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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 140v

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.

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The machine reads it as

  1. X + M. X- M
  2. XFU, X 2, prodnt
  3. seu reddendam extrahibilem, liat X sit quo X=
  4. q
  5. ex _b s 4 a6, in 5 1t +9Y6
  6. debet esse X+m, = _0D X - m = x st Xtn = sp X n= bp X+ n = 5Q. X n = +t e
  7. st = 5)
  8. ita XX - um in XX -nn, = De B in 7OOg COV in D44; quod libet autem exhis s,t, C, Q es
  9. six compositum ex duabus irrationalibus simplicibas.
  10. inolli caeteum intelligo aequalia vel quasi, id test, aequatia,
  11. Effici potest primum, ut sit Xt m = B00
  12. effici etium potest, ut Xam sit productum ex robus, quomunum dividat xon, alterum n
  13. vel non nisi
  14. dratione constanti differentia
  15. Z_, possit intelligi producta
  16. ubi A et p ente, HC et 6o quaesitie fit et B++ sh+ V 1,
  17. quae deo habeant communem oivisorem
  18. videamus an generaliter quaevis formuta ut
  19. fit 1Gt + o L (12 Y + 5V ) eti f ures oro procedit
  20. ex uit duab. nt +
  21. x = bdt + cYB, sut +916= b5t + c96 + bg + 15) st6 0 - hd
  22. (+ V
  23. t+56
  24. 3 (X + n = 00 = Eih + Hti S + iila 1hS. fiet Bbg+ ( et = 2hta et BbsG + Bc96+ (m = HEHt5
  25. anisut X-m = 5 sit bft + C90 - n + ba + C F) t 5 = pYL + 456 + (p5 + qY) 746 fiet
  26. g + cf = p5 + qV et bf. h + c98 - m = prt t. q5
  27. X +n =5q seu
  28. b5h+ C95 +n + (b9 +cfI YhC=
  29. PBh+ do . + (pro +qu) 146
  30. psh+ 9lo, Y1q+ S+ 1d
  31. tit Vst + cg6 n = p pBh + quo s et botes 1
  32. X - n = 2Q sin rut + 51C, v. 1E + 10. - rrt+ s1os + (ro + 51). 1E6.
  33. unde sit bFt + c9t = n = rnG + sio 6 et. Xbg +s _ = rW + 5V
  34. bgf.) hK q = p5. + qu pro + qu ru + sD
  35. 2d: D = 5-9,:, p. h pV (5 - 91: p. r) + qB - p5 + qY
  36. pariin ps-rq, : ptrq
  37. vip. -r = pCps + rq; rCP)+Y4). seu
  38. prs qudo pro duebus valoribus ut 2hkaB, inter quae postitur
  39. H his ergo aequationibus non videtur elb difficurtas, sed vieniendum ad illas ubi explicare oportet v et 6
  40. fit p5. V( pao +pqu ran = pps + jgr.
  41. habemus ergo v et W absolute. Restaut duae ag9.
  42. 8 1b5 - pr) ZD = m, :, 45- cg, quae aequatio
  43. sit H = ut 7Zt A 8 = AZ + a + (5bf7 + Bbs da + (3
  44. divellenia est in duas, ne tu habeatur per constantes, et fer Bbf hh, 45- cg = bf -pY, KK = (3C9
  45. etico rics
  46. 3b5 BCA 8 = (Bbf - hh) t + BM 3 =, XK-
  47. Rursusque
  48. C (b+ - pB) t +n; : qu - c9 = 15. rv) Z. n, 5u-
  49. 4-9u +cg
  50. KK = bt BCG = prKK + pr BCg ex Bq. sit 2q B95 + KK = 2 βC
  51. 3, 95 - cg d = 1, KK βC) Eodem modo ex n, hatebitur
  52. Exaquor sit in fit bf sid C lfc9 - p CYW + B C9B(2 b5 quo _C b fCg) rqov + rego et ex ( 1t sit (5-quo2C
  53. Sed ut c valores ducti ex m, et ducti et n connectantur inter se, opus est valorem ipsius. S ex aeq. 8 si placet, aequa valori
  54. Ex sq. 9 fit 3bf95 ( β0fC9) = hhqu = tihcG.
  55. ea
  56. ipsius X ex aeq. ubi et divelli aequationem in duas et sint bt -pr, qu- c9 = t - pv, qu -cu et -M, qu- cg = +n, - c9
  57. ex proretiot bf quo (= bs C9) - pr quo + prcg = bf q5 b feg - pa5V + pcgD et m: n q -c9, :, cg - qu super sunt ergo
  58. 17,18, 19, 20. Ex aeq. 18 fiet per 6
