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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 231v

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: 0.77.

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. 232r); this page is its left half.

The machine reads it as

  1. Resumumus
  2. sit aequatio
  3. y 2 tah
  4. al
  5. V _ rah V 4 ael po. Multiplicetur per Y +P. fiet:
  6. +alpr 7B.
  7. sive per compendium: y +Py ad V alp o.
  8. siuve y =F y Laa FI
  9. et conferendo posterore partem cum quadruto alatere S al 4 e
  10. quod est,
  11. fal + repY F al
  12. sit aequatio V X
  13. + e
  14. Pa g+ ahy + ael
  15. y + ng y3 +nh y + nlay
  16. ng. 4 pah. + mae ( M
  17. Y + g3
  18. a V+ ng Y=
  19. +rnanga
  20. + ma
  21. surys + e, () n = y + ingereta + et
  22. lan
  23. eit ers 9+ ma. et er ug tenmarna
  24. = ah - a l
  25. (nh, tatiu
  26. JEmg +2g
  27. +ng
  28. Ennigu
  29. mt
  30. +em a2
  31. 4an
  32. + alpr (+ ad
  33. multiplicetur per n y + m. fiet:
  34. Ergo ratix ahu
  35. 1. Vorim lar
  36. sive+ahn
  37. +inegr
  38. +2mta
  39. Jami dividendo aequationem pone: -aalix + agegu a nl
  40. residua aequatio erit
  41. hinc n y x F
  42. qenca
  43. 2g
  44. am
  45. ea sinl pjma
  46. an 17 l a +lah n m + coti n
  47. E 1 12 an 1 Xla2
  48. g- gah. residua aequatio ert: Emae av
  49. 2gr. aah Zlahrt alin
  50. sed ita ruisis invenietur valor ipsus qui non nisi unia es quantitas aderque non nisi semel haberi pobest
  51. meque adeo aequationem sic dividere licer:
  52. adeoque:
  53. Aliter pone 2m a Platitnos +aete m
  54. in l. uph n + At mn
  55. residua aequatio est: = a ah f + 2 f9 Mlaei a 1 nY + lah +m. sed hoc quoque mulile
  56. si sit m nhali et am +an fiah, B maam anla. Dii sed hoc apte non fit
  57. si ponus ngrut sivi nei mg. fiei n m
  58. sunt duae aequationes
  59. aequatio: d + at. sit _ ab p az. fiet. ytri
  60. X 1 tul fe ponendo y tah paz. fier: yZ al. pro Z pone (∞+ ra
  61. fei: ah p S∞ + ra. et y y alv + alt
  62. v+
  63. sint duae aequationes una ad para adeoque
  64. S∞+ ra
  65. V + F
  66. alI B + 2a v+ + a Lsv +ra= an-ah +
  67. adeoque as svrasera rab varsura ra
  68. +av + eu l P alt. + 3al va Bt 4 a(3F3
  69. Pahv sattr aa
  70. 2sraaliv 2srathtv
  71. r’aahav +raat
  72. siponam S+ alae +shro
  73. si ponendo
  74. Sed hoec nihili
  75. Redeamus ad rem nostram, mutationem sclicet propositionis tructabilis in intractabilem vel contra.
  76. sit aequatio: X ah Y + ael po. multiplicata per y Pa dabit y Vtah caly 4 1a
  77. sive. y + FY ( + at 1 ( ph
  78. m -emnen + p m- n + ahi dae 4 al p
  79. +2ma -2 ma
  80. addatur et p
  81. auferatii
  82. m- n
  83. + ais
  84. -Emn +n
  85. +h.
  86. pro -a l ph. ponamus compendi causa a d
  87. et pro y. ponamus m- n. fiet.
  88. Addatur et auferatur 2mn. dissuaturque aequatio adscripto:
  89. imn- 2mn rata, in duas, exquibus una erit;
  90. m.+ 2mn + n 7 alp
  91. sui fict. (+) i - n p Y+ al Ressidua pratio erit.
  92. mtamm ina sive mtne P Y + al
  93. erit amn + pman tah p da. et multiplicata tata a hac aequatione refidua per m- n. fiet.
  94. CFn
  95. Hor ebut sinbi
  96. substiluatur ejus valor praecedenti aequatione inventus, fiet: (4 Ps + al + p S+ al mon (4) ate t f al p7 da imun
  97. ope hujus aequationis quaeramus valorem ipsius M, et fiet:
  98. per compendium ma O n + 20
  99. Dn +H3.
  100. et fet 87 h ie B 7, 14D
  101. (+)
  102. n ppar al n (4) alpr al
  103. +dar
  104. lat x z n
  105. C da
  106. OB 5+ al - da
  107. itit
  108. quotiens
  109. +mal
  110. datamtt
  111. ly

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 231v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0462?run=74