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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 10v

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: 0.79.

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. 11r); this page is its left half.

The machine reads it as

  1. Redeamus ergo ad X3 = h + Ist, h- T = A d + 7 sA, d - 2sM, 5I+ 7, 51- 3In
  2. Si sn = ∞ fi et 5V7 = DD. qui ha B et + non possunt esse simplices, saut secundi
  3. per spaginam pracedentem, sint secundi gradus, ut amplius resolvi possunt, et quia
  4. et ex trahanda est raix ex h + 7Il, G- Tst, et ex 51 + Hn, 51- In,
  5. ita ut alter sit quadratus, alter divisibilis per quadratum sit h = 10XX + 11aX + 12 aa
  6. et 4 - 20XX + Z1 ax + 22aa V debet eb t2o XX HL + 21 ax H + 22aa Hl quadratus,
  7. 10XX = H1aX - 12 aa
  8. et 120Xx N(+ 2 ax Il + 22 aa Sl
  9. + 10 XX + 1 ax + 12 aa
  10. etiam quadratus; vel oportet ut
  11. nam si radices eorum sint AB, CD, fut ABCd sit quadratus necesse est aut utrumque esse
  12. quadratum, aut, quod non licet aequari quodd variuntia inter se. Est ergo
  13. XX + 2 a sC - 11d aX + 22 Il Indaa ~ Xx + 2bX + bb, et fiet
  14. 20 l- 10
  15. 20+l - 10
  16. 24 b = 21 Hl - 1_ et bb -
  17. 21. 21( - 2. 11. 21Yl + 11. 11
  18. 4, 20. 20l - 2. 10, 20 fl- 1 10. 10
  19. 2, 205l10
  20. ut - 211. 21 ANC + 1 = 4, (20. 22( - 12. 20Yl = 10. 12
  21. 225l- 12. pt fiet
  22. 4, 20l - 10
  23. Et parijure 21. 2 sl C sed ut alter etiam sit quadhalus oporset tantum
  24. mutari signa in 10, 1, 12, et siet
  25. - 10. 21 Yl
  26. 21 l + 2. 11. 21 Il +11 = 4, 20. ul + 12. 20 Sl 4 10. 12
  27. Fn, 1 - n.
  28. -
  29. in
  30. A
  31. + 10. 22
  32. (3
  33. -l: In
  34. 2= Tstanin
  35. sIn
  36. Cnhendo fit 4. H. 2, 4 4. 11. 21 NV = 8, 12. 20 + 10. 22
  37. Ex priote aeq est Ex posterdore aqu Ex aaq. 2 est 2t Al + 1 2 (2, 1220410.24. A pari jure
  38. C + 12. 2en CC
  39. e
  40. l
  41. + 24
  42. si a etiam 51+3In, et 51 - 7 sn debeant esse quadrati, redit adhuc semel aequ. 3, et
  43. Ex auua 2 fit 21V +1
  44. prodit aequo 2 et pro aeq. nova prodib 2tn +H = 2 v( Id. In
  45. 10. 22 s
  46. hendo aeq. + aeq. 5 fint (2) 2(s (2) (... l..) - (2) 1(.. . n ...). Et si dividatur aeq. 4 per Al, et
  47. aequ. 5 per In, et detrahatur noc a illa proveniens ab illo fiet ce
  48. 1H: M = A M(... l.. .) = +(.. . n. ..). Sed in aeq. 6, pro 21 substituendu
  49. in
  50. valorem ex aequ da fint 2. p. 20d 2 a (3) tC. . l. .) - .1 (.. M..) Ergo ex aegg. 7. et 8, invicem
  51. 2-1 Su
  52. Av. 2IM
  53. (9
  54. fiet
  55. duolis latere dextro in deptudu ctisinistro in secundam,
  56. (..L B +.
  57. (1.. B. ..) 21 f(... l.. .7 1.. n. ..)
  58. In
  59. sin
  60. Compendio sit, 10. 22 + 12. 28 = 202 et 12 2 + 10 20 10. 12 +20. 22 = 104, et 2- ll+ nin = 103,
  61. 2510. 2 (28 Ist +nin) L
  62. 3
  63. quae est mere cognita, fiet 2. 102 2 1ento 2 = (... l...) = 1oblF 201 sL et -. A (. . M. ..) = 1IB+ 20. In
  64. d
  65. fiel
  66. sIn
  67. 212. 203
  68. et denique +4. 100. 207 +1, 101l, +101n L 10. il 10c In - 4. 100. 201
  69. 1205: l 420P: n (22) 201. 201: )
  70. 201 : 1 ~ wortR
  71. 101: 201: Mn
  72. 2 post cosu
  73. Cortn+ 2o1 (2) 201: 1l 201. rn
  74. quae aequatio silsulsacit dab tiet nisi i axbitrariae evanescant, dab. l 201: 101 aequatione
  75. 2.101.201 2.101. 201
  76. quadratica. seu 10. 22+ 12. 203 :, 10. 12 4 20. 22, adeque adeoque H: 20. 10 tantumque cavendum ne simul
  77. ne sit to 4. 4 = Hc tantum cavendum ne fiat 10 20 : 10 = 22: 12 = 21: 12; ia
  78. Sed videe si potius procedendum s a exit tam si M =0, posumus vel X facere quadra
  79. enim constans ratio foret ipsorum
  80. tum, vel saltem formulam qparti gradus factam ex quadratoet formula secundi gradus priore
  81. casu X+ L, exirre debent esse quadrati (ec sed posteriore altent
  82. alteruter tantum. sit ergo x X = NAX ses AB NaBa Si N Z7. 1 +
  83. Xa et X+ I = Sux 7N_ SV5V Z +l seu Suse 87 a + 77 it A L, : 27 1 71
  84. 7377 et py Zat + 27 A Nal debes a quari quabrato quisitaah3) X3 7 aa =
  85. a- et 77 , it a t = aGB + I 1I a 3B - Z it sal = 5eg 7 aa. Videamus
  86. X = NN ZGII
  87. an liceat facere hPa t 2it Vel = susa et hBa= +p sal = s Ta idem cal culus institui potent pro
  88. aa hGBr
  89. sit s ~ eo GB = 10 N 2X pMa F = 20X 121a
  90. sit 7 = 10X + na 5V = 20 k + 2Ia 4 7 = 30X + 314 BF. -KaXX + frax + 42 3B = 60XX + 6IaX +62 aa
  91. ∞5I
  92. L pouendo n, et pro G1 ponendu
  93. fiet que oX na) tee aua ilxrna=
  94. Et fiet

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 10v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0020?run=74