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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 25r

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: 0.81.

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. 24v); this page is its right half.

The machine reads it as

  1. Resumamus O aequationem et eme paginae primae W1DrI Z F 14DGF 2D Z HBDO+, 2O= 0
  2. compendio 12 DG + 11390+, 23 ZOvocemus 10DL + 100L6, et fiet 194 ubi Notu = 1124 + 113 et 10 1 2300
  3. 142 1488 + 14. 1448D + 114 DD = 112∞5 = 111. 144. D - 10. 144 25 - 140. 144h5. Itaque hoc dextium litus
  4. debet etiam esse quadratum, sildensi per constantem mutiplicetur. Eyf 9∞ - 4. 10. 144 5 4. 100. 144. h0
  5. 114 - 4. 1. 144 114- 4. IV. 144
  6. Quod comparandum est cum 37∞, DG + sest ergo fiet 2. 10 14. = a et - 4. 100 144 t 6 = si se
  7. 1142- 4. 14. 144
  8. Qu (114 - 4. 11.49) seu (4. 114. 14 - 112, )100. h5 = 10. 144. 4t seu si et
  9. 4. 116. 144 hE
  10. (4. 14. 144 - 1142) 1346 = 144, 1125 + 2. 112. 113. C + 13. _C
  11. sed inde sequeretur C et G rationem habere constantem quod non est permissum
  12. Set si initio fecissemus 1 4 4. M. 144 = 0 feret D- -10oho, Grrot, qui debet esse
  13. integer seu 127C delebet esse divisibilis per N2 + 13C
  14. itaqe praestabuit in faltor, intio statim venire ad divisionem, ob aequationem hajus pugicae primam
  15. si faceremus 1447+ 114D = 0, f et 114 - 111. 144 = 0, superesset D = 100h5: 1otu se et ha valor
  16. Quod videanus au fieri possit
  17. tuea I DD + 1448
  18. fiat Z - b~ lv + mh, :h
  19. quaeritur ergo modus generaliter efficiendi ut x si Z0 sit divisibilis per bZ + ex fint R- tath, et dibet esse
  20. erit integer, sec 123GC) erit divsibilis per mQ + 1130
  21. i ut dinisbilis per lov + nhv divsibilis per bZ + . v, id est per +blx + lnitum, pud fiet ergo lnv+ Imto
  22. t b m fit. n = b et In = bl+ ch seu bl = bl + ch, quod non licet, nisi sit c = 0
  23. R eoeamus ergo ad aequationem primam hujus paginae, et videamus a ex qua fit
  24. 111DD +14489 = 114 58 = 13DC, :, 112D + 1236 = 3103 + 3030 + 300; 000
  25. 410. 410. 144 3 +E. 410. 403. 144 18 + 48). 403 144. CC + 2. 410. 400.144 Dh + 2. 403. 4co1 446h- +. 400 qao 2t hil
  26. sit 8 = 410D + 403 C + 40ch et fiet M AB, :000
  27. et fiet 1et 8.3. 800. 111 DD + 000. 00d. 113
  28. 000. 40. 114 DV + 000. 403. 114. 55
  29. + 000. 400. 1149h
  30. BDD. 112. 310 77 +000.113. 303 9O + 113, 3031C-+000. 112. 300 Dh +000. 123. 300Dh
  31. Redeamus ad aequ. 7 et 8 expressas compendiose, et tollamus simul 44 et 04
  32. 000. 123. 310
  33. + M. 59 +1 YF+ ut ) f + n2 5+ 13D 138O + 12380 =0 2
  34. 2D + 14 O8 + 14Y + 1129P + 1130,: 144
