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Leibniz-Handschriften zur Mathematik LH 35, 15, 2, fol. 4v

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: 0.74.

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. 5r); this page is its left half.

The machine reads it as

  1. fB Pa
  2. ad curvam aeliquam sit. d ZXC. f
  3. X
  4. ordinatim applicata termino diametri seu basis Z
  5. (1 ( Nosmaliter noistens: ubi literae. d, C, f, denotant
  6. Saq2m Con. = 0
  7. Cd = E+ f Z
  8. quas libet quantitates datus, _D, n, X indices potes
  9. tatum sive dignitatum quantitatum quibus affixae.
  10. Adq eo. f ) Sunt: fac 8f1
  11. itaque
  12. 5
  13. it
  14. 4L∞
  15. X+ X= 8,
  16. s XC +f=
  17. CL, et Nn - n = X, et area curvee erit 2 in
  18. 2
  19. 5
  20. r. 1 x E A
  21. s- 1
  22. 2- A V C∞
  23. LH
  24. +
  25. X =2 Y ED
  26. 5= 2
  27. 2y = 2 3Y ec
  28. S 3
  29. s =
  30. )
  31. 5= KC. Citeris C, B, C, D, _e. denatantibus
  32. tr ferminos proxime antecedentes, nempe terminum
  33. in
  34. S
  35. B terminum.
  36. 2.2
  37. s- 1
  38. X EA
  39. Ke. haec series,
  40. subi r fractio est vel numerus negativus, continuatur
  41. B
  42. infinitum: ubi vero r integer est, et affirmativus
  43. in continuatur ad ot terminos tantum quod sunt unitates
  44. en eodem Y, et sic extibet geometrucam quadratu
  45. inmussram Ccervae. Rem exemplis illustro.
  46. = h. 3= 1. Cpe. 1. Proponatur Darabola, eujus ordinatim app
  47. -1v. vMata sit V az; haec in formam Regulae neducta, fit
  48. Asit (. . C X O = a ZZ: Quare. est d = 1. 0 =0. E = 0. f = a.
  49. 1. adeoq 2 = 1. 5-=- 1 Z à Xa E)Z. N =0
  50. nDin bed E arca quaesita
  51. aXa ZIZ in F, hoc eot, 2 = Vaz
  52. ita nona, posit 1sm et sic in genere. Si cZ) ponatur ordinatim applicata,
  53. prodibit area
  54. -
  55. 5
  56. n+1L
  57. 7 =1
  58. Ex. 2. Sit ordinatim applicata.
  59. a. 4Z
  60. Cs= 2CCZZ + ~
  61. haec per reductionem fit a AZX cc -2 =
  62. etiam a A= 3
  63. - 1 1 Cc=2
  64. est d = a. t. 6= 1. C = cc. f..
  65. adeoq X= 1. s=- 1. Z
  66. a4
  67. A
  68. vel.
  69. Jnprioi casu
  70. 1. H = = (2
  71. RcC ZZ
  72. X= +2.
  73. hoc est
  74. 2cc- 122 N = 0. Et area eurrae = R in Z0
  75. id est
  76. a
  77. RCC = 2Z=. In secundo autem ca su est
  78. Cd= a 1 O = - 3. e1 f- cC. n = - 2. 7 -2.-
  79. 1- 5 = - 1: Z = a 1
  80. 2cC X
  81. 1 + cc Z2) 15
  82. id est.
  83. = a 1Z =
  84. aet aari
  85. Ae = fh. Z- dZ
  86. Z= co- E: f (t. t)
  87. = scon E) es
  88. ita res reducta ad crninos
  89. um
  90. sit in homus hh= 9 AI
  91. O-5, 1d t (91. Co. dio
  92. unde si a st integer
  93. habetur solutio absoluta
  94. tis vege hic scriptiorioxa
  95. si loco q assuisit
  96. D=5, c- Egl. Co, IJora
  97. ergo si q rationali,
  98. tunc fdG g. b+d 3 E+ 5Z
  99. randiour ad aliquot finitas
  100. 1, b + d. c, eC. C
  101. Haec maximi momtati
  102. sit integer polu
  103. set
  104. mibus
  105. non
  106. icem
  107. sum
  108. ediuis huraro
  109. (+ 5. 8
  110. Nin _E_ = f. Z
  111. et
  112. FZ- vbi. n - E. fl t
  113. in 0D= C,:f( 0.
  114. dA 1Z. Zm (+5Z1 k.
  115. esse integrum, obtenta est
  116. depressio mo gentraliter
  117. sattiet si h sit 1,
  118. adhibili quodcung
  119. quantitate sub irvationalis
  120. tenta resoluta in plunes
  121. dicisores, et unum ex
  122. irrationalem povendi v,
  123. habetur deprossib
  124. tetanez
  125. cit.
  126. u v

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 2, fol. 4v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068204:0008?run=74