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Leibniz-Handschriften zur Mathematik LH 35, 3 B 9, fol. 1r

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.

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. 2v); this page is its right half.

The machine reads it as

  1. dul. 1675
  2. LATE RUM
  3. DEBIs 2CTIONI E2
  4. Radices irrationales nova, quibus ad resolvendas aequationes utor, primo statim
  5. aspectu mihi dedere tabulam aequationum quarundam, omnium graduum quae
  6. resolvi possunt per has ipsas irrationales sui gradus. Tabula autem haec est continuabilis in intinition;
  7. 2
  8. 7
  9. Z
  10. 76
  11. e
  12. etcus
  13. A
  14. 1 4
  15. 1 + p (+3P
  16. N + r (+p L
  17. N. + Y (+) op Z - 5
  18. 1) + qu (4)6 p Z+ - 9p y2
  19. 1. 3. 5. 7.. Respondent ergo eotum constrctro, constructioni Tuangul;
  20. 1.4. 9. 16
  21. 1. 5. 14. 30
  22. 1. 6. 20.50
  23. N = X 1f7 p Z - 14p 73 (4Xpd Z
  24. N + Y (48 p Z6 - 20p Z+ (4 16p Z
  25. eK
  26. ete
  27. etc
  28. ete a
  29. 2
  30. e -97Z
  31. A er 19 p27. 27pe Z (FBpPZ
  32. Hanc Tabulam initio velut v particularem concerderaverm neglereram, sed
  33. Lattirum
  34. postea re altentius inspecta comperi generalem in ea contineri sectionem Potestatam
  35. Laterum
  36. latere altrens
  37. Sectionem autem Poteotatum appello, expressionem potestatis a Toto, per sotestates
  38. à tata in serieres, aice dente potesate aequate detig rone
  39. partim a toto partim sexis a partibus Latens qua de re non nisi duo habuimus Theoremata, alterum
  40. Euclidis pro Quadrato, alterum sive scixionis Ferrei sive quisquis is est qui regulas invenit
  41. a Cardano sublicatas, pro Cubo.
  42. ACpF AB, (BCB - 2L 11BC
  43. alicubi
  44. Sit linea AB. secta ulivis in C. demonstravit Euclides quadratum ab AB aequari
  45. quadrato ab AC, + quad A CB, +bis rectanus. ACB.
  46. alterutra
  47. alitume
  48. Et idem demonstravit,
  49. quad ratum ab AC, acorutu partium, aequari, quadat ab AB, + quad. a CB. - rectanus ABC
  50. AG BAB-BCB Inventor Regularum Cardani demonstravit cubum ab AB aequari cubo ab AC, + cub. a CB.
  51. A B +B = cb
  52. ter Rectanu sol
  53. +3 Rectangs. solide ACB A, sive Ccomprehensex sub rectis, AC, CB, B A: et Cubum ab AC aequari Cubo ab AB,
  54. = cub. a CB, - 3 Rectang. solid. ACB A.
  55. Haec Tabula, continuata, pro omnibus aliis potestatibus altioribus similia Theoremata concinnare docet
  56. Nimirum. Surdesolidum ab AC aequatur surdesolid. ab AB, = surdes. a CB, - G Rectanu ACBA in tH C, E AD
  57. quod concidit aequationi Z _ +r - 5p Z3 - 5 pZ, si ponamus Z AC.
  58. a Daiean D al+ FI soc
  59. modo
  60. si penamus Z ( AC.
  61. IBAC+ L+ ABC
  62. pe= ABC
  63. et 4Y 6I AB. _ CB
  64. est enim - EPZ = sPZ A SPZ in Z + p soiee est autem pZ e) Rectanus solid. A CB
  65. fitque
  66. E ⊓. + (5) AB. = 5 G G ACBA in ( AC
  67. B
  68. FS ABC
  69. Quod verum esse calculus docebit
  70. sive in literis, sive in
  71. numeris
  72. FCC 1676. Numeu Tabule sic progrediuntur oligu descnsu.
  73. Arithimetici Pascaliani, moda prima series, cujus caecerae
  74. sunt summae aut summarum summae, non ut allic sit
  75. 1. 2. 3. 4. sed 1. 3. 5.7 Unde facile hujus Tabulae
  76. uneri ex allipsuo separita catento Mvemur possam si
  77. illi dpicantur
  78. petetatis pue. a qua
  79. tionis purae.
  80. Latus voco radicem
  81. Sed ut seneranter
  82. 3H D ACBA
  83. A A ACp

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 9, fol. 1r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068259:0001?run=74