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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 48r

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: 0.72.

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. 49v); this page is its right half.

The machine reads it as

  1. IriHusperbola et Ellipsi sit g latus transoeisum seu axis directus, e diestantia socorum
  2. in ipso dec etemat sacriphcrae eut di t t r latus rectum h axis conjugatus.
  3. fit Yg = hh et ee = q9 +hh. sit y ordinata ad axemdirectum, oidinata ad
  4. uxem conjunatum, fiet gus = finh: 49) ZZ 4 +hh Et = in Hyp. est +, in Ellipsi est
  5. sit dre elimentum artperppheriae fiet generaliter dic = dz - ee Z2,1:, L.9= 993Z) D
  6. fiat 7Z = g17 fiet d = Zd7 = 2= qdv. 2 et dz = 4d0: 21qu. 2 et substitatione facta fit
  7. dedo . felv,. (q 7 L qiu qer (44 erq s., q
  8. seu 2d4 = dx +( 9 ees q - dv f(49 - eev, 4 4q - qub A,
  9. eo
  10. tlipsis cum foci inceretrum cocunt sit circulus. Hyperbolo cum foci intentium coeunt fit recta
  11. fiet de = 9dp (49 ee q El et 2dn = do 1:
  12. qi
  13. s
  14. -.
  15. Etqu.
  16. P - quv
  17. 129 -eer des
  18. V....
  19. Fxaminemus valores ipsorum summas ipsorum dv
  20. 119 - 99V
  21. quae omnia possunt hiberi quadratura rationali. Compendii caussi pro =G ponamus 94)
  22. dv s du s..
  23. pB . B ....
  24. aa 49f - eer = cded. fint ej qyf - eex onscoto queoco et v = 45C af (9-co) , ee gco
  25. 4f - qqu 2 et fiet ggt eer = fcoco- veoco et fiet v = (9 ct) gu loco, f:, ee -coco
  26. et dB = fico, 20 (es coco) trco (9q. colo) = faco, 2co (99. LDC)) et co dx = f deo, 1oco (99- ) sit 49 e gy
  27. qu (e-10c0))
  28. qu (ee=C0co) male
  29. _ fiat (g cdco: gg (ee Coc1) - Y Y s a+ 1 = C Bocossus ec iide
  30. e
  31. ee coco, ee loco
  32. 12e
  33. qu (2+c0) (e. C0)
  34. qu (ee=Colo)
  35. -, e- co + et co e = 4
  36. 1i2e e t
  37. 1.28 = 2e
  38. qus e 1o) et Cmpo tunt
  39. Et sandem s
  40. est aut
  41. ...2
  42. qu (et Co)
  43. eto +e- ed
  44. ana
  45. .
  46. = 20
  47. e 1.2
  48. quse quterco)le co)
  49. + ee-c0co
  50. = Tec qu e c0)
  51. Coco
  52. qu (e-co)(et C)
  53. Hoc ex eo dumpoterat, quod
  54. 2Cold
  55. Eon L + qu (Ct) -coo
  56. Qu (2. c0) qu (era) A, P- co
  57. 1
  58. + 4 eb - cocs
  59. enco + et co = 4 qu (etuo)
  60. qu... .)..
  61. ee coco, ee o1 B, qu (- c0) L
  62. Woeo, Lu +
  63. 28c0 =
  64. et co, o ena erco
  65. sit e co = , fiit 9929C + Q =W010)
  66. e et et coto
  67. = 8-28e +e 1 - 28. +2
  68. qu (2. 10)
  69. 8) = etco+l
  70. qu( etco
  71. 1 = re log1 - ee = e+ 10 = 20 log (et c0) - ee
  72. tco
  73. sC
  74. +2e log (e - cv) + e
  75. et erco = _ tit coco - eu- 24 (1 = 1 - E + jam lco = d et fiet
  76. co
  77. qu (et co) fcoco. S csto dus - (99 - 28C + ee -de = - 99 t y g + C9- log 5- sul. 1) re e . 1u.
  78. Je
  79. coco deo
  80. seocoduo = (e - e et ex A_ = L 1 1 - e ec log = 2 qu ( et ) -e (e+ ) + ex log (e+ C0)
  81. gy9
  82. etco
  83. ( -10
  84. Ergosit 4ee coco - - et lo + 20 by se c0) reC
  85. et 4440e 4q du 41, - = etu
  86. Qu (eeci)
  87. = L qu (C - 10) + (e- c0) = ( log(e. c0)
  88. + e (et co) -(e + C0) + e log (e+ co
  89. +a
  90. logle ce) by fet co)
  91. et v= Z2. 9 = 4g. ed ita in casu ultimo fit co quantitis in finctae, sit
  92. 4 G eeV a.E
  93. Ergo mutemus Hypothesu a ficiam (q P - eeto : a - pB) = 9: eo ita erit cd in ultimo inffinite parva
  94. in casa ultono fit Z= 293 - cer
  95. +4- 4
  96. et fiet 995. ees = 42. et 49 feocd = eep coco = 99 syque - q u, et erit v = 9t - q9 g :, q recoco,
  97. i enim loco = 24- qqe
  98. 49(- qq cocet d ∞ =
  99. qu (99 -co co)
  100. 44d
  101. 495 200 + ee 2 49f2 ( Be a) + ee 24 (15- 49) cro) du
  102. ju
  103. a ad _ b Ao + 2 PC495
  104. Cuijo Eup debet summani 2
  105. debelit summam
  106. 12
  107. 12
  108. deo
  109. 99.
  110. q- levo
  111. qu (9 - ee coc0)
  112. qu -coco
  113. L
  114. qu (q eCcto)
  115. + 99- coco, deo jam = ig
  116. p egio) pusgerui) gg alo quloguud 22 qusque
  117. 99. Wd
  118. qu (99 Lolo
  119. d
  120. q. ee = 9d
  121. I 129, 1. 2g
  122. g- a +9 +cd = g g.t
  123. 9 -c0co
  124. quao
  125. + 2C
  126. quege 18) gg- coro
  127. 1
  128. ( - XY
  129. (1 - XX
  130. qu (1 = XX
  131. 39 (L X X)

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 48r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0095?run=74