Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 275r

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: 0.81.

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. 269v); this page is its right half.

The machine reads it as

  1. Hyperbolae curva mesuram recipet per summationes
  2. Enrum hujus
  3. XX + a: XX+ b. ubi in fallor signa inensi
  4. in nominatore sint negaliva, in numeratore sunt afformativa itacredo
  5. Aogleipsis videanis
  6. sies meretur ut calculum reapse exequamur, quia tandem
  7. viam reperimus sit aequatio pro Ellipsi foet Hyperbolas
  8. fZ - f: C ZZ = yy ubi flatus rectum, c latus transversum, seu axis
  9. directus, cui scilicet applicantur e ordinalim applicatae normales. ubi si c sit quantitas
  10. ponamus
  11. +C-x. fiet (ex aequ. lper
  12. (3)
  13. (4)
  14. Exle sec Z
  15. negativa, ex Ellipsi fit hyperbola.
  16. et: ZfC = fx - f: C ZCC - Cx + XX _ (pel 121) = yy = (ex 3) = se - fX - 1 fC r Gp - f. CX)
  17. Haere ut ad lineas
  18. seu destinctis destinendis ex aeq. 4. fit yy = fc - f: CXX
  19. applicemus erit AB sint vertices A, V foci FC ordinata ad Focum sit FE
  20. i quaevis alia ordinata ad ellipsiu sit BC, occurrepa BL, occurrens
  21. axi in B curvae in L, ef et REC _f FE erit Zf (ut a me
  22. demonstratum est) AV erit C Medium axeos punctum seu E centrumfigurae C
  23. CB AB erit Z et CB erit X ubi
  24. notandum crescentibus et BL, erit y. Ubi notandum crescentibus y
  25. et C AC erit LC
  26. 14 X = c. F y- 2cc jam sit d + (sax + du = arcui Ellipseos et _ ex aequ. 5. fit
  27. (5
  28. c. f gix crescere Z, sed decrescere X.
  29. y ay = f:c X dx. Ergo ly = fiC X: y dx. et d dy = f ff. cC XX: ( 3sC. F a
  30. (y
  31. et 8 et 5
  32. ergo fil ex 6 per 9 fit (ax tra s x
  33. (11)
  34. 10)
  35. cc At i3 X
  36. arcus Ellipseos = (dx Y 1 + f: C XK: CC - XX = sax +
  37. 2)
  38. 2CC = XX
  39. jam f: c =1 = f - c, :c fc - ce: cc jam in Ellipsi est chitres
  40. est fC = hh, posito polito n esse daptam ipsius lats axem conjugatum
  41. seu duplum ipsius CG. (nam E AC in FE = CG) itaque fiet rursus
  42. est autem ubique ee major C seu AV major quam h seu bis CG. ergo
  43. et ec major quam hh seu fc, utique quia c majost quam f, in Ellipsi in Hyperbola
  44. la Bcetarundea E
  45. vero contra. Cumelgol Itaque aeen fiet Arcus Eltipseos
  46. Arcus Ellipseos GEL = (ax 2s hcc-F xx quia X sen et crosnte id
  47. Unde cum amba
  48. tam numerator, quam nominator habeant suas omnes radices
  49. c
  50. ZCC = XX
  51. vo
  52. C
  53. Et quia in Ayperbol
  54. Ellaipse elique curop honca res succetit
  55. dimenset in H perbola
  56. no Ellipsi
  57. pro Hyperbola non potest reperiri punctum G. Ergo pro ipsis X substituamue
  58. et.
  59. antas
  60. ipsus quae scilicet crescunt inde ab A, substituamus ipsas
  61. 12
  62. 2) l14
  63. inde ab A, ut habeatur arcus AL,, est autem X = 2C - Z et dx = - dZ
  64. (17) (per 16
  65. fiet (ex 5) feet XX = cc - cZ + Z2 et L cC - XX = ce Ece + 1Z- 22
  66. et (per 16) f: CXX = 2 fC - fZ + f: CZ2. Ergo LCC - =F Xx ( CC - XX + f. C XX)
  67. (18)
  68. =(per ( ex 29 per 17 et 18) ce + cZ -22 + + fc - 5 + f: CZ, seu ce
  69. 20
  70. i cC - == F xX C +f e C= fZ 4 Z- - f: C ZZ
  71. (22)
  72. (43
  73. et fit
  74. SC 1 L C Z - f: C22. posito
  75. sed redcamus ad aequationem quippe breviorem, et eu ea jam odaramus solutionem
  76. Haplibola, vam Ellipsi arcuem Ata
  77. cc + cZ - -
  78. e fcouentiiorem affirmativn sin Hyp.
  79. tam
  80. nempe ita transformando formulas per x expressaancta vel miuuta X ut nominator
  81. in Ellips
  82. nohinator habeant divisorem communeus sit x- v+ e et est fiet
  83. = 12cC - ee, trev - c5 vv- Ee p Numeraloge
  84. 2cC C - eV - VV
  85. + cc - XX
  86. (24
  87. 10
  88. ero Rominator
  89. divilatur Numentor per - F. et nominator per - 1 itaque debent vV =Lev + ec = C. 2Cf, et vDFe
  90. et
  91. CC = XX
  92. habere divijorem communem, videamus jam quando duae formulae x vv + m V+n et vV F pB +9 debent
  93. habere divisorem communem, quomodop i inveniatur dividatur scilicet una per aliam, residuque debet
  94. esse divisor communis, qui invenietur actu dividendo vDmtn + 1. sit residuns m-pl n-9
  95. hoc iudatur prior diviso, fa L + vV + pV +4) _ v + p- 7
  96. n- P
  97. + mmq +49 etvisi binibus pe
  98. e l ranus
  99. (empu +3) 4
  100. = vp -
  101. vo
  102. map
  103. desetne pb.
  104. Ergo fit -n- 90
  105. Inn + pr + 4)
  106. = vo - pP - 9
  107. + q= 0 se q. qe
  108. im- p - a +q seu
  109. seu fit qa 9 m-p = n.
  110. seu qui rampl qus = nem- lxp- nule - 1m p) quD Cqu 19
  111. fici
  112. = dx =
  113. y
  114. .=
  115. lrgg. 2s
  116. Xx = f: C 97 - = sC
  117. +appn. + nn = nip A

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 275r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0545?run=74