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Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 14v

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: 0.84.

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The machine reads it as

  1. X, y. 7. 5. E. B. ) M abc de
  2. a. ab. abc b ali beq ode Thh
  3. Mertious haec tenenda; quia omnes
  4. a aequ X. a + 2 ab aequ. XX. Ergo a aequ. p-
  5. ab aequ. y
  6. ab aequ 7
  7. litr
  8. esentutus
  9. ut formae quae ad alar invenitindlas naturagli ordue
  10. ab + 3abC aequ. yX ergo ab equ. y.
  11. servire debent jam sint praeinventae, ita for,
  12. abc + +abed aequ ZX
  13. abc aequ ZX t
  14. MVaebed serit ad inveniendu altiorem ejudemgradus
  15. a aeq xpurg a t ab aeque Cy. x Ergo a aequ X 3yX + 3Z hac metrodo quam
  16. a baequ yx 3Z ab+ D.
  17. ab
  18. abaequ y. ab + 2abc + b abcd. aequ 1 y y. Erqu a b aequ. yy - 1ZX d
  19. abc aequ. 7.
  20. Zy aequ. abc + 3a bed + 10 abede. Ergo a bc aequ. Z y - 3dx A 15(5E
  21. 10
  22. abed aequs dyrego a b cd + 4 abcde + 15 abedef. Ergo a cd aequ dy - +EX + 9 D
  23. 4 EX - 29
  24. Ergo eodem modo erit
  25. ab cde aequ Ey -5DX + 14 5)
  26. Habetur enim facile progressu in infinitum ex ipsis nundiis combinatorius.
  27. Notu in
  28. puncta a sinistro dextrorsum. in sequenti _ ert imtium l. 2. 6. 20. ilaai 3. 10. 38
  29. aoc aqu. Z Laequ. abc + 2 a Bcd+
  30. abed aequd dZ aequ ab cd F 3 a bide + Boabedes + 35 a bedesust tbabedesq
  31. 2
  32. de
  33. 3Cy - 1B t DoBX- 705
  34. 1
  35. Ergo ab d rgo 3Z 3CY + 5DX - 7 A
  36. Et continuando progressionem ... . ... Ergo ab ed eaequ. 2Z. 467 +91X= 16
  37. Hinc sine calculo per solum progressionis continuationem colligo esse.
  38. Et sic in infinitum.
  39. ratio
  40. ab d’aequ 5d - 2EZ + 26y -25 X + 2n
  41. abC de aequ Ed - 3BZ +5Ay - 7 MX + 9Y
  42. a bc d’ef aequ 8d. qt Z +9 ny - 61 X + 258
  43. Et generalis habetur regula inveniendi valorem cujus cunque formae ex solis t
  44. literis quadratis et simplicibus compositae.
  45. iam a ad formas qua aictontt )a pocedamus. legantissipo desriuntu
  46. a aequ. XX - 2ysaa, X - r yr aego a + a b. erit a aequ XX yA +3Z - Exy seu a aquX. 3yX + 37.
  47. yX - 1Z
  48. ab aequ 3X - 3Z , prX- 3Zp aequ ab + 2 a bi abe er it a b aequ y (Zx + 4d - 2gy
  49. 179- 4242 1Zx-95
  50. abc aequ ZX - 4d XX - 4d X equ. abet Ea fic+)a bed. hi abeagu z x- dx + 58 - 2Zy
  51. 225-6sx Y105 3dX - 15E
  52. abedaqu ex- fE dXX - SEX aqu ae bederabicdarabide. Eit abida P. XX. Exr6B- 2dy
  53. Esy. B extis Ax B
  54. Et continuando progressionem . . . . . . . . . . . . abedeaq. ExX. Bx F . 2Ey
  55. at
  56. ubi notari posse videtur rectius sae scribio aa
  57. abx aqu. vyx - 2Zxx + 2dx aequ. a b + a
  58. ZV. 3dX+E
  59. abCxaequ ZVX- 38XX+5EK aqu abc + 3abe+ 2ab cd
  60. eu
  61. 372 65y +bEK- D
  62. a aequ XX = 2Xy yX + 32
  63. cb yx 2yG, - ZX +40
  64. abe Z1X. yY- dx +5E
  65. A aguX
  66. et enite a
  67. X
  68. Notetur egregius ille modus
  69. a revocandi ad harmo-
  70. niam cun caeferis dum
  71. 37X divellento in duas
  72. partes = yx et - 2xy
  73. nam caeteroquim ua hiutea
  74. erat niadus series statim
  75. L.4.d M. multiplicari
  76. er 3. 4. 5 etc
  77. os 22 40 xx ubi omnia eliganitissime destruuntur
  78. ab aequ yyX 2Z +SdX - SE = ZY +4 2y. seu a brago 7YX. 22 + Sd X H 4y
  79. abeu pz yX- 3dXxNIEX- 128. 372+4 8y
  80. aby. gexeripd
  81. abedxago Syx = 4C XXt9 B aequ abid, 3 alic abede abedaq Syk -rem 19dX. 21 A 3dZ+ 6Cy
  82. 2y52-9Ey + 158X. u N Drey-158X+ 41 1
  83. Et continuando progressionem . . . . . . a bed eay Eyx - 3BX 19) X. 3 p 357188y
  84. et omnino totius Algebrae clavem continet.
  85. item
  86. ut et in praecedenti,
  87. idemque fit sem per
  88. si progressionem
  89. retro continuare velimu
  90. ponendo 1 ante a
  91. et a6 autea
  92. item ao ante a
  93. Nam pron
  94. et
  95. ab cX aequ. ZZX- Wy X pECX X - 26X aequ abC +abD bEr qu 27X . d + 2EL -R +36y +3d
  96. abedk aqo der heyasdu rxe abcdiq abe e abie. Ergo erit ..... ab2da, in 3 + 14 mati
  97. add. gerige snige (ex. 8ds tibssorip
  98. bC. Patet autem
  99. facilius inveniri
  100. forma
  101. explicundae pet X. y. Z. et. ioeo jam in
  102. et ipsae ja formae rjum indeta per ipsas formu
  103. multiplicandi
  104. valores per has eat
  105. plus qum rectangulis seu formis simplicibus
  106. ad quas omnia
  107. redulere volumus
  108. affinitatis
  109. habet
  110. abinitio, quod concoquere
  111. non poteram
  112. 1
  113. aZ. DIYX 5OX. 7A) aBC p. Z7X- id yE + EXX- 7BX 1Z+ D P, til
  114. Nam ita apparet primum
  115. X. y. Z etc. multiplicari per aseu
  116. X 2G. deinde y. Z. d etc
  117. multiplicari per X. denique

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 4, fol. 14v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068217:0028?run=74