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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 169v

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: 0.86.

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. 170r); this page is its left half.

The machine reads it as

  1. Formula l xx + lmaxalnaa est ita aequanda quadrato fi yy, ut fiat
  2. a 3022+3) a Z + 3raa
  3. 3027+31a2+32aa
  4. dprehendi posse fieri 22: 2 = 20g 39: 30 = 43: 40
  5. et ita minui aequationes comparatitias seclvocalento
  6. suppono praeterea Denominatorem 302Z + 31aZ + 32aa esse quadratum a 2130 + a Y32, unde fit
  7. 302Z+ 24Z130. 32 + 32aa et fit 31 = 2 130. 32 et 31: 4 = 30. 32 seu 32 =31:4.30. Ergofiet
  8. 22: 20 = 31:4. 30 = 4240
  9. H, 20. 20 Z7 +2. 20.21 aZ
  10. lumm 20.30.. + 1. 20. 31..
  11. 1. 21. 30,
  12. ln, 30.30. +2. 30. 31..
  13. l, - 40. 40.. 82. 4091..
  14. (1) aqu. 0 (2) aequ. 0
  15. aaZZ
  16. + 2. 20. 22
  17. + 1. 21. 21 Z + 2. 21. 22 a3 Z +, 22. 2c
  18. + 1. 20. 32..
  19. 1. 21,31..
  20. 1. 22. 30
  21. + 2. 30.32.
  22. + 1. 31. 31..
  23. 8- 2. 40.42.
  24. -1. 41. 41
  25. (3) aequ. 0
  26. + 1. 21.32.
  27. 1. 22,31. + 1. 22.32..
  28. 42. 31. 32, +132. 32
  29. 82. 91. 42.. A1. 92. 42
  30. (4) aqu.0 (5) aequ0
  31. si po 22 et 3 cer substituantur valores, coincident aeqq. 4 et 5, cum aequ. 1 e1Z
  32. seu aequationes natae ex destructione termini seu ultimi et eta de
  33. atimimpenaltim et altimi coincident cum aequationibus ortis ex destnctione lepmini primi et
  34. secundi. Nam ex aq. 5; fit 20 32H+ 29. 3 20. 327 + 26. 30. 3234 +30, 32. 32 40. 327-0
  35. unde divisis omnibus per 32 prodit tadem aequatgo quae ex repmino primo; idem
  36. Eodem mode terminus pepceltumus reducitur ad secundum. C sufficiunt ergo aequatione
  37. 1, 2, 3, nascentes ex destiuctione Termini primi, secundi, tertus.
  38. Exprimo
  39. 20l + 20. 30lm + 30 In = 90 l. Habetur ego 20 per 20 et 30
  40. (2. 20l. = 1. 30m) 21 + (1. 20m + 2.30n) 31 = 2. 40. 4 1su comperdio _ 7o l2 + vol 31 = 2. 40. til
  41. seu 70. 21 + 80. 31 = 2. 40. 41 u et quadrando 70. 21+ 2. 70. 8D. 21. 31 + 88. 31 = 40. 91
  42. Exsecurto
  43. As 20 (4. 90 - 78) 21. 21 + (. 40 lm - 2. 70. 8oll) 21.316 + (4. 40lh - 9dU) 31 = 0 5V
  44. quarum una non habeat i altera habeat, quae erunt:
  45. 2 20.22l + 20.32 lin + 2230lm 12. 3032ln= 2.4042 e (n sit EP
  46. vellare int dua
  47. usiderari debat, ut involvens 1)
  48. sit 42.42 = 32. 32 In. f 42 = 321 nol)
  49. et firt (20. 32( + 22.30) lm ~ 2. 4042
  50. e 32 = 22l =0 seu 32=_- 22l: m et fiet 2. 21. 22l( - 22(: m) 21M L 22. 3,m = 2.3, 2 l: m) n
  51. 2. 4V4C2. 4132 S(n: 1) seu 21. (23lm F (22) 3imm = 2. 31 (22)In (== 2. 41. 32lm Y(n: 1)
  52. = - 2. 41 (27)1(:. n) Un) s(n. l) C. =- 2. 41l AIn 42 = 3+(4. 30) In: 1)
  53. fiet 4. 3P: 30 = - 22. l. m seu 22 = - ~31 m: 4. 30l
  54. 4. 2oUm = 2. 70.8013= (4. 20 Um (F 4) ~. 3olmm t 4. 3o lmm. 2l 30 2es Elgoki r3oik Eli holion ihrutryu - 20. 42 = (+) H
  55. quid si Hoc ejqu omisso videamus an liceat aequationem destructitiam Termini medii
  56. 24= 31,4.3
  57. aequ. (2. 40. 317+ 4. 30. 417 =) 2. 20. 31 U+ (2, 20. 30.3 1 F 2. 30. 31 b) . (30. 7. r 2 30. 70. 80. 21311 38 863, (ll. 46).
  58. 4. 40= 76 = (4. 20+ 4. 2030 lin 4. 30 br (. 4. 28l 4, 20. hol m) 3omm = 50 (atm - mm) - 30 pl
  59. 4 40 170.8o, = 4. 20 H+ 4. 2ogolm 1 F. 3D In 52. 2olhom 2 2. 2ol. sn 2 3on- 2. 3om. 2om- 2. 3m. 2. gon
  60. 4. 40- 7 = (4. 20 I(+ 4. 20. 30lm f, 4. 30 ln (= 4. 20U 4. 20. 3olm 30mm = 20 (4ln - mm) = 30 pl
  61. 4. 40Un -80 1 = 4. 20Un (F 4. 20. 30 lm, 4. 30 lnn) - 20mm (-4. 20. 30m 4. 30 l nn)
  62. 30. 21. 21B = 2. 20. 30. 2.31-+ 20.35=0 seu 30. 21 = 20. 71. quod es non licet
  63. Ergo rec licet facere 20 22:20 = 32, 30 = 42:40
  64. etiam
  65. Ergo ex aeq. 5 fat mattilicat pert, fiet
  66. et fiat
  67. Veniamus jam ad terminum 3tium seu medium quidaf ubi pro 32 ponendo 31: 4. 30, et pro 22 20. 31: 43 8 d2, 90. 2: 430
  68. 2202 2 0l + 1. 4. 30 . 20. 31P. 4. 30. 25 (+ 30. 3i, ( 4. 30. 2. 3lm (4 30. 3 m 2. 3d. 31 438 dinx
  69. et divisis, omnibus per 30 fit (4ac 70) cessu ta q 90) 2t q + (4 40 30) diln
  70. = 2. 20. 30l (mm - 4 ln) = - 2. 20. 30pl. Et tandem explicemus
  71. = 2(20 l (4 ln = mm) = 20 pl.
  72. multilicata per l, et divisa per pl, fiet:

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 169v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0338?run=74