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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 188r

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: 0.70.

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. 193v); this page is its right half.

The machine reads it as

  1. equationes locum ad crculum exprimentes
  2. stohiaus rcctengulo AC Bs C. adcum pepsabus
  3. AB, b. AC, C. AD e CDR V
  4. erit e bx - 1 Y + y
  5. sit Recta AG. AE. anguilo quolibet BAE.
  6. adquam ex puncto C. in cuiva concatur perpendicularis
  7. (5D. CG. vocem AG, Z, e CG V
  8. Tiangula CDF, AGF ABE similia sunt:
  9. V EF CB ac Ergo CD CF y CF a
  10. et et H Ey FDBVF
  11. 2CC
  12. CF A e
  13. in AD sie X AFDFD, sve AF ( Sun y.
  14. ano AH
  15. CFE Egd AFB CZ. Ego XB EZ() S V.
  16. cD
  17. a
  18. CG H G () C F sue v, ( a V +: FG. MFGAB FDnDV..
  19. + AGIR
  20. Ergo FG1. sin Z. Ergo v ( y + J.2 Z.
  21. Et Et Ve (4 a V (4) a Su. Z
  22. e
  23. Ergo XBah as R -
  24. Suc X+ (eZ + E B (2
  25. e. Z
  26. +
  27. aq
  28. 2
  29. Ergo X af Z
  30. Egu Eigo 1 Yi 12 - 2 . VZ + et 9C ad
  31. 2a
  32. 1 iaes BZ
  33. et X rC B + 2Su. VZ re , sut A91 6
  34. lide aequatud Rerior explicatis X et y. talis erit
  35. 2
  36. 1
  37. ba s V + ba 3 - 1 V = 2a S.. VL
  38. + a c
  39. -
  40. E. ZA e
  41. (au )ca..
  42. +
  43. 1
  44. eiZ
  45. 14. s. YZ + 1 Z (4) ca1) ca Z
  46. et is quo se destunt lablatis, fred. ba s. V. aba Z - v- 21,
  47. ees
  48. er
  49. Hince con sequendiae daci possunt non contemuendee efrimum anim ita habetur
  50. locus trium arbitrariarum, C. b. c. et adhuc duarum, explicatis Z. et V,
  51. V e
  52. Imo fuissent adhic opinor, si ab initio. loco le t adt buistemus:
  53. bx X + Ba 5 + Cy. eadem enim Da addenda et productae. Habemus ergo
  54. aequationem ad Ciculum hane.. 22 + v2 - ba L
  55. quatuor
  56. (4)
  57. (+) ca
  58. Hinc l guntitates in andeterminala. B. C. F S1 - a. D. a se inicem indes endentes
  59. Tempe ptue sic fier. C Z2
  60. 2 B2 - b Z - b sud B = 6 0.
  61. (Vc.
  62. (+)
  63. .
  64. Quod infiguis est usus ad aequationes ad Circulum determinandas. Farle aliae adhuc
  65. provenissent incognitae, si AG et AB non se secuissent in puncto A. item si
  66. punctum intersactionis in Circulum non incidisset aut certe a puncto A in Talitudine est
  67. etiam aberrasset. Omisso autem, 6.. Hujus aequationis ope tamen sutis
  68. indeteminatam videtur obtuceri posse, sine extractione radicis Ponendo v.g.
  69. V p co + a. unde c et yd
  70. ita Quod usum habere potest ad evilandas
  71. +1 = ba 4 = ba su c0, + d C
  72. ambiguias radices quarum qua lineae praeparatoriae,
  73. (4) a..
  74. e
  75. comparemus hanc aequationem cum ista:
  76. e
  77. () ca..
  78. e ba
  79. ( cada
  80. dmabliplaatus
  81. 22 4co + (y + mco + na po
  82. fiet Om ina Ego dB na Ego. Ergo -ba a + 2na m.
  83. -b2
  84. ce ⊓ 1.
  85. -ba sud (4) ca S.. (4) ca sud (+) ea 4 na m. fiet
  86. lsu +ca sim +Ca +na p m. ponendo jam e BC. fiet.
  87. vel eta ponendo e aequalem cuidam cognitae minori quam a, caeterahabem,s sed
  88. si en sine radicis extractione desideramus, quadranda sunt omnia, et postea explicanda
  89. quaedam. Jam si loco ipsius eb aliam CH obliquam substituas, quae sia is t
  90. MZ et vr t. ed GH s1= a B
  91. At, sine s AG sire ZB. AH - GH, sive ZBs- sun t. Et gd 5 - 2sm st + +t
  92. et AH 15.. Ita ut
  93. D
  94. cG1s
  95. vot er e
  96. u st - ba s.. 5
  97. 1
  98. 12
  99. bact
  100. N.
  101. tu
  102. b - ba sudesum b - l ejo 2)
  103. 1 2
  104. 1V2C. L. 1.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 188r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 44). https://leibnizlegible.com/page/00067993:0377?run=44