  59. 2 squ (5 - 4), pstru ex 20 et (8. fit
  60. 15, 16, 17, 18, 19, 20, pons oamen D et 10 ape 5 et 6 dollantur ex
  61. W = 3C9:, suq = nCCg. 95) + egm am in lvaim 19 pro ad ponendio valo rest, ex 18. fiet.
  62. 194. 1= 2c
  63. abtEgu - 2prcgq = bf95 = prcd 5 - pcgv, 5- 9. seu v = 2bfC99+ 3prC99 7 b5 95(3, 9 =p 5C95, 91
  64. Restan o et 20 runtenda ex 17 tollantur, ita hhabebunus gaa
  65. literas B, b, c, f, 9, h, K, p, 9, r, 5. Vidramus an in 17 liceat facere p5 = rg.
  66. praestandis
  67. ita omnes calculi valde contraherentur t
  68. sed tamen et valde mutarentur, ita _ fieret quadratus et hunc fieret vel pa r = 0 et 5- 9 -0 ex aeq q. 3et b vel quod mallem, pro utraque
  69. (23L= (EX5) pari P5 trg, :, pe5 - r9
  70. iceret
  71. una aequatio p5 +rq = 0, unde revera nihil supposstisemus. quia aepono suppositio non diminuisset numerum aequationum. Verum enim vero non didentur simul
  72. stare pose hae aeqque p5 - rq = 0 et pstrq nam fiet p5 = rq = - rq, ergo frt Y et quaansus fiet r920 et r vel 9 = 0 et p5 = 0 Ergo p orl q = 0, qui
  73. tert p et 9 sint ipsis r et 5 aequel
  74. pi ee qu pro gn. se
  75. Ergo p5 = r9 =8, necu sune multum
  76. Eaperior aeg. 7. manet sine mutatione sed in aeq. 8 pro pr fit pp pro 4) fit 4. id fot etiam in aeq. 9, 10, 15, 16 sed ita in aeq. 8 fit vnt
  77. omnia non sunt permittenda. Ergo fiereto facere oporlet p = r, et 5
  78. d
  79. itq utiue tutemus et s substituem
  80. = 0 vel 9 = 0, faciamus 9 =0 et videamus quampda horc jam Formetur calculus. fit +er. ()RK = p 2q = proxqu= po
  81. an respective proportionales
  82. seu KK = - 344.p 4. ex 17
  83. to perq. a nn
  84. sit imentica eua succedit sponte sua. aequ 1B etam jamhabetur. Ex aeq. 19 fiit Gguo- peoco = b fqupaaB et divo
  85. bflo - p bsq - PI D. Etaqu. 20 dabit m n = 49. - qu seu m. H q: W Num ergo pautatim omnes exhris valores definiamus
  86. A =0 r - p s=g 10 = -gn: m = Cparig reformatam) q(bf- pV): (bs- pD) fietq Cop - bf)n (b p∞) M. et fiet hinc
  87. e
  88. ca =0, id est v
  89. Ex 7 fiet
  90. 1x aq. 15fiet Abf -ntra - b5β + Pp (3. Ergo
  91. Clit = lit Y BPF, seu ( = tih + PP, : 2βf. Ex 3 fit per valorem ipsius W0 fit 264 = - 4(n: m) D + qu, seu v = 2 (2 + (2: m)) p
  92. v. bF Cm n) = + PD, in ex + q 1b suit KX = (344. EX 1q. c6 funt KK. = = β.
  93. sed sup paulo ant. v = (th + βpp _, : 22) (m +n) 3: jm +pp. fint P + ppm 3 2( (Em +n) = hit + Bpp, m + h. m
  94. unde habetur h per B et β. superest ex
  95. et ex2 sit hq t = pF BP9 = qu- seu h = (P. V- B. unde
  96. 14.. - Cpp + Ppp, a+ a, m. Ergo p = - m ted 9 e 5 manent artihrariae
  97. ex aequ. mmpera fit pd + ppm, 2 (3 (en +n) =
  98. 561 + Sc
  99. ex h uvat tum 5 - +
  100. 1 - L - E ut B
  101. Do neu vabo 1ra munt etam 1, - E - 5, 15 1 6, monb larm 1 2d - E + - E
  102. E CE = E - 10 = - 3 = (90 4+ E- E) 2 E+ E- E
  103. 3 = - E = 30E E+ E - + = (405 - E) - 210 4 - 2 + 2 - 2
  104. 312 - E+ E - = (313 5: ∞5) - 13 E- + +
  105. 0B3- E, invab 1 sulum 20 , + E - mon Geeror non (30 E, - +) = 23E- +
  106. 2105- E, _ = (2 E, - 1) -
  107. esolirsprant oersare Hanmumes eg vavet unenm ep. 313 + E, - 5, + E, a1 pr 1 arjore
  108. +
  109. u m
  110. iu
  111. 3
  112. 56

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 140v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0280?run=74