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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 165v

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. 164r); this page is its left half.

The machine reads it as

  1. xle. Epplicentur et fiat a Lt +50.Z + 500a.
  2. Assume _ = EIX +2a
  3. 4025+910 ap +quoaa
  4. 610r+601Z7600 a a
  5. de uenauar sed contrecavi
  6. et eo
  7. 3. in aeq. 1 substituatur valor ipsius X ex aeq. 2. contracta, et
  8. et fiet 3) 11. 510 aD + 10. 601 az. aequentu. vatorestini ipsius Z ex aq9. 3 et 4
  9. IIdocisto.
  10. + 2, 301. 510 aaZ
  11. =11. 401. 510..
  12. +20. 310. 601 ...
  13. 21. 510av +20. 601 aZ
  14. =10,402. 601
  15. 01. 601 aa Z2
  16. L20. 401. 601
  17. +20. 300. 601 cZ
  18. = 16. 408. 601.
  19. or thaZhvav +30ona
  20. non viden opus tot arbitrarus et possi
  21. et et aeq. 3 fint 302Z + 310a0 Fxo
  22. Cies + , 21. 310. 510 auve + 21. 32 510032 20302.601 a
  23. -11. 410. 516....
  24. 10. 410.601.
  25. +r. 300.510 eV
  26. -11. 400. 510..
  27. +21. 302.510 +20.302. 601 + 2. 310.510 8+20. 310 b01 +21. 301. 51
  28. -11. 400. 510 10. 400. 00, -11. 402.510 = 10. 402. 601 = 11. 410. 5i0 =10, 40 6
  29. Compendii causa fiat +21. 300. 510
  30. Eit ex vq. G fier loa prndio
  31. 100. 700 200. 700 102. 702
  32. 00d. soda VB + 102. 702 4271
  33. erit o ( = 000 710a
  34. +000. 701 aaZV
  35. +000. 810 ..
  36. +1 av
  37. 202. 702 000. 710
  38. +202. 702 a33
  39. 4 000. 801 aa22
  40. + 200. 700 aZ
  41. haec formula comparetur
  42. fit.D+ dCa o
  43. +000. 701 aZ + 100. 700aa
  44. D = Z 102.702 22 4000. 810 a2
  45. P= 20270273 +000. 801a 27 +200. 700 aa Z
  46. + 3)
  47. H02. 75 Z 4 9. 000. 102. 701. 70247 +2. 700. 102. 700. 702 a a 2Z
  48. +2. 000. 10. 701. 700 a f. 100 1aa
  49. 210702 n. +1. 000. 000. 701.701 ... . .
  50. -4. 00o 202 70r. 710- 4 000 000 . 710. 801 ... . . 4. ub. 20. 700. 710 e Z
  51. nltisciat i... 102. 7or Z +Zol . Z + 102. 102. 7o2. 1o2 a Z
  52. formulae datae per 10
  53. instituendae sunt aequationes iderte
  54. dcatoria quatum
  55. Ob teminum tinum 102. 702 Lap = 100. 700 a seu 8 700 = 102. 7or Lap. : 100 a
  56. ob terminum penultimum 710 = 1000 (701 +910) : 2. 200 = (Ob secundum) 102 (701+81): 2. 202
  57. unde fiet 100: 200 = 102: 202 seu 2021 = 102. 200 : 100
  58. super est novissime aequatio ob ZZ, una ubi interpretando 700, et 710, fiet
  59. . 102. 7027 ap(. + 000. 701 + 000. 810 , :, 2, 000. (100: 200) (701 +810) a = 8 07 11t
  60. cor pocapo
  61. S et hi valores inventi omnes id commudi habent quod sunt rationales quodsi pro allis compendio
  62. assumtis
  63. nec pasum contrahetur calculus sisat putosliceat ponere 701. 0 seu 401: 301 = 21: 11
  64. ita manebit valor ipsius 700, et H et 202. et 71 = 100. 810: 2. 200
  65. et 8D1 = 102. 702C + 2 Tap - m) +000. 818a, : 2. 0007 (100. 20) 810a
  66. est autem 80l = 20. 301. 601 = 10. 401.601 et 401 = 301. 21 : 1. sot na 1d 11t
  67. et erit ocd. 801 = 301. 601, 20. 11 = 10. 21, : 11. ego sir 3. sublato 8D set
  68. et
  69. hiet 301 = 208, 102. 702 (2 lap - m) + 005. 810 a, : 2. ∞. H 601 (20. 11 - 10 21) 510 a
  70. ila pro et 80I rem reduximus ad hi numerum initio assumtum 30(
  71. Eodem modo ob 100. 700 a = 112. 702 lap fiet 21. 300. 32 ap + 21. 302 Lap
  72. et ob . 7. 200. 710 = 100 _ 810 = 2200)
  73. et ob 200 202 fiet
  74. 100 10g
  75. 30 - -
  76. (tav. 300
  77. 11. 40H
  78. es fiet odid
  79. 10 400 (601
  80. ad 50 ea
  81. quat ( loot) sp- M)
  82. quad M 4or.
  83. Edo ter
  84. c f. 66t. P 0407 (420 16) a
  85. L. d. B. B01. C.10. 410) C- 21. 101
  86. +20. 300
  87. i od
  88. -1. 402..
  89. 21601 L0. 400
  90. et
  91. 510 +240
  92. quar (126. 1
  93. S1B. 510. quadr (=il. 2) C lap - )
  94. +601. 601 quad (t 10 410) a
  95. +20. 310 +20. 11
  96. 510. 610, - 1. 410 ) - 21. 10
  97. uibus quatuor novissimis aequationibus si addatur 401 301. 2
  98. fint 401 ut 301 in aeq. 4 ha
  99. itaque ex aeq9. 4 et G habemus 301 et 401
  100. Ex aeq. 2 datur 4 per 400
  101. Ex aq. 3 dt 2t qr per 400
  102. ec
  103. Exags Ex aq. 2 latuo 48t per 40
  104. (d .Cax) =, adx
  105. itayu haum duarum aegq. ope
  106. Gubetur 40d, et 302
  107. Ex aeq. 1. Datur atoa t. god per . 300 d. 00) ilqe hatum
  108. itaque ope G aoque valiorus auterm inverti isfel o 1 ipsim 410 et ipsolum 1302, 402 substituantur in aerp. 4 et 5
  109. ita tundem, a habebimus absoluta valores ipsorum 410, 302, _02, 301, 401; remanentibus ad hac arbitraris
  110. 310, 300, 400, 10, e, 2012, 510,601.
  111. =10.101. 001
  112. et adhuc compendiosius
  113. e00 ruativ + a D +
  114. in
  115. dlar atax

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 165v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0330?run=74