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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 30r

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. in
  2. sax or
  3. Quaeritur sex unde pendet quade dimensio Linea conicae, et plerarumque
  4. quad incus
  5. hunc multarum cu
  6. DX+C
  7. in
  8. 10X + 12 in 50X +52, aequetur quadrato, posito x explicari rationaliter, vel saltem modo
  9. revocabili ad rationalem. Sit ergo 10xn B y+EE, Boyy. Similiterus
  10. es sit ergo X= 41y +42,: 3oyy+ y +32 qui valor est revocabilis
  11. ad rationalem et fiat 10X + 12 = B 219+22, : 130yy+ 31GH32 _50X5 = PIIy 162,: L3oyy+319432
  12. et (pers, D) eKCd VIX+I2, 50X152=2y+22, in, 619162, : (30yy1 31y+32 qui
  13. valor etiam revocabilis et ad rationalem, et simul ad rationem cum ipsa X (aeq. 2.) correvocabilis ad rationalem
  14. superest ergo ut tantum efficiamus aequationes 3 et 4. explicando X per aeq. 2.
  15. Ex Ex 3per 2 fit +10. 41 a1yy + 10. 2. 91 42y +10.92 n ( 2I 21yy + 2. 21. 29122. 2
  16. + 12 30 Hy + 12. 312 +12.32
  17. i
  18. fit 21 Si. aF13o 22= 10gr +n, Z2 et 2. Sioai+n3O, 1042+n = 2. 10. 41.42,: 12 3)
  19. Et similiter
  20. ex q2 61 = 150. 41152. 30 62= 150. 12 +52.32 et 2 150. 45 + 5. 30, 50.92+ 5232 =2. 50. 41. 427 : 52 = 31
  21. Et dups ipsius _3. valores (ex 9 et 12) inter se aequando habebitur 4 (13) in qua sunt
  22. Incognitae 41, 42, 30, 32, ex quibus tamen unam ess mmaratiam jam tum
  23. alsumtsti
  24. patet ex valore ipsius X. Sed et ex tribus reliquis una supl superflua est;
  25. ob legem homo ut eventus docet, adeoque si ex quatuor assumtitiis incognitis
  26. duas faceremus impossi aequales nihilo, v. g. 32 et 41, omnes incognitae evanescerent
  27. compandii causa fiat 0= 10. 4(2+, 12. 30, 10. 42 +12. 32 et D = 50. 41+52. 30, 50. 42 +, 52. 32 et B - 0 1 501
  28. Ergo ex aeq. 13 fiet , 10-, X D = Bnseu B41. 42 seu 52 O + 12D - 2, 12. 52
  29. B41. 42 seu
  30. 52O +12 + 2. 12. 55 0D)+ B 41. 4242. 51.D B. 45. 422 4) 2. 520D. Videamus
  31. 2.
  32. au liceat n 41 vel 42 facere = 0 ita enim plurimum contraheretur calculus. Nempesit 42 =0 et
  33. Ex aeq. 17. fevet Gr0 = 12D seu 52. 12. 32. 10. 45 ( 52. 12. 32. 12. 39) = 12. 52. 32. 50. 41 12. f2. 52. 52. 30)
  34. fieret 52. 10 =12.50. Quod est contra generalitateem datorum.
  35. superest ergo, ut si calculum contrahere volumus faciamus vel 31, vel 30, vel 32Z
  36. Sed tentemus in d, fit 0= 16 41 43 + 10 12 2Bq sed tentemus in 32 et sit 32 0. fiet
  37. en
  38. O 16, 41 42 +10. 12. 30. 42 et 3 = 50. 58. 41. 42 + 50.52. 30. 42
  39. 510 = 5i, (1091 424 2. 10312. 30. 4. 10. 12. 30. 42
  40. 1218 = 1, 156. 41 42t 2 58. 52. 30419d +50. st. 30. n
  41. B.n= 41, 92, (10. 5224. 10. 52. 50. 124610. 52. 5012 4. 10. 52. 50. 1 + 50. 1
  42. (4
  43. 252. B. 31 D-,- 255. 4142 (18.52. 11. 92118. 12. 52. 30. 427. 10. 1250. 52. 10. 41. 9V- 2. 10. 12. 50. 52. 10. 12 3042412, ∞. 10. 41. 4 150 10170
  44. 2M8 qnD - - 2 1 M N, (10 52. 50 11n + 10. 52. 5952301 = 2. 10, 12. 50. 52 50. 41 1 - 2. 10.125052 5052 3a 47 12 50. 50. 41. 3 10. 5 5220. 9V
  45. 2.1251O -- 2.1250, (10. 50. 41 42 16.50.52. 30. 41- 42 + 10. 12.50. 30. 41. 927 10. 12.50. 52 30.9
  46. Hanc ergo aequationem , ex aeq. 19 per 21, 22, 16 explicata factam, ordinando destructis destruendis
  47. fiet
  48. 41,
  49. ao.
  50. 4. 10.12.50. 58.
  51. 4.50. 52. 10. 123.
  52. 30, 10, 12. 52
  53. 50.52. 12
  54. =a 10.125857
  55. -4. 50. 58. 19. 12
  56. ro 1ese
  57. =2. 10.50. 123.52
  58. quae aequatio dividi potest per 1050, 12, 52, adeoque tandem fiet
  59. 30 4 41, 12501 1052 5052 125d, : 10 521501-2 1. 52
  60. Ergo cum 32 fecerimu o, fit inde similiter 30 = d nisi f dato permittant feri 105 e
  61. nisi data cermittant Aeri 1 1on 2 1 5o: n 2. 12. 51 = 0 se 10 - 22.52 70127:52
  62. et ex 10x +1.: 50 152 siet 2. 12 52 - 50. 15 X + 11 52,., 5057 X +52
  63. Sed ita evane scit 41. et fit 30 F 10. 12.52 - 50.52. 12 = 0. Ergo fit vel 30 -0 vel fit
  64. 10. 12. 52 - 50. 52. 12 =0 seu 10. 52 - 50 12 =0 quod ipsum non licet,
  65. sed nec licet
  66. facere 30=0. nam si simul 30 et 32 sint 0. tunc ex 9 et 10 vel 31 eliam sult 0.
  67. contra desiderata, vel fiet 31 = - 4. 10. 41. 42: 12. = - 4. 50. 41. 42: 52 et fiet 10. 52 = 12. 50
  68. quod nolumus.
  69. (241
  70. haec aequa
  71. 10. 12.52 -5051. 12
  72. 250,6.1 52
  73. 18.52-12.50-c

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 30r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0059?run=74