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Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 227v

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: 0.87.

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. 228r); this page is its left half.

The machine reads it as

  1. Ut jam ex hac progressione rationem Aggregalorum ex applicatis, seu
  2. assignata
  3. II sequitur
  4. si ex data quadam altitudine X, applicata sit y. erit ex altitudine 2 X, appli.
  5. calam fore R4c8, RCy3. et ex altitudine 38 applicatam fore Rger7 DYe
  6. Applicatae Parabolae ita procedunt Paraboloeidis ita procedunt:
  7. Si ex assigna
  8. ta quadam altitudine X. (eadem quae ant) applicata sit Z. ex altitudine 2X.
  9. applicatam fore RgCB RCZa.. Ex altitudine 3X. fore R9C 27 _Rc 7a.
  10. futurae sunt ergo applicatae Parabolae ad applicatas parabo loeidis, distantiis
  11. a vertice proportionalibus ut RC
  12. Esto figura ABC semiparabola Alticudo abscissa
  13. a vertice AD = X. applicata DE = y.
  14. duplicata abscissa ut fiat AF = ZX. Quadratum
  15. applicatae DE = y. duplicetur producti
  16. Radix quadrata R9 y erit = FG. applicatae quaesita.
  17. applicatae ergo aequalium axis portionum
  18. crescent ut Radices quadratae numerorum naturalium
  19. deinceps ab unitate; Rg. 1. Rg. 2. Rg 3. )Rg4
  20. Esto Figura AB C Sarabolocis Heuratiana, abscissa
  21. a vertice X AD =X. applicata DEE = Z. Duplum
  22. abscissae AF = 2X. cubus ipsius AD est X. Cubus
  23. ipsius AF est 8X. quadratum applicatae D. EE est Z2.
  24. Ergo Quadralum applicatae F- GG erit 87. Ergo.
  25. applicata FGG erit R48Z. applicatae erga aequalium
  26. axis portionum in larabolocide Heuratiana erunt ut
  27. Radices quadratae numerorum cubicorum deinceps ab
  28. unitate. Rq. 1. eg8 (R9 27
  29. Restat figura, quae.
  30. Nunc quemad modum reperta a Geometris ratio est, ope
  31. Arithmeticae infinitorum, quadrandi parabolam, seu colligendi
  32. harum applicatarum summam, ita tentandum est, an colligi
  33. quoque summa paraboloeidis possit, quod ita tentabimus.
  34. Applicatae parabolae ita crescunt, ut dictum est:
  35. seu
  36. Rg. 1. R92. R43. Rg. +.
  37. 10R91. 22892. 3.R43. 4084 4.
  38. Applicatae parabolocidis ita crescunt:
  39. RgI. 148. sq27. R964
  40. seu A41(1. 292,2 A43, 3. R44,4
  41. Ryt
  42. 12 16
  43. 3
  44. a
  45. Si utrobique multiplicentur per Radices Numerorum naturalium, fient Aexplicapplicatis parabolae
  46. Ex applicatis paraboloeidis
  47. 4 et applicatae parabole
  48. erunt
  49. 1
  50. a
  51. Agt. RG2 43 R44.
  52. 16 et applicatae pcrabolyi. 1
  53. s
  54. 2
  55. a
  56. 16
  57. aei ago Ex et
  58. 9b
  59. 4. 16 36 64
  60. A91. R92 A93. 194
  61. X RqBL B R, 128
  62. ers
  63. y64 Aqu R, 2S6

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 3, fol. 227v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068200:0456?run=74