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Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 265r

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: 0.76.

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. 266v); this page is its right half.

The machine reads it as

  1. a b X + CX2 + d X + e exciletur L Itum
  2. O
  3. b X +2b∞ + 2 + 2bCX
  4. +C +2d, +2ICX
  5. X + p X + qX + + X + sX +X + v
  6. + 2bc +2d. + 2be + 2ce tide. + e
  7. + C. + 2d + d2
  8. 4 d. +2de X + e
  9. Ubi manifestum Unum aequationis latus smistum scilicet esse quadratum, i ergo simstrum quoque tale reddatur, ope aritratictum
  10. b. c. d. e. Conferatur cum alio quadrato, ibi venc in mentem compendium elegans, si successus respondet tum
  11. d
  12. si coincideent, ergo aequantur nulto magii. Si aequantur, ergo (6) a 20D + S Z(02) Ergo 2OD , quae
  13. aidem Jani superest, ut non tantum aequar, sed coincider quoque ostendamus estatem. Ubi hoc saltem lucramur ut omnes quantitates in quibus
  14. P F X +2f9X +2fghX + 2flX
  15. 92 tigh - +2gl X
  16. (its . 2t. 2df. 2es.
  17. + h. =+ rhlX + l
  18. 2b9. 2cg. 2d9. 2eg.
  19. 2bh. 2ch. 2dh. reh.
  20. 2b1. 2cl. 2d1. 2el
  21. P 40 h c d
  22. +s h
  23. tollantur, adeoque non nisisi
  24. torm
  25. Unde sine calculo statim scribemus: d) +1 - 2 lh - tv + hP
  26. Extem bp 4- f Exem. ult. eriV. C
  27. is
  28. 2
  29. se invirem, statim
  30. N extmll. b4 p. 19 cf ixtem pnit. es t - 2hl. - adl
  31. ) 1 X LpX +GX ArX +sN +tX AV B
  32. Jam etiam tres valores ipsius e examinemus,
  33. et quoniam perfecte similes sunt ha
  34. tres priores, tribus illis posterioribus, ideo tantum pro pon
  35. faciemus pro a
  36. ponemus
  37. f
  38. 1
  39. 9 d
  40. Extem. H bp7 9. 259. 5. 40s e9
  41. posu
  42. 2h
  43. Excotlatis duabus prioribus ipsius b. valolibus tieb:
  44. 7da 1osn (g pt. 29- us sie cri Ps s9 datos
  45. ex collatis primo et ultimo,
  46. 95 - 2529 - 9f - 2d f = 2c95 cs h. - h5 2
  47. 2
  48. et c e 9f-2529. 9f 2d f, -ha + hf
  49. 295
  50. et duos ipsius C valores aequando fiet:
  51. pf.9 59 -92t 9 f 45 - 2f9(9 5) - 2d f3 ab f + ts
  52. uc dri 95-sg- alit + h53 1s9 +50 +9a - 55
  53. quisqe e istamerntia
  54. et CF SM -13h -v9l + 9B, - F IM + P. L. + hi v - junvenimus ergo duos ipsatum d. et c. valores. nde duoi noved
  55. vsultabunt aequationes sine ipsis, invenimus ergo b. c. d. e. quaedam calculi satis ordinati specie. Ubi notabile est
  56. Ex tribus valoribus ipsarum b et e. unum esse, quem nec c. nec e ingrediunbum quod rursus ad calculum contrahendum
  57. magni est momenti rursus ex valiribus ipsarum d. et C, possumus eligere breissimos breviorem. Et ex Termino medio
  58. seu quante habebitur. (1) (+4gh fV, +FVFCa fI et 15 9(-Hsd) -to f g (+ hlS, + Ps 1H (( rB - gat h (d s Y n
  59. + a lf (= Vf), 1 Y5
  60. 4
  61. Supersunt jam aequationes duae ex duobus ipsarum d etc. vatoribus, quae duae aequa
  62. tiones inter se simillimae sunt servatis tantum substitutionibus quas dixi, ac primum collatis duobus valoribus ipsius d, fiet.
  63. +152 - hf3 - ho f + hV F 9f 1 25 g1 - alif l(+ hf 1) - pf9 l’ + f5 l +gal S 1 Et sinliter satis drolus catuibo iestus
  64. literae C, fiet
  65. pf1 - 2f9l3 = ga 1 (+95 BF S1 f - 2Bhf - v9l5 49135) - + Ihf + Prefe etiB - h 15 7 8
  66. Habemus ergo tres aequationes eleganti quadam ratione congruentes; et pro illis resolvendis, quatuor literas indeter-
  67. manatas, f. 9. h. l. Faciamus _ fl n c. et gl 1 A et hf 8. et fiet
  68. veof tAf -hg vf
  69. aco P p9 1 - hg a 1 B et rco2
  70. Grodsi jam ponamus in aequatione abesse terminum
  71. medium quod semper effici potest interventu
  72. = + a f 11g cor eeb- a12
  73. 2coA..
  74. =p cost
  75. +a)
  76. N Ng fcel-co292
  77. aequationis cubicae, i explicando incognitam saltem explicatione minori
  78. et Zp cokI sco - vAf
  79. =20. + c0g
  80. + d.
  81. aeqes.
  82. + 82
  83. +v92
  84. =D Hl vel - co ep A2
  85. si item faciamus preterea +V a, quod semper fieri potest p per radicem puram quadrato. subicam, si denique faciamus p, AtA
  86. prisna extubus equationibus novisimis dividi potenit per f4l
  87. exitque acc + p9 - hga p0
  88. sive
  89. -2p2 +13
  90. -qY
  91. pee rsph
  92. +ah
  93. spFho+
  94. teo ig duabus residuis aequationibus
  95. hvs
  96. phist
  97. et Ap 18, svi 914 Phf
  98. afl +phf -ngerio. erit Ae P Z
  99. Vii ex Granda him dieruum coripinaum, S ag l +qu paot ad A 9s et 1 pti = B +t
  100. Explicando jam 9. et l. habebrimus in
  101. sph H+ - it f
  102. eth
  103. Crp
  104. afl = pht
  105. na
  106. X + pX + + aX + Y X + SN + F X + B 10

Cite

Leibniz-Handschriften zur Mathematik LH 35, 14, 1, fol. 265r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068201:0529?run=74