  35. fint 144. 223 = 13. 244
  36. ad tollendum OG
  37. seu exsticando 144, 244, 133 229 Ex 24
  38. +21+ D +21282+ 21330,: 21
  39. 2a. g2. N. 98 +344. γ1300 + (2314. 4. +525. 11. 4) 04 seu ex a4. 7 t 8 fiet t ( b. h (b - a) (H +hib. 1), g9 (g9. + h (b.c)) = h (b - c) (99 + b - c) h) f. f (5f ilb. - a) h)
  40. seu 100. 144
  41. 11a - 4. 14. 144
  42. +=
  43. =: 212 W + 223 C 4
  44. pel (b- a) 0g = (b- c) ff et ex cgg. 7 et d compositis prodibil L 114. 2447+ 112. 244Q + 11324C + 122. 147
  45. incompendio vocitur 42 F +1 + 42C + 43C; 4 - 144. 2141 - 149 312 8 144. 21C - 144. 2227
  46. Hinc valor ipsius . substituatur in valorius aq in aequ n13 + 19+ XF + 1 B Y + 1I2 D + 1330 + 130 =0
  47. en compendio 31. DB + 214 8P+ 3147P+ 312 D9 + 31380 + 34907 = 0
  48. 24. 5 22 . 2138. +223
  49. 372. 41. H.. +344. 92. 128G + 344. 43. 438(57 F2. 34 45 41. 1 C + 2344. 91. 4310 +2 344. tr. 170g
  50. 114- 4. 11I. 144
  51. 314 414 311, +
  52. 1. 323. 47 44..
  53. Videamue quibur casibus efficere lieat, sit Y(22G+ 59300 + 5. 23 8D) extiribilis, posito d et D esse sumplices
  54. H4. 4g. 42
  55. rationales in capitulibus sit b2c; +63(C 460 = 0 seu = 630 + 69: 62
  56. 2.52263.60 -5236062
  57. 1(+533.62, 62C0
  58. =523.69,6300-5236062. Ch
  59. potit . 60 + 32. 63.6 4 5 3, 62 62 - 519. 62. 63
  60. et ee
  61. 60 + le tee
  62. qu (. 2. 522. 63.63 - 5237. 60. 62)
  63. 4. (522. 63. 63 +533...)
  64. cur. 60. 80
  65. 522. 63.634533...
  66. fit P = 2. 52267 53 - 523.60. 62, h
  67. 522:63163 + 533, b2. 62 - 5 23. 62. 67
  68. fiet qu (2. 522. 69. 67 523,60. 62) = 4. 522. 60. 60, 522. 6363 + 533662. =523,.60. 62
  69. seu qu 63 (4. Su. 6 60 F32f. 62. 65 - 4. sir. 5r2. 60 62. (3, = (1. 52, 65. 60)1 . 522 533. 62. fo - 4. sir. 123. 68. 62
  70. Et divsis omnibus per 52. 60 fiet (525 - 4. 522.533)62 = 4. 522. 523. 63 + 4. 522,523. 60 = 0
  71. 4. 522.523, 63-60.
  72. c
  73. 523.523 - 522.533
  74. seu Sc= 4. 122. 527. 63 - 4. 52 2. 523. 60
  75. Alliter 12027 + 102 vV + 112 3V aequandum quadratae in integris simelicibus capitalibus sit 00 Z = L 1X + 10h 0ov - 21C + 20
  76. ite ZZ + 10 12 523 - et 2. 533
  77. fiet 120. H. IIXX + 120. 2. 11. 10Xh + 120. 10.10 hh, jam ut 30XXF31 Lx +3Chli sic aequesur quadato, fiet
  78. 102. 2. 21 un + 102. 2. 21. 20... + 102. 2c. 20
  79. u nn iami v.
  80. 303. XX + 30, 21 hX + 9 31 3 h = 4 3. 3ebl - 30. 32hh
  81. 30. zoxX + 30. 7C hX + 30. 3 chlr et AL 31. 31hh = 30. 3eth
  82. nopod tet
  83. 522.60. 60 hk
  84. 302. 69. 8 1 t se3. 629

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 25r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0049?run=74