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Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 151v

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. 152r); this page is its left half.

The machine reads it as

  1. 102 16) 5105
  2. 265986 13289
  3. 1+37
  4. Es
  5. inscriptaa
  6. Figure similes similiter positae habent idem
  7. centrum gravitatis, ed contra quae figurae
  8. sunt sinile habe similes inscriptae habent centum
  9. (in eodem plano) habent centrum gravitatis
  10. commune sunt similiter positae inscriptae.
  11. Demonstratio haec pest cum in figura stropora
  12. Honaliter ab omni lalere in se recodente, omnes
  13. radiis
  14. lineae proportionaliter diminuantur lineioesou D
  15. et per centrum gravitatis tendentibus proportionaliter
  16. diminutis aequalis erre diminutio utrobique
  17. ergo idem manebit centrum gravitatis. Imo
  18. + in circumferentiam
  19. ne explicari quidem ista diminutios proportionalis
  20. potest sine radiorum istorum contractione.
  21. problema maximi momenti: datis duobus
  22. quibuslibet ex his tribus, area figurae,
  23. centro gravitulis sradio, peripheria,
  24. tertium invenire
  25. Turvilinea parabolicae curvam
  26. rectam aequalem invenire Nam
  27. Datar
  28. Datur area parabolae, datur ejusdem centrum
  29. gravitalis, per dem. Archim. Ergo et peripheria
  30. per prob. praeced
  31. quadratura prbo Hyperbolae datur turvae
  32. paribolicae recta aequalis, per probl. praeced.
  33. ergo et quadrature Hypertolae per
  34. ab Heuraetio
  35. t est, dameter ad circumferentiam
  36. ita est figura circa suum axem voluta
  37. ad superficiem cuovam.
  38. rada _ = D
  39. circab supocyst sup hem.
  40. Ergo sup. cyl.
  41. sup. hem D
  42. Ratio Cyl. ad Hemisph. est ut 3 ad 2.
  43. ergo raio quadr circumper. ad quadr. vel
  44. Quad. diam. ad circ. ut A4 3. ad R92.
  45. Ergo diam. 1Y. R. diam. 1Y. erit
  46. qua, 3 - - i - 1 _q 2 qu divida,
  47. R4. 3.
  48. tur per 1s seu radium fier Ag2Y41
  49. R93, 25.
  50. seu R48+44 semicircumferentia, quae
  51. ta 3V auplicata seu multiplicata
  52. t4 3V per R44. dabit.
  53. A932 Y44 X lircumf. et Hosipr 12 A 1rg. dabit
  54. R43214) Rabo
  55. R93Y44. Aqd. tiam
  56. 143,, R93r9.
  57. 1s esto 1000,000. Eup H. 1000, 000, 000, 000., seu R9, 1000, a0, 000, 000, 000, 000, (0do, 000
  58. . . ....
  59. multiplicatum Ar R4.2. seu....
  60. Culriplicetur per Rg+. fiet:..
  61. dividatur per M4 1000, 000, 000, 000. fiet.
  62. A2... .
  63. Aq 3.
  64. R48. ......
  65. Ag 5 5 Y h. 6et 11d la 6666666666663 9.
  66. quantitate
  67. 0e6000 5 1000 ud
  68. 5980
  69. 100 d oos 20 1000000
  70. oo
  71. 16
  72. 5986
  73. 1000000
  74. 1060 ed 25 00a
  75. R43, 0071000, 000, 000
  76. R4320000b000000 circumf
  77. R9 32,000,000000,000, ooso, 090, 00 est
  78. 310de, , 090 0yo
  79. 29 32 1000,000, 0ec.
  80. dian

Cite

Leibniz-Handschriften zur Mathematik LH 35, 12, 2, fol. 151v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068195:0302?run=74