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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 42v

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.

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. 41r); this page is its left half.

The machine reads it as

  1. as +bkK aeq. biquadrato sit f= 120βB + 11 B3A + HO B, + 100X et R eadem solu pro 1
  2. fiat aff= a 120
  3. a lo2 M
  4. 1091
  5. 1012∞
  6. +2. 4. 120. 111 βX + 24., 12a1or BpH + 2. a. 120. 110β3 2a. 120. 101BPA Y7 a. 10 ( 2a. 10
  7. a 102. I11 BX3 + a 11I II
  8. eidem modos bkK summu teinde aff 1b) CK
  9. ex extilabitur ex
  10. 102. 101 A
  11. equemo biquadrato quod
  12. 300β + 3015) +300
  13. 110 105 CNV 10I XEY 1I
  14. MI. IIO BCAY
  15. 111. 101 BMY
  16. vereor ne eo ipso tam aff+ bKK debet
  17. ut eotandem defungamur aequi biquadrato, redeati ad ipsum quod
  18. Hlabet autem justitiae consideratio plurimum esus in calculo tum ad p. par sitiones, tum etiam ad diminuendam ejus
  19. nitio fuit a quastione
  20. prolinitatem, nam cum literae diversae pari jare utuntur, unius valore seripto, alterique vales pine calculo scribi potest. prod est atia
  21. ad calculi examen. sed place hunc calculam reup praesentem reapse aggredi ontvides com sit plitera constans seu
  22. sib r pro unitate compendii cava sit (4t) aCf + bhk = C et 6t0) aec + btq = D _ ) res ibls, n
  23. e(5() 2acF + aec 4 2bgK + bhh = Y e (7mo) aB +bKK = S et (Qvo acc + bgg= Q et sq) fict
  24. ex 1 fiet, 390 = 284. Ex 2 fint (10mo )3DD = 288. Ex3 fiet (12mo) (D = 450. valores ex
  25. 9 et 10 substituendo in a4. 12. fit e ASC
  26. sit
  27. eat)
  28. e
  29. 63
  30. c
  31. 8:9= 165548 sen 1340) = 6 100 unde exet 10p 13
  32. si 1653 e (15+0) D4 = 16∞93. Tergo valoris D, D, habentur per
  33. per 6 et Q seu per f,. X, C, 9. jam quaeram porhas etiam e et h. Ex 4 et 5 fit
  34. (1to) e= = bhK,: af = (17mo) D = bhgg: aC, quos valons aequando sit
  35. DC =bchk = Df bfhg. ser (18H0)h= Sc = Df,: bcK = bfg. et pari
  36. jare (19no) e = C) q = DK,: af9- a CK. Hi valores h et e, substituantur in 1yh
  37. fint (20 m0) C99 + C - 204K (+ (C) cct PN- 20D es
  38. +(3a cf +2bgX (0sR99 + CC KK = EfCGK) = et fgGH= 2fCgK
  39. compendii causa foL CK sit (2) nd) = r9 et (ad d0) ac f+ FbgK = rrB. nima
  40. sumta Yer
  41. incente pro
  42. 4aCC X
  43. 4ba9
  44. a
  45. 10
  46. e unitate. et a in aeq. 26 haec substituendo, ut et vafore
  47. 13t1g
  48. 14 15, funcer _g. 29c siet _
  49. Yord. 9r95Q+ 2Yy) 2r ab 844 = Itab. 6
  50. seB. ex 13,
  51. + +aB
  52. es aCC + bg9) 5 idem quod 60 et lass +b KK) idem qua quoque
  53. CQiKK
  54. quoa dE. Exrom X9. E5 omnia hoc reducuntur, faciumus ergo Z= er WW
  55. Sed exZ et
  56. itta ex aq 2Z. si divilione facta per 2. fiet E. ) grr W3- 4 rron
  57. +ab 899 ab 5abgqW. ob atic. 24 7, 8 tit ass ibi.k e rbgC
  58. (96t0) i qu’ an eroo per aeg9. 21, 22, 26 quaeramus sipsas, k, f, etc. Nempe
  59. ex 21 est (27 0) R = 59.rq): C et ex 22, f 28VOIK= Yrefib
  60. quos vaton aqndo fik bfgg- ibgg = rrc8- accF seu 90) fiet
  61. rrc Arbgg: accbgg unde parijure fet B0mo
  62. rrgq ragC, i bggotacC. NempC pro a, C, aponendo respe
  63. aive lu cive b,9, =q, et vice versa. Ratio autem cur pro
  64. C=
  65. o
  66. aponatur a est. Qvia in aeg. Funeda mentali 21, set X sic difserunt
  67. ut f, c,4se Lhabeant respective, utik, 9,-g. Sed hoc obiter. Fun
  68. damentalis autem esse respecm ininq jam valoribus fet K (inventi, per 2930) substio
  69. tutis in aeq. 26. per 8, siet Ar Gci rrabb 4499(+ 2r3 ab99 c∞) +r685
  70. erraabquae ( 2Y a49CaO = (21 mo) r OOWH
  71. et destendo destruendo, dividendoque per rr, ordinandoque, B
  72. rr58 + ab94, GC = r489 wu ergo vel fiet 9 =
  73. flet (33ti0) rrga +abga- Laviv, seuqque no resteat
  74. ed uras est gu (3a10) = 4rru?- ArrGWW,, 3ab- ab 8 quoe duas
  75. aores aquando fit
  76. S1-+W- FuW+ (3 = 4W- 4gW
  77. WW + 388W - 3 = 0, id est (6to) W =O = C
  78. Seu W = _; A unde per 33, ut fit qr 127mo) g= s (nisi scil. ut dictumqus
  79. 35t0) 13
  80. u
  81. caciamus a seu acc + bgg =0) hinc per 37 et 21. fiet B5) f: K = c:9, qu
  82. Etet ex agg. 29,30, posta vam q= 0 Hinc et si in aeg. 29 et 20 posito
  83. 0 imdrituantur valores ipsarum et X tiunt 0gq. identicae. idemque est
  84. 100Y
  85. 44. 26 pro, W, , K substituas valoris per 26, 22, et 38. Pata
  86. tiam per 18, 19 hince foce
  87. snu remrieta
  88. expliceno
  89. d)
  90. phicemus C et D in 244. 18. 14
  91. (39) OC-D5=0 ut 40) 39-DL =0 quod et
  92. quod si jam distimulandor seu f9 - Cx esse B
  93. imihiingreditinontita
  94. ima rc, CV0 Sir e irb. ex ile 1 B
  95. et quia ex 3dfitiaomo d.
  96. ao
  97. +
  98. eb

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 42v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0082?run=74