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Leibniz-Handschriften zur Mathematik LH 35, 6, 7, fol. 21v

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: 0.79.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. GWd: WC: FG:: HC: CK: KH
  2. NM = AK CK = CMM
  3. CKin FG = WC in K H
  4. sit CP, _X sit M et CN = a fiet NM. Saa -XX: : a : X
  5. seu NM = a raa -XX: X = AK. sed AH: X:: a: saa - X
  6. fit AH = Xa: Vaa -xx et AH + NM = K H dabit
  7. a( aXX + aXX: XTaa - XX - v X quorum proindedatur
  8. summa, ex suppo sita summa secantium ad arcum
  9. porro KH in WE = Xq in GW
  10. purr
  11. et KG = K R seu a, +R9
  12. est autem CR: XR seu gK: CA = Rg et fiet RG = aa = X Y Aa : XX X
  13. seu AQ = aa -xX a sit FP = _ fiet a a = R9 quae summa pendet ex
  14. XX
  15. aagu
  16. Quadentura Hyperbola et KG = a + aedto - a= alqu + ab et summ
  17. da-ec
  18. aa
  19. dunium kq 1d Gu erit lx reducetur ad loganthmos.
  20. sed Si ag= 1og la et 2 log. a
  21. X adss
  22. ho
  23. sa . Evu
  24. a
  25. . 2 at
  26. Ca loque sario
  27. sca ysto
  28. 0
  29. NM. IF ix NNE CN: XM: MC:: GW: NF: FG.
  30. a90
  31. a-
  32. NM NSM sim GWF NM: SM:: GF: WF et VM WoF (autadx saa- xX)
  33. =(GF SM. GF. Sed MM(in Flementum arcu) aeqo secant( in oliam
  34. demto C5 seu Cp (in elem arcus.
  35. sinum CP: CF:: GW: bF
  36. M
  37. Sed CP in GF aequ CF in W
  38. Ergo si sit arcus AF (ipsis X a minimo inceientitus
  39. fie it seuentes complement in Elementa arcs dent cinta demto volumt
  40. om
  41. rectangulo ATFS sub finu opeen et et siun versone aequates sib secantia, complement
  42. omnibus ad basin tangentibus complementi ad basins sipplicatis, seu omnibus tangentibus
  43. compl.
  44. residuorum artuum ad axem applicatis, seu su omnibus tangentibus
  45. pesiduorum arcuum ad axem applicatis porro secantes
  46. complimenti ad arcum applicate sic invessigantur Ek CM vel Ckin GF
  47. = RH in WF. sed WC Est autem KH = a3: X (aa XX et WdF: GC Sanx. X
  48. KH in Wd F∞ = sed (H in WF = Kg in GW. Gu sit de
  49. seu FPl) fiet HG in WF KCQ in S W = a deo. t purre si porro
  50. Habuimus curnan paulo ante
  51. ac
  52. jam haec inventa ad nostrum scopum applicemus:
  53. quaeritur Sadn: datnn, ipsa n, incipiente a nihilo, prima orchuata 10, 11 erit a
  54. ultima 12.13 erit a, posito 10. 12 scilicet esse a. sit ut 10. 14 vel H 1s est N
  55. sic 10. ns vocetur X et erit X = ~: aa + n
  56. quaeritur (a du: Saatun ja Cit 10. 11 vel terce, n (usque ad ultimam 10 12 (agra))
  57. sit n et res 11. 14 eri sit X = a: Saa tnn, naxima xordinata 10. 13, quando
  58. n est minima seu 0, erit a, et minima, quan fiet _ X n + X a = a seu
  59. _ n 14. 1b vel n = a Saa =XX : X. ergo cum n est d, fit X = a
  60. ergo incipiendum ab X = a jam faax taa - Xx +X Ergo ad circulo si CP
  61. sinus compl. anguli NF (ut incipiamus a CP = a seu a CN) sit X, erit
  62. tangens NM, s araa-xx: X = n, res ergo eo redit
  63. ut inveniatur summa tangentium adm axem, et habebitur area
  64. 13. 17. 15, 13. jam NSM sim: GWE. Ergo NM: GF:: SM S WF
  65. sit SM. GF = MM. WF, jam SM = CM - C5, et CS = CP. Ergo SM. GF= CM. GF-CP. GF
  66. sed Cp. GF = CF. GW: et omn. CF. GW = FPC rectang. FPC. (porro CMM. GF= MV. WF
  67. (MV = KH sppra) vil CsA. GF = jam CM. : CM: MV = GW ergo
  68. CM. GF = M. GW. sed Mp = M9 + 94 tq = MN: m e. MN:C
  69. in nn: a = _ a. aa = XX: XX. Ergo Me D a3: XX a: aa-
  70. GW =ded WE- ax. siet MN. WF, aded: aa adeo
  71. ut Et cum X crese. (per 1, 4, 9, 14, 4, 5) = n dx. et su 13. 17. 15. B
  72. asc: aa- = aed. sed (X dx 13. 10. 12. 15. 13(2) B. 17. 15. 13 4 10. 15. et
  73. 10. 15 = (10. 12 (seu n) in 12. 15 (seu X) ) nX siu sx dx = (n x = nx (quod et
  74. ex caljulo patet) jam Ergo ex 16 sit sed x a: da + nt. ergo fit
  75. Caedu: saetr = (a) B. Aa- Gy -ay n X log. satY add + nX. sed ay+nxo
  76. a
  77. quia nL a taax: X et C iaa - XX. Ergo ex (27 per 24) fit sa aa = a log Vat
  78. =W
  79. eton (a dn: sa +=ordinata curvae catenanae posito n’esse catenam inde a vertice
  80. sirum n et tmad et g esse et fit ec
  81. iteo
  82. est =c
  83. posita 1parametro B numem primario, et C = 1- XX
  84. itnn-n
  85. si CP, X.
  86. NM, a Taa -XX: X
  87. t
  88. iler
  89. diAe
  90. ad sin vers o
  91. sit ene
  92. io
  93. alsie
  94. n
  95. (11)
  96. sin est
  97. C
  98. seu diametres
  99. verse
  100. , ad scy: an -s
  101. l0g
  102. entn. Mtum.n
  103. LEn Ln

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 7, fol. 21v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068052:0042?run=73