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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 67v

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: 0.78.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 68r); this page is its left half.

The machine reads it as

  1. proponitur ydo = do SCafvr+ ag,: Wtahi) siat v - bbc + a 2,:R et yX ca + a 5,: 7.
  2. a, F, B, h sunt datae constantes, b et C sunt quaesitae constantes. Q, R, S, T sunt variabeles simplices ex certa aliqua
  3. assumta vartante, varinti si etset R= 10Z + na, aut simile quiddam.
  4. Affumatur sit Cd = ILM + AP + K. sed
  5. compendiosioris calculi cnusa put posse K= 0. Ita dabitur sc ubi L, M, N, P, K, erunt etiam variabiles simplice,
  6. ex certa aliqua Z. Itaque seo az haberi poterit per quadraturas rationales. Quia autem quantur ydu
  7. seo CC+ a S,: T, in, bdR dcoib: R) + bc d (1: R) + ad (Q: R) palet quari non tantum eodzue multipl. (per rational
  8. axque debere summari; sed et codco, et cocodZ. Unde patet debere summari Y LMNB, sed
  9. hic nimis assurgeremus, nisi fiat M = , et summati tantum debebit dz. M +LP.
  10. itaque omiso tentabimus an omisso K, liceat facere co = YLM +M. Utque hinc tollatur irrationalis,
  11. fict coco = LM + MN + 2 M LN et ct + 2 Lmecoco + HN + L n = (+ LmmX)
  12. DELMAN
  13. Apurjus gy = af votag, :, vorah, st et proy et v substiturno valores, fiet ct coco + 2ac Sc raa ss,: TY =
  14. af bbcoco + 2af ab ZW + afaa QZ + agRR, :, bb coco + 2ab Zc0 t aa QQ + ah RR. Unde fiet
  15. bbcc W0 + 2abec QCo3 + ag 29CC coud
  16. taasshatiea
  17. + 2abbc Su + quabe sq coco + aa Z_traC Sco errEF
  18. ah RR
  19. + agbb 53. dt
  20. ah RR
  21. ~ bbcc cet + 2 LmibbcCoco + LLmm IH.C
  22. pata
  23. MKS
  24. + MMNN
  25. = 2LMMN)
  26. seu S = cib Et ob co fiet
  27. ac 245 + hc AR5 + ab 55Q_ = A6f TY Z = 0 ubi pro S = ponendo valorem, fiet
  28. Et has aequationes idextificando,
  29. fiet olo c9+C=0
  30. -ac 22E hc RR P + ab El 2q = _bs TY =0 sentabcc Dcck RR 1 2cf-
  31. a0 2Q + CkRR + ab S5
  32. Aequatio secundum cdco, seponi potest, quia ejus ope habetur LM + M N
  33. superest aequatio secundum cd., in qua si posset obtineri extractio, haberetur LM - MN, it uterque valor
  34. non continet nisi formulas rationales integras secundi gradus, Aequatio uttina explicatis set T
  35. a E + ah ZCRRQQ + acc htRREQ + acc R gR = bbcc, qu (LM - MN)
  36. bbF si veliuus habere exfrahibilitatem
  37. seu aget + 2ah RRZQ + aYhg: 5) R = (4 qu (LM - MN) et fa h = vatg: f)
  38. ita stabit:
  39. seu
  40. aatiti = a hih = atig: f vel h = ag: f, seu g = hf. a. sed hoc non licet, quia
  41. ita haberetur afvo+ aeg: en +ah, fieret constansu
  42. schibatur at L + 2ah QQRR F aahh R+ = b qu (LM - MN)
  43. (+ a hg: f R =
  44. -Z. aath.
  45. a qu (a2Q L hRR) = bb (LM - MN) + RR 1 (4 19 - aahh.), Nbb(LM- MN) = RR + (a b9 - aahiti)
  46. t
  47. sad et possemus agg +kRR, aequare uni invicem ductor (mutiplicato per K: a, et alteri multiplicato per a: K
  48. sed ita fiet q et R inter se habent rationem constantem. Sed Itaque sae ambage, idemforet si siumpliciter assume remus
