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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 138r

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: 0.81.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 139v); this page is its right half.

The machine reads it as

  1. Quaeritur Sdx xx mm, nx. nns quadratura ratinali. C facere posimus ex um = B0D et xx. un - D 84 poterit
  2. radix extrahi ex Axp- um, PX -nn) = ODQ. Quia radix extrahenda ex Xtm, X- n, XAn, X. n, genralitatis causa faciamus
  3. rudicem extrahi debere ex X+ L, XtM, X+M, X+Co. Ad sint O et Q simplices ut.. +. ; sed X et D duplices, uti th6.
  4. faciams Xr = XFt, 1st = eid Xtm, B = D- hB X faciamus XtM = β,F B0 X; β B X+ m B= O
  5. X+L, : β= _Y C_ Xtm, β = 07
  6. XI QN Xrn Qs X+c, V = 22. ex xel, Xtm, Xtn, XtCo,
  7. sit e = b+ Atb siet 3 gt = bit + +h6 = Cod pst +9 +6
  8. Xs XGl it afiGS= C, est 1 d96 + (cgt s) HtS ubi noto par ex literis ajumtitis unum videri inutile, nam si fecisemus
  9. O c+dNS X 5A+916
  10. 2Zh I + H 1b. Q=
  11. () = sccq F td YddB, et postea faceremus cch = t et ddB = S, macaeterae, f, g, hiK, p, 4, b, statum suum retinere possent
  12. fiet 17 X5234E
  13. detineamu, tamen has literas vel distinctioris calculi causa, eventus enim quid in iis superfluum docebit.
  14. Ex aeq. 1. per 6, 4, 8, fit lB + bYG6 ~ CfZ+ d96 + (C9 + d f) Y5, seu (11 mo) = B cft + Bdus - l
  15. et (12 mo) b = β (c9+ d5) Ex aeq. 2 per 7, 9 fit 24 + Bm + Bb 16 = ChEFdKB + CCK+ dh) 14B seu f
  16. Ex aeq. 3 per 9 et 10 sit +n + bYL6 ps 19961 (9+ 9() 1t6
  17. unde (i5t0) Q = ypft +1498 -n et 16to) b = V eeg +45) Tandem ex aeq. 4 per 9 et 10, fit 18 +) cox bLBa PhiL + B 14 9(XGB
  18. (3t) 8 = L cht. + dk6 - m et (14 to) b = B CCK + dh).
  19. conferamus jau valores
  20. xtam ipsius b, qui sunt mere constantes, ex aegq. 12, 14, 16, 18, quam ipsius ex c99. , 13, 1s, 17.. Et quidem
  21. sumamus primum conferamus primum omnes valores ipsius b quiape cum his insint merae constam
  22. unde tste) (17 mo) Y = eatue + J. gk 6 = a et (1Bvo b = = (PK + gh)
  23. ex 12 et 14 fit (3( (cg+d s) = (19no) CK + dh. ex 14 et 1b fit Ex a9. 16 et 18 fit (20mo) YV (p9 +qF) = BK +Dh. Ex
  24. 20, 21 tollamus literas d et, q. Ex aequ. 19 fit d = C, eBg-X: h- BBf
  25. posea substimendi etien in aeq. 2t. t
  26. sergamus nunc ad valores ipsius 4, ex ae49. 11, 13, 19, 17. Ex 1 et 13 fit (251) 8 = (βh) Ct dm:, K - P(9, 0
  27. aequ. 12 et 16 fit B3 (c9+d f) = V (p9+qF. ope harum trigt
  28. Ex aq. 20 fit (23tio) P, WV9 -K, : h - )VF = 9. qu duo
  29. et ex 1) et 15, fis (2 to) _8 A pis B(h. ets)ChF C BCm n),., (3g. ex 15 et 17 sit E6to) C
  30. aeq. (24tu) p: C - . . . . Adero
  31. VV9)4. Denque ex 13et 17 fit aequ. 11 et 15 fit (27 mo) 6= (c. 19) f. ((- n); (3. P)
  32. cncodentiai cum itio, sed brevi aliuud provit s aequentur inter se et fit
  33. siprimt 2dus coincidentientur interse, et ob constantes fit (28V0) g. d - (H BCg: K 1 9) V. B (2 co, lum)
  34. =(99 f -h) . - 7 (n - Co),: x (F
  35. reg. K, pss ): (Bes h, VVg-K) patet
  36. oiants fit 2tahic srgnot ses t pnt itaque hec equ una collatio vaoum ipsius e nit producit novi
  37. princt et secundus valor ipsins 8 aequ
  38. sulstituam valorem ex aequ. 1t, f qui est h. BB: C egK
  39. 4 cq. D K eeo
  40. fieri S- (BBS A) et B( ritr k BBg C (BCD K h es) seu fiit 6 = qu Bes- 1) C- B(P5t) (l- m,:, C, que lg
  41. efiau, ex arp i3 sit d. P - Et -h
  42. etiam hine si in ratore F 1s aequationis 25
  43. per 2, f et 9 per 3, h et R per 4, faciemus BB9-
  44. = 1ZCt - β(Lm): - 140
  45. et 1 5 = 23 pts - V (n -co),: = 249. et pro d et 9 ponendo valores sit 8 = 13Ct - (3 (la m), : - 14 (.. 14: 13)C feu 6 = 13. 13 ct - 13(3 (. m). 149c
