +12523. 12723(12523, 12723 27712 4 23512. 12523.127154
  45. si aequ. 4 et s eodem modo conjungas ut aeqg.
  46. et prodit idem nempe aequ. 1
  47. (22) Quo brevior autem imposterum sit scriptura pro
  48. et ex aequ. 1. articuli praecedentis fit: 200)
  49. 12523, 23512; 12723, 23712
  50. Conjungamus jam et aega. 2 et 5 articuli praecedentis, considerando
  51. tm i ifferre signas,
  52. 523. 275. 127 + 1712. 125. 237 ideu podis si dividas aeg.
  53. 712. 235. 127 erq cpant.
  54. Ex his jam fubus equatur nibus articuli
  55. deu piait quod aequando et
  56. (lujus nempe 2, 3, 4. solvi possunt omnia
  57. eadem praesturi possunt quae ex aequs. 4, 5, 2, 4, 5, E. arliculi 20. quoniam ex eo quod composita diverso modo
  58. et fis oteo dividendo s per aegr fit
  59. susterestat aequemus aeqg. 2 et 4, quo case
  60. 7123: 7112, et 1723. 1712 quorum valores substituti in aeq. 4 dabant aequationem ali illis liberatam
  61. 7127. 115. 127 47112. 235. 237
  62. Haec ergus ut praestemus pro, aequ. 2 pa artic praecedentis per constendrum scrbatur (e
  63. 1723, 231.12771712, 125. 237
  64. ndicum est leas non nisi tribus aequisollere
  65. 100, 210X + 100. 20, y. seu X: y = op. 20. it o 2
  66. +(25 + 235, 127 + 237)125.127 + (125- 23531271 57) 195. 137
  67. Et pari modo ex aeq. harticuli praud. 1 B 4 (ir5 +2)5, 127. 23 ) .3 5. 127 4 (125 335, 12 H . 11 25 57 4 ande X - + 31 4d
  68. noK LIBV,: 210X+ 201y 100, 200
  69. indi Adeoque restituento priores quantitates 2
  70. 1(125. 235, 127 +231) 235.127,. Cu p2oG 17 - 1 ) 125. 13), uti tip 2 et R - 7123 (t - 7112
  71. articuli, 20 icet enum illa non sit comved homoschetia, tamen vel ide
  72. quae obssant, aut prodibit quod sicebit duplicare percuutando et
  73. 7123 et 171E tolli in aeque. 4 artic. p 22
  74. et ex aequ. 2 et 3 713 = 9 7112 (17A= Z 1723
  75. D-struS, etcL 6, D, 8. Gsehabent
  76. ata meVI mostimoci
  77. 25 1u, (125 - 236, 17- 257) + 23 5. 23, (125 F235, 713, 6- + (125 + 235, etc
  78. Cinsirk niress, urtn) F 135. 2Bus, antIE((125H235,127-237) 235. 127 4 C125- 225, 127 1297) 125. 257
  79. 1((125 + 235 177+ 297) 15. 127 4 (125. 135, 127 - 237)235. 237
  80. ys127 (V2st2y5, 17 - 237) 235. 127 425 - 135, 127+ 237) 15. 2y, )
  81. 5. 27.G +u5. 235. 23F + 295. 237. 127 f. 235. 251
  82. 4 12s. 23 (125 - 237, 127 + 23)) 235. 127 + (123 +235, 127- 237)125. 257) cue
  83. odeamue an non nihil contyahere liceat C = +, 1251. 127 = 125. H7. 237 - 235. 125. 127 225.12i2t
  84. D = 1252 127 +125 127. 237 + 235. 125. 1272+275. 125. 127. 137 +125. 235. 237. 127- 125.95. 23,-235. 257. 11 1275.9)
  85. 8 = 7, 25. 275. 127 = 125. 235. 127. 237 +2352727- x352. 127. 237 + 125. 237. 127412522372- 235. 125. 237. 127 -235. 125. 237
  86. = 125. 235. 1272 4 115. 235127. 237 -235t. 127 - 235. 127. 237 4 125. 237. 127 f 125. 237 +235. 125. 237, 127 = 235. 125. 737
  87. rnnsae fr u2 23512. 25712 um n am mst
  88. (12523. 423512, 12723+23712)12523. 127234 (2523 - 23512, 12723 - 25712) 23 512. 25712
  89. cem prodit mo) oratroon
  90. y123 4(12523 -23512, 12, 23- 23712) 12523. 121
  91. Qua bavi, autem imposterum
  92. 137I

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 67v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0134?run=74