  49. R in ratione constante ad Q. Et ita LM = MN, haberet rationem cistantem ad 2, Et LM + MN, haberent etia
  50. rationem constantem ad G. ergo LM hatebit rationem constantem ad s et MN, etiam, quod non licebit, nam fierent
  51. sLm et Yme extrahibiles.
  52. VBl a
  53. U+ bl g +bbC
  54. 17 hb = et
  55. l=
  56. R, a +2Bh 22 + B
  57. dape
  58. ab + (abboac
  59. sit =m +f
  60. + mmt
  61. mits
  62. itn q
  63. 9a
  64. a RR
  65. h9 - (n (a l mo ( du .
  66. - lina), 22 + h - ((in 1b8q), a - b MM, qu (L - X)
  67. tota formulo Z +... etc. in quadmor fuas
  68. redoes resolvatur necesse est ut ut mobis sit rndix rar aequalis, finge enim omnia explicari per Z
  69. aa aass) RR
  70. et B esse 1oGtua et simuliter explicare M et L et sper Q,, et quandam radicen multiplicari per
  71. recesse est aequari bis radices, quod sne mulatione determinatatam conlicet
  72. Aliter tentemus: Retineamus K et facamus
  73. 5= 0 fiet 2 = 2Kbia ex co
  74. a Atetbbi au. - af s1. f T = bbCCKX - 2bb ce E
  75. acchRR - af bb TT = 2bbCCKK = 2 b. bCC (LM + MN). sed video nos hrac ratione
  76. et ix e seponamque aequex, et ex co fit acc ZFtR
  77. estiam eo tandem redituros, ut formula ext binis inter literis inter se legem homogeneorum
  78. servantibus sit aequruda quadrato, quod tali via non est impte. Itaque apparet S, Q, et L serrandetere
  79. cu
  80. video revera nihil protasse K, nam si pro co-k ponas constantem novam, ut W, tunc lanelimodo
  81. alitisoganss
  82. at BBa1+ Daf abZco + affaaqueque
  83. quid si faciumus x Bco +aQ,: R. fint Wesvotau = agna coco tragaa pco + a graXR = 9). cotrTM
  84. et C1otaZ, :, c0+ T
  85. vvtah
  86. cocoL2RC F_ RR
  87. BB c0ro +2 aB gco + aa
  88. st et B Bco+ aZ fiet fuvnaqu =BBC2aDque at Coco + rah RCo + ah RK
  89. FBBgCo + FBgco+ aat eZ Sa PC + aR
  90. gy = cro +2 ARco + ungra
  91. exeocotre Bocoha e 2
  92. Ccotas Aps cocogrtissio raati RR
  93. 00 +a
  94. Ad
  95. sed videotioe in variabilibus seu unversaliter praestari non pots
  96. RR
  97. namen set sit Q in valoibus yav, imnalit poserunt
  98. sit y= exD + aa
  99. a
  100. aa
  101. F
  102. a
  103. et-CC oco + 2a esco + nuss
  104. Ddcoto + EADFOF ATY
  105. eovtaat eccoco +2aCRWgnAAE a
  106. Ad fgu CB ataqu in qu ( eto taT) = equ (BC + aq) in qu (C a + a 5)
  107. fit gque pco + ap)
  108. ubi p et D suntoconstantes
  109. aspondant Bet O, s et R
  110. C +t D, 5et T
  111. haipc+aR)
  112. ut desmantur Coh et cd, sint 5BBDGCCDBBDL T FGADAT = 2eBBCaS + 2 lpp CaS
  113. seu F qu (Bcotaque ( qu Dco ta r) = e ((cot a5)) = qu P a taB), (AquC Cco + a 5) = gqu (DCO + a T)
  114. quia jam hoc coincidentiatadum cum _ Co + 2LM dco + qu (LA- MN) = b necesse est ut
  115. hoc quoque divrti possit in duas partes, quaum quaevis habrat qualtor rabiees prioribus coincidentes
  116. eersa ereta
  117. BC +2CLa coc +eucom mo naC ss
  118. 3t
  119. . A dh aquacedt
  120. t
  121. +g
  122. +bon que

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 67v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0134?run=74