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Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 260r

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 259v); this page is its right half.

The machine reads it as

  1. secns auy dy l’ est
  2. et tuosus accus dupliest quadratum eadi a quadrato seranti adentumd
  3. dcans arcus dupli est a
  4. ab +2 a b + a
  5. B et linvestiges
  6. Targeotomums daplis
  7. sinum rectum arcum
  8. dupli habebis
  9. A
  10. a - +ba b2
  11. Nota si tangentem
  12. seu
  13. berrab
  14. at+
  15. ab+ at ab + a
  16. a-2baF abtra- 2ba a fra a
  17. b2+a
  18. (a6 2 ab pa - a + 9ba. 4b a ab s + 4a-
  19. La- +ba er ab a
  20. ab1+ 24b + a a 642b- at qab abta
  21. Senitus
  22. a 2a b + b+
  23. a= 4a b + 46+.
  24. de ab sabi ra = a 2 aeb + a - a+ 2a b b- 9ab- 2ab
  25. a 2a67 (it a b
  26. rangentem arcus lnic patet pangentem semiaum non inepte assumi pro basi, cum dipso posito commensum
  27. sin vero in vestiges
  28. dupli habebis
  29. Aada
  30. ut a Pellio ostensum bili pleraque
  31. a- Es
  32. alia commensurabitia sint Quemadmodum et area futeri arcus integri, quod
  33. ara fiet ab area fuleri.
  34. Unde sin Rectianu ractlnde brenoris calculi causa, si mndo suius derus carcus totius dividata per b et multiplcetur
  35. est. 2a
  36. ad Tangus esde arus 2ab per a. fit filcum. Ergs. si adjeriis ad
  37. seu 1
  38. eeL
  39. serenula faciis ab
  40. +b
  41. 2b
  42. at3
  43. b etq halebitm sactor.
  44. 3bi est
  45. aio au a a eba a5b
  46. + er
  47. a b - b + h1 - b et fulerum
  48. Semurcorunt lum sub sum recto et langite
  49. semiarcus est b’a
  50. aes spppputa
  51. = a
  52. emirectangulum sub sum recto ed verso CP langenle semnitars et
  53. -
  54. b + a
  55. 6ta 2 quod si diuides facit:
  56. harhas . et
  57. a a2 pa
  58. Ergo habenus valorem sectoris ita expressum: a
  59. Ila poro
  60. b3a
  61. ba bEa b + b b2 esc.
  62. b + a
  63. +62
  64. 6+4
  65. ab - + a C2 a q et
  66. ba= ba + Va- b a ett seu a l etc.
  67. Jam sector est Fulerum + segm.
  68. + siniecau seije p
  69. a + b
  70. + a
  71. + b3 - bu e seu posito a -1 fiet b - b + b - b + b 2l
  72. dae nia
  73. si a semorectanus uto per geartes subtrahas, erit
  74. 263 465, 66 8b) et vel omisso a, eut: 3b - + b + 6 B - 8 b3 e
  75. 3a 54
  76. 2
  77. 70
  78. 9a
  79. 24 4a 64
  80. a22
  81. a 64460
  82. 8a6
  83. a- 24b7 b
  84. e(A
  85. qu 2a5 b+ ab 246 + ab 7a b ara b b
  86. qaeb4
  87. a 44646a b + 4a - 12 a b 19bd
  88. 128ab
  89. a-4a Cb 10a b- 12a b + 55 b8
  90. Eaque progressio faile contimari potest si tantum innerator sne a, intelligatur quadiatii productumque ejus
  91. mulliplicari per 2a. Nmetor. Nominator vero quad retur, hac sola adhibila mutatione ut
  92. notae ultimae, in qua b ad potestatem numeratoris ascendit nunerus praefigatur qui sit differentia
  93. intermaxima ipsius b. polestattuo in numeralore X nomimatore quadrandae fractionis
  94. ut in sequente fiet nota Bi6 in munerulore mulliplicetur per 128 - 55 = 73. Et
  95. toin
  96. 128
  97. n2bd fiet. B. inouritatore adhoc sequenti 326r5 B.
  98. 31728
  99. 32675
  100. Appro pinguationes Gregorii quarum mechodum suppressit
  101. videntur fieri per differentias
  102. B est
  103. It seretum
  104. -b
  105. ab + b a a +b, ab - ab
  106. Hii quadrur ado serminui procodentus
  107. seu sinus Rectus est ad
  108. suum Tangentem, ut
  109. Tangens semiarius ad a ab
  110. adium.

Cite

Leibniz-Handschriften zur Mathematik LH 35, 2, 1, fol. 260r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 44). https://leibnizlegible.com/page/00067993:0521?run=44