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Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 42v

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.

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. 43r); this page is its left half.

The machine reads it as

  1. supere
  2. tu
  3. sit (4) 2+ siet sf + 99 +2B) (2 (3.) F
  4. Aalia Methodus ex natura numervum, solvatur plene
  5. pars problematis
  6. Cas invenre tres numeros ata ut ductum quorum libet sit summa
  7. quadiatus, ita, ut Tabula ecrum condit condi possit
  8. quae ab
  9. solvatur deinde et plene _ altera pars problematis invenire
  10. ries numeros, ita ut differentia duorum quorumlibet sit quadratus, ita ut etiam
  11. Tibula condi possit
  12. Hae rinae Tabulae irunt quasi duo loca
  13. quoum in Geometria, quorum intersectio dabit quaesitum. E
  14. inverta autem loge seu constructione Tabulae, apparebit, quando
  15. concurrere possint
  16. ax L ay = I ax + az - mn
  17. ay +az= nn,
  18. et fiet
  19. ax = 1L - ay = inm = aZ et ay = l - mm taZ = nn - az, et fiet H- mn -nn -
  20. Mm + nn - U1 = 2 a Z
  21. U + nn -mm = 2ay
  22. tmtum - un = 2ax
  23. Timsus AX ay = pp ax - a Z= 79
  24. 2a
  25. demm un= itaque satis faciunt tres quivis
  26. quadrati, tales, ut duo quivis sint tertio
  27. majores seu quadrata laterumcursos trinihiti
  28. ay- az = rr, fint ax = ppt ay - 49AaZ 99 + aZ
  29. jus a fit qu + az a pp = rrtaz fiet 9q = ep +YY
  30. Ergo mane est fit non possunt eq hoc tres inveniri literae X, yiZ; sed assumta _ y pro artitnio et posits
  31. imm son pp Rrnnum si quenn
  32. cpptay et az = agApp- 49, prodibunt aequationes duae em na ppL su him i
  33. x = +aZ sit az = ay rpp - 4q, sed rursus = _ ay- VV fit Pp + rY = 49
  34. ax = eV ay epp et 2aZ = 2ay - XY; et 2 2ay = U +nn - nm
  35. Utmm- m
  36. t op se U= untgue req
  37. de Utnn- mn +ipp = Utmm- nn
  38. seu a pp + nn =mm
  39. res ergo ad has tres equationos reducta est
  40. PP + N = 99
  41. mm+rr = U
  42. Utnn-mm 2rr = mm +nn - U
  43. seu u mm mmtrr = U
  44. a pp- gq i + ubi U et un occurrunt tantum semel
  45. antpe
  46. sp = 19- rr
  47. Pem An Ipp = um pp +rr = 99
  48. pp + nn = mm
  49. sit m s s G iffgu sit a = = ff f0g et am = 259 fit al = f + 99
  50. tursus) ap = + dd q ee an = 2de am = d dd + ee = 2fg
  51. stat d+-2ddee + f++ - 2ff99 = aagq, et pro g ponatur ddtee,. 2s
  52. siet s 4 erddee +f p quod si praeterea Ydd ee aepur s ff- gg +f +gg possimus
  53. t aequare ipsi 2de, habetetur aq = dd te = am, sed non potest aquni
  54. conicet, aqam si facimus +s 4 gg 59 +dd (ee - 2fg, h fieitaque = ffrgus, sed
  55. haec rursus non licent d+ = 4ssu Eddee fit 4ffgg BddDC f4+ g- 2ffg9 = A 194
  56. sit f + gt + 21f99 = aaqqueet 4ddee quosi effet 2de (1 f+ gg et ag =
  57. id siesset 2de = (+) Ss () gg et aq = 2f9, satisfieret etiam huic aequationi
  58. q tantum opus est, ut simuls+ 2de = (+) B (4) 99 et dd + ee = 25g
  59. fit dd+ ee t2de = + ff + 99 + 2f9 e = (+) sf (+) g9, : 2d, quo valore
  60. substituto in altera aequatione fit dd + s4+ gt- 2559) = 2fg, seu fiet
  61. 4
  62. +d
  63. 4
  64. +g - 2558 = gddfg (A)B ()gg = dd Y 2d sist- Dd) solvasum
  65. dglaraliter aff. dd= quadralo
  66. (H) 99 =
  67. e hh sit du Fd = fβ h= f9V, fiet 2ff. s + 2B+ BBH
  68. ( +) 2(fβ) (5_)) seu
  69. (+) S (4)99 = 2ffa2(2) ( + 2
  70. BB+VV seu βBB - 2β) = ff + aq jou
  71. sa
  72. =que Be+ YY) Y au AN sin tou (8P. V). qull6+y)= al. et
  73. a
  74. fb.
  75. et
  76. lristererorisro
  77. et f = β(+) P: 2(3+))
  78. spus 4 qu (3(177

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 3, fol. 42v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068000:0084?run=73