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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 423v

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: 0.74.

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. 424r); this page is its left half.

The machine reads it as

  1. v-12 sm + estum v + af vB + ag dalot esse aequalis quadrato cujus latus ap + GsIm
  2. a-
  3. +udUlmm
  4. + 123F un MN
  5. rafvo. +
  6. aLm
  7. + 4. 112. 123 lmm In C
  8. 4. 12. 123n MM VIn
  9. + 2. 112. 123 af M rin
  10. +2. 12. 1233 a mm.
  11. et m Umm +612 us Enmm +1Eaflm + ag = aa pp + En 49
  12. 129 inmm
  13. 125 afn M
  14. ubi substituendo valorem ipsius B, siet
  15. 4. 1. 125 np 2. n usasnm
  16. Hac aequatione divisa per ln, fint comprndio 9 u ar 49 = ideterminatis,
  17. 299= ar quar- 4c5). Et quia q debet esse ration.
  18. et
  19. eb etiam 29q erit rationalis in ipsis indeterminatis; adeoque Caarr -44 5) debet esse quantitas rationalis,
  20. quidem talis, ut ea addita vel subtracta respecto ar si proveniat extrahibile, ut tandem in rationalibus
  21. determinatis habeatur q. Porro l, m, n debent esse quantitates rationale
  22. m, et si
  23. n
  24. implae, et ideo
  25. im quarta
  26. et n possunt integre ltohalitar e ica possent L m, n, tamen res e praestito res reduci posset ex
  27. etiam l, n rationaliter integre simple explicari possent per n, quippe per quam X sit explicari so test
  28. Hinc posset fieri l= 10M + n a et n = 3o + 31 a et ln = 10. 3o mm 4 10. 2, a M + 11 31a a.
  29. in mm = 30. 30m + 2.30. 31 a m + 31. 31 aamm
  30. 1p = 10.38 m X 18. 3Bam + 3.
  31. ArOu. 10m 4, 12. 10. uan + 1t umamm
  32. ar.
  33. 13. 30 n, +2. 125. 30. 31 a M 3 + 125 F. 31 31 aanim
  34. 612 nJ. 1930) 6.1E. 13. 10. 31 ar3 +B. 12 125. 11. 31 aa mim
  35. 16. 12. 25. 1. 30 an . 10 a f rmmt 112. 11 a F m
  36. m qerolia pus
  37. +12330. af mm + 125. 31 f m
  38. 2. b. 40. 0. 31 a m 3. + 0.l1.30. 3 aamn A 11. 31s1 a
  39. (4. MEAS. Eo M + 4 1 .19. 1oIam Z. 1E M J. 16 1 SIaaN + 1211E. n5. 1011. 51am + A. M. 13. 13 31 atm
  40. gtens odon
  41. i l hs o s ari +n. 16. 1 . 10. 3oaa n 6 4 4 l. 15. 13. 31 a m r
  42. . l l 16 1 1 15, to ti cum 24 4 112, 123, 10. l1, 30, 31; cum 123,12, 30 31, 10, 1
  43. ue 1n35 6 o d. f. se toe ta estatit
  44. m si umm mnneactm ra) aqq = sa euillut anm i s 1) 20 X + 2.2o nX t 2. 20 vaarx ger.
  45. 12 pnnum 123 afn M
  46. 6. 1rE. 13 Cnmm
  47. xrationaliter integre simple explicari pet
  48. assumeretur velut X, per quam
  49. ln = 1830m + 102
  50. niuion hon aam 1n S. N. Di _n
  51. +8. 1. 2f. 112. 30 aa M
  52. 14. 1 a8. 16. d0 af M + G. 12. 2J. 1011.30a f m 5 + 4. 1 23 pi. 3oafm L + 4. A2. 18. 12. 5. f M
  53. +16.12E113F 10 HZahtaamB
  54. +a 1E. 1232 16.31 a f M + 18. 112. 125. 10. 11. 31 ∞ f 1
  55. idem rarsus, nisi quod permutari debent a, 123, 10, l, 30 3l; cum 123, 112, 30, 31, 0, 11
  56. +qrapq sn
  57. 46. 112. 12s bn MM
  58. d
  59. 12 aF R M
  60. 0 = + a app
  61. +9q ln
  62. 8.12.5 n m adeoque
  63. 2. 10. 11. 30.30 a + 1010. mm
  64. H. 11.
  65. +2. 10. 11.30. 31.
  66. Un = 10. 30 m 4246. 11. D aM = 1I. 30aM
  67. +1S. 3F amm t2 1O. 11314 n 17
  68. I = 1030 u + 2.1030. 3, am + 103i a m +. 11.3 a3
  69. 11. 302 amm t 2. 11. 30. 31a M
  70. saciamus _ q 10m
  71. (112. 123. 130 aM
  72. + 1E.123. 10. 3042 3 1 ~ AL. 13. 103 es 1 + 12. 125. 13 a7 M
  73. un -1o ma tu. spsem esiaa
  74. ln.
  75. Compendio fiat a5 = 60 n + 6) m + b2 aam + 63a m + 64 a m +65 a m + b6 L m + 67 a m + 68 a
  76. comprudio fiat = sem 40
  77. a3Y = 50 M + s1 a M + 52 am + 530m + 54a
  78. So M E+ 2. Go. sta m + 2. soma ni sr soss aur2. so. _ an
  79. 5ISI. a m +2. Sus2an t2 31. 53 an f. 251 59 am
  80. 75252 a n + 2. . 53. a m + 252. 59 am
  81. 153. 53a m L. B. 5iam + 45ta
  82. compendio fiat
  83. ar=
  84. (1E Im + 125n p. + aB) Lmm F. 2. 12. 115 lnmm +2. 12 ar lm F aarr Svestmm +2) + 4 u2. us si un t 1e emtag. 149
  85. es arntr
  86. ap= 1 lm + 123 um tar = 2113. 1g lmm + 112. 123 fm-: 9 seu uiti
  87. e
  88. velmqus 1 . (2. sa nnon.) 2t. rs Cmma + vr. 13 asm brmf.eti aa)
  89. B. p3rEL
  90. sit q tm:a et r= sin t adlage, et prodtunt hae duae aequatores: 2.B stnter 2M a a iaq p 1s snop sparus ii la mi itus u ag. betftiaa)
  91. a2 t: glimm, + (t: a) smyl a(t. a) a sag= 2. i. 13 lntr turrs apt 2. 135 snmgs + 2. n ap
  92. 13 t. a) tm
  93. Hiac duae aequationes ad m.
  94. 2. 112. 10. 50 m + 2. 15. 12 5iam + 2 13 ustaam
  95. 190
  96. 50. 50 H + 2. 5a51 am
  97. A. s.Soion en
  98. 12. 9
  99. n osen
  100. indaltiin nia taq a
  101. saaco
  102. cis te inor
  103. 125 a Ncap. 314
  104. +ratag st a
  105. ii
  106. et s = 10. 5omm 1. stam 4 nsiaa sa = 30. 50 min + 30 siam + 31. 51 a
  107. An sieprostel. duae aequalionis sunt 2. ir arlm 4+ aarr = 9 102. tigrlarum + 112 astem + a9- b 44
  108. et n= 30m + 31a
  109. S=om 151a. fint A5s n = se resanitsian
  110. et aegla Farq= 2. ud 2glum rur rasm sed ita encul g aqque pant i tistius etc l m
  111. t purata e fin sm t sit anen tme ne naect atm

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 423v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0842?run=74