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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 439r

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

The machine reads it as

  1. XLB L M LN BL
  2. uXEC
  3. CGBC CG 2 BCdB ex data cycloidis dimensione
  4. (BAD F BF NB probandum FIGF
  5. NBeD EA CRyp Cin. CAFG, circ - F iG
  6. F1H CG- AF Ergo FIBACG. A0 EFBB DL DFHE
  7. (E) DFiAO
  8. er rectangulum FIGYB CGBAC - AD, AC
  9. Eogo FVGFB F1GY - F1GF B CG, AC - AD, AC, = BL DF NB
  10. Ego et CAiG ( CG, AC) = F1GF (N BL D F 1) + BLDF NB
  11. + BAPB
  12. ALN arc BL. DF p an BLd. C PS arc BLP
  13. LN+ psam BL parcBLP. et arc BLD) arc L PC.
  14. ergo LN + BS arc BL B + arc ZYC F, semicircumf.
  15. seu BLc CG. Er idemque fit ubique ergo
  16. Omnest N. exc. seu Trilin. BDCGFB(d A= ACG
  17. seu circulo. Et haec omnium simplicissima est cycloeidem
  18. metiendi via
  19. porro LMFi KL. et Pq P. etc.
  20. NX CG = KL - LN
  21. p- (13) CC
  22. exiaetius Ergod PSf NX + X, Bklix urtu 7gr 13
  23. Ergo NX fiS.
  24. et circum ferention
  25. XL f Ps- pQF Q5 entius
  26. Eodem moto MN Zs7.
  27. Et NXGN, (20) B BQS B.
  28. AB7 r.
  29. CG - AD DF ergo
  30. CP5-
  31. (22
  32. sit C peripheria sit 1, aBD CG
  33. c= r a . Ergo E1 - r. Sx FI GF E per 1809.
  34. GIF p BMEFNB per 20.
  35. ACGI ( . per 21, 22.
  36. ACgI = FiGSF + B ME F NB f NC ACGI per 18. Ergo per 30 e 2g. enit ACGHS ACKFEL
  37. Ergo pr 30. 29. erit ACGSF + BMEFNB F r. seinci BE DBFYC per 21. 22.
  38. apegente circhimedis theoremate. jam BCD
  39. 2BCDB Ergo per 32. cur
  40. (3
  41. BDCEB. per 19. Ergo esut
  42. BCEBF rCo Ergo per 31. erit BCEB, ACGSF+B EF
  43. utrique communt AEZC si utrinque auferatur, fier B AEMBF ECGSF + BMEFKB. seu
  44. BEG) B. sed hoc jam notum
  45. si a circuer duplicato BCGH auberas circulum ACGi, quadrantem BADLB; et B H IFB
  46. restabit BD F NB.. jam BFY BH) IFB F GHABFG = GIF
  47. e Rursi si a circdupl. seu a BCGH. cufers
  48. e
  49. BMEFNS, BDEMB sen) BA DLB + BLd FN
  50. BD si acirneo supticato BH auferas BAIH, auferas
  51. Ergo Circ - quadrans smilte +G1FSG,
  52. simicire.
  53. IBM KAB N BIDFAB (B LBEMOsu, quod
  54. Jungantur du recta BVF et BD. Triangulim BDF erit quadrans ergop DABL d. anferatr
  55. communis atrique, BVLD. Ergo seguentum Trianus. BAD ips DFVLD = seum BVB
  56. superficies hemisphaerii est aequalis superficiei cylindri ejusdem altitudinis et basis adeoque semicirculo
  57. Junus aus
  58. e Si a Cycloidi BFG, cujus vertem B. basis B
  59. ur
  60. si semi cycleidi occurrar recta per centrum sirculi generatoris transiens basi
  61. paralleta. j segmentum recta punctum occursus et verticem
  62. in generulons
  63. sit semicyclodides BFG. cujus vertex B. altitudo BC. basis CG. centrum carculiq odi
  64. meratoris Aper quod transcens recta AF basi cGparalleta, occurrat curvae in
  65. segmentum figmae cycloctdatis BF N B. aequari triangulo BAD
  66. TrianguloB AD semel seu seriiquadrato radi quod ita demonstro. Jungatur. DF, ae quatur quadranti a incumferentia
  67. erg triangulum ABF cujus basis arc quadrans circum ferentiae, altitudo AB, radius
  68. ipsi AD= B DLB quadranti circuli. porro Retorta BDF B aequaturdu
  69. qaoitur
  70. qulediaso
  71. siu radii, ut a scriptoribus de Cicloet de patm epreso nnutur u ostenditur ut Wallisio et
  72. ponorato Fabzi, ex aliis ut de Honvillaeo facile duci potest His postis facile reliqua absolvema
  73. Triangit BDF escosiB ADL BB+ BF HB _G segment cycl. BF NB aequa B segniento
  74. quadam circut BD. LB a (Retort. B DFB seu) quadr. Trianqu BDF + seymento cyc lo 18 B F NB) aequatur
  75. B segmento Circuli BDLD + relortae, BDFNB. Nam ut alterus it BDFNB. pro Triangulo
  76. 13DF substituatur ejus valor, quad cans BAD LB, vel rursus pros quadrante, ejus vator, Triams. AHD + Segm. circ. BD
  77. denique pro retor quoque substituatur ejus valor quadratum radii seu bis bis Triangulum BAD. et loco prioris aequacitas
  78. semento crculirob a bis tua o is du
  79. segmento cruli BdLB + Cretortie BL BF AB cu) vis Triangulo BAD, ablato unobiae egnidtanto ieu
  80. ut
  81. Bri
  82. padatisteu elides tium
  83. jam
  84. F1
  85. (23)t
  86. ergo FE B a
  87. ACGHF
  88. Y
  89. sit jam Racdius seu
  90. i
  91. BC
  92. EB)
  93. BAEMB
  94. Trapez CAFG) ra- Trilin. IGFS
  95. genhatori
  96. restabit segaculum
  97. cyllordalesue FAB
  98. aequale
  99. AE.
  100. gorat
  101. 407

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 439r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0873?run=74