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Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 82v

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: 0.75.

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The machine reads it as

  1. e
  2. simplices
  3. CIdeamus quasuam fonmulas irrationales reducere liceat
  4. a formutam irrationalem duplicem seu implicatam, sive
  5. ut vulgo vocant Ueniversalem 21. Hoc ita fiet in exemplo
  6. CH
  7. X + bXY CX, +EX +f d-X soxtf-et
  8. = X + 2CX + 2f)
  9. et fiet
  10. + coca ux + 2 fCOX +
  11. +2O XX + Xf X + 2fC0 =O
  12. coco
  13. Xa bX + C = h+ X = e
  14. sit formula X x + 12X + 124 V 14,
  15. aequanda quadrabus 132 h +2. 132. 133 h + 133 : h, tunc actu extra hendo fiet
  16. e
  17. 23)
  18. + 132t + 2. 132. 133h + 132
  19. e 80124 hi
  20. +2 128 hh
  21. ec
  22. 1
  23. Cipsi
  24. Quae formula per omnia similis est aequabioni 21 (adeoque et 20
  25. modo faciamus numerum assumtitium 101 (adeoque et 55,
  26. aequalem nihilo
  27. Valde memrabilis videtur via initio hujus paginae, quia ita differentia in summnado comptehensi
  28. et explicanda nil turbat, verb. gr: A iogu ngx gy + ayx + bXX + y + eb+ f
  29. noguept assumta sumatur valor X = m∞ + n: v+ P, quo substituto in aeq. 1. siet
  30. LVIt 2pH+ pB yy + ay. v+ p. motn +, m. ∞ + 2 mav +nn = (4 vD + EpoF
  31. e mv+n v+p + f v + 2pB + pp. = 0 Haec aequatio coparari pt datae
  32. ad lineam propositam, nam reduci potest ad quadratura avalem quod
  33. sic estendo: aequ. 3. sit data, ergo inea figurae quam expriunt
  34. quadratura datur si detur. ydv. pajam pro V substituas y, ut
  35. hubet aeq. 2. habebsis aeq. 1. in qua datur per extractionem tuusferma
  36. tionis in rationate capatem, explicardos B rationaliter per 2. et
  37. N dv etiam datur ruvaliter ex x differentiando aequadem _. Ergo
  38. l
  39. ta
  40. est ad ravalem
  41. tota quadraturque qua sita o
  42. valde memorabitis videtur via
  43. Ex aeg. 3 fiet. fs n m 2 mn _ P n n_ (4) am B + anq gy) initio hujus paginae quiagita differen
  44. mp
  45. n
  46. anp
  47. =2p5
  48. due
  49. +C V + CP
  50. ∞ + P
  51. i in sypengndo caprehensa, non
  52. Ambat. siter+ ex+ ec assu
  53. X + gquo LX t om
  54. qeu
  55. +v, 7
  56. Aex + ex + de etooxis
  57. procu figum quartanda, itaque quaeritu
  58. valore
  59. Cydx. Ergo pro v sulistituent
  60. y) et habebitur s hatimaliter per;
  61. et N0 exaeg. 2 habebitur iraliogarita
  62. sed reotitici
  63. porae aquadis
  64. padratura
  65. E
  66. 229
  67. 3
  68. sut
  69. u
  70. ras
  71. hac
  72. tam
  73. rancs
  74. = n
  75. Epsi
  76. pr
  77. tramnis + a
  78. Aramep
  79. 42 an C
  80. (2CC
  81. + ranc
  82. + cepp
  83. a ∞92
  84. etfinemm
  85. 2sa
  86. tcc
  87. .Ter volatur X hadibiureus 3.in
  88. sumatur v Bex
  89. punturfint g.
  90. smatu
  91. amni
  92. y assurger ad yy, et v ad vE. quae cri
  93. 2+ M. Ex
  94. amvan
  95. - c - ep
  96. ad aeg. 3 ∞g. 2. fiet aeg. 1.
  97. p
  98. B ZV + 2P Intrinallum reducta est. Tpatama XX = bg - CX- eC, substituatur in 5q, 2. fit 1V= By. Gex.
  99. ventis ad rationalitatem. Ergo quadratota aegu
  100. d
  101. sn XE +by- SeE +99- veo: scat, quos Rursus in vy. 1 et 2. mulliplicando per aucem
  102. fit gg ee sit sgbus - 39XX oex e vD sit , eC- by 99. vv Z =XXG9 +XX VB-exg ot BV
  103. et u 9. per 10 fiet
  104. -2XXeC F +XXby - fxeC + f_bq et dibisis omnibus per x fiet: X
  105. X = C99- v - feC + fby,: 5ee - sby eq-49 + bB, adeoque fiet ex 3 et 8 f19)
  106. Sec gg -5cevr - Sefee - 5cfby - f cgg+ ferv + ff eeffby(+ 6)2) 4by - 5 ee t 9g - 00h=
  107. et sC- vocesdi n et ex aqut put b
  108. 6 sndu causa Aet Lg voceti th
  109. et ex aq. 8. fin ( M3 - cv∞ + fby,:, D-bu - tih + vV. Ergo denique aequando 12 et 14, sietsm n3 - mC vV + m f by 4 bYVB 1t. h v V G lH+ Ggit
  110. compendii causa sit mn + h
  111. mC + ath = gq C. nf b + Slabla hu5 b +2. Gfh = Y3. Ergo ex 15 per 15. 17. 18, fit pF - q v0 + v+ + Y) 35. brBy +5 5+by9L
  112. compendio -10 = 18y + 12gy2. f. - 10
  113. Y
  114. 4. 5br vu+ 4. 5 5BV
  115. seu y = Y. 25t 15bq 1b 4556 V
  116. 2= y1: 12 + ye seu P ∞50 12 + 1183: 412 = 11: 4. V 4 y 113: 12 + yy5 C1= 410 - n
  117. = r3 =+ 2. 5 bb vB, : 2. 12 qi
  118. eu
  119. vanuit in vinento est qua
  120. tae
  121. ponem
  122. inem connesbentila
  123. potuisset contingnes si in aeq. 1. scripsisemus by = XX L Cx +XX+
  124. terminis, ut p 4
  125. Id sib elatere ponita
  126. sd
  127. 2.1
  128. tura et
  129. CX +CC
  130. poaiturs, u sensi loco e ponatur Ct 17, quruum in fie pudem seceri sinus
  131. nam ita Deudesi ac si
  132. 16Hrg 32 Be+ i

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 82v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0164?run=73