  46. et f = 2ypZ - V (a- co) : s - 24 (. 24: 13 p seu 5 = 23. 23pt - 23) (n. c0): 24 24p. quos duos valores ipsius 8 ab a d et 4
  47. netinso per l3 3. C e. 13
  48. liberatos inter se coincidentiando, ob variantes fiet 13. 13: 14. 14 = 23. 23: 24: 24 seu 17. 2 23: 24. = + 13. 14. Ante explicationem
  49. 13C: = 140.
  50. aeque. 25. 26) unde aeprndo fi
  51. p. - 249, seu 13:14 13. 24: 1423 = dp: ca
  52. qu B . unde tanerm qu 13. 2t = qu. 14. 23 seu
  53. u s h) pt F (3 B- 1) Cnaco) i qu (VV9. K). P. Et Contidentiturt veores 2b, 12
  54. : 1
  55. valori
  56. + (oBF-h, in ((3g- k
  57. )DCC. m): e X qu (eBBH)C et ex
  58. obque ipstis
  59. compendio, B,
  60. E 1 B(L. m): qua+ 14. 14C = 23V (n - c0): 424. 29 seu β((- m): 14c = + V(n- c0): 24P, seu p: C =
  61. 23: 24 = + - 13 + 13: 14 ut ante
  62. ecundum variantes fit (30 mo) Vyf - h, : VVg- H = +, βBf- h, :, 3(39.k
  63. +, (V: B) (n - Co, :, l - m) (14: 24) seu tandem simo) p: c = +, (V: () (n - C5, :, l- m) (+ 13: 3) seu tandem
  64. Etiam ex 23 fit (32do) g = + p, B3G -k, h- βf
  65. proportionales, quodu
  66. (c: p) D foret = C sed si quod (in quam nollem
  67. se si + ~ + foresit C et Q
  68. et ex aeq. 26 fit
  69. fiec (31 mo) p: C = (V: B) (n. co, : l- m) (βBf - h, :, Bβ39- H o
  70. ed si f ~. - fiet G = p sq - (pd: C) 15 et (C: p) Z = cst - d6, quod placet. Ergo essu pro habeat
  71. unde ex 32 et 22 fit g2 β33tio). q: D = _ A d:c si ic
  72. tollem. Nam C C posito O = C Ih+ de fietit Q = p sB + (pd: C) 16 unde
  73. 24, sit et ad aeq. 27. tollendo q ex aq. 21, fiet ex ea
  74. c(4: 13)f = Ypa R + ps (4: 13)), seu
  75. YP, :. A3C = 13g-14 f,: 13g + 14 f
  76. sane si esset 139 = 14f foret
  77. fg f. g = 13.14 = . lid s in toret g = si la . 11 5, d: C) 5 et foret s = 5 1G - d: c)FB et (C. B = ct- d6
  78. 21 (unde fit Xqu Z ~ aq
  79. 4p5) unde tandem
  80. + sit _ p: c = (1: V). (139 - 24f, :, 139 + 145) seu
  81. 5)F): CePs - h)9 = (BB9-K) F
  82. qui valor comparandus valori
  83. Ergo B+t) = sit =
  84. 3. C13cg - 14c5) =) (13p
  85. =e prasit
  86. Unde rursi ne sit)
  87. cincidentiari debet alius valor veluti repertus aqu. 2. Sed pricus
  88. =(C :p) Z per priora) quod non placet. Praestat ergs
  89. eu 35to) p: C = 3: V, Kf -hg, : (Bβf -usg 4 (Beg- X)f
  90. S- (BC - D PHG - (L - n), : (- Y P (24. 25 + Bc (+. 13)9 se
  91. bto) S = (Bc - y pi fH. - (1 - n1, :, (+ 3 p+ BC_, 14: 13) qui valor coincidentiari debet valori 28; qui erat _
  92. l- n, 14. +C = _3 (1- m) 3 L pF BC, 14: 13
  93. m- l) :, 47 3Cl-n
  94. q
  95. Restat aequ. 27. Cujus valori ipsique e
  96. ex aequ. 27 tollamus d, 41 R. fut ex pti e
  97. Calculo dubiu contra es homogenestm, nam l, et BBL, non sunt homagenea, quia 14 continet e
  98. 13H P +704 BC 7
  99. (3(3gm (329933+
  100. Ex varventitus comparando _q. 36 et 28 fit
  101. g. l-m, =Y + C. pis p. c a R
  102. (3C- V p)814f = 139C + )p+ BC) seu (3 - 3(gVp Kf BC + Kfpp
  103. est p L(BBg
  104. BBg (m - n) = K (1 - n),: = VBC L- m)
  105. B 1)9p 14Vfp = 14f fB 1329C - 145 pC et sit p: c = 3g (9 v) 13 g (, 139 - 115, : 1yg
  106. quam aeq. compar ido cum aeq. 35 fieret 139. 4 14f = = 139 -145 seu et foret posito + 2 = feret
  107. seu 139 = - 145
  108. seu (37mo) su p: C =
  109. 139 + 12f 139 + 14f = - 139 - 14f seu. 2 139+214 f -0
  110. compurando cum eo ex qua per explicutionem facta H aeq. 35 fieret eliam 13-145 =0
  111. non consistit, nisi fiat 14 =0 et 13 = 0, ande elim foret 23 =0 at 24 =0 sed haec non licent

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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 138r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0275?run=74