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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 168r

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: 0.78.

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. 167v); this page is its right half.

The machine reads it as

  1. Quo tulior sit calculus cem in cumeris exhibeacuus. Numeri per et notam otterminato
  2. habeantur quasi ea abesset. et lsint numeri pares sed l siqunt sonarius simul tet naus
  3. ita n= 2p et l = 69 Ergo 20 = 30. 30 2p - 50.50.64,3, 2.50l m seu 69
  4. m= 3Y Iq
  5. 2,- 3-39p atg 347 :, 269- in seu m +- sp 234, se
  6. 2-1st +B G,. 60 et 18 = 1 136, 1 c 5.6 31Z
  7. M + 209 = 3p =259 seu M = 459 - 3p id est si q et p sint 1
  8. fiet m = 42. comprobemus 2- 33 2. 18- 150,: 60 - 3. 42 quod succedit
  9. habemus ergo n = 2p, l = 69, _ m = 459 - 3p et 10 = 20450, erit
  10. 40 _ = 7. q od 1t debet luccedere nam 40 = 9. Ep - 2. 3. 45 9 4 3. 5.3p f5. 64, : 1069 2 9
  11. 2b = 9. 2p = 25. 69 +2. 25.69- 3.5, 459 +3,5, ZP,:, 2. 358- 3459 + 9β
  12. _ 2+5 = ex 9. - 5.5. 64 4 2. 5.5 1. 5. 459 + 3.5. Y. 3: 2. 5. 69-3 459+3.3p
  13. n2+5 = (9. 2 4 3. 5. 3) P + _. 75 (4-9)13:, r 15 (4-9) g + 9p - Daeg 759 + qu 6
  14. sed video nos ninls cire determinaffe 50vel 30 pret
  15. porro 31 = 2 130.32. st 32 = 12 et res procedet nam fiet 31 = 2 Y3. 3.4
  16. 3 327 = B29 18 puo impto 120
  17. 21m +2. 31R = 41. 42 +2. 12.2 =9304
  18. 21m +231 = 2 42 + C 1= 2 21 l4 1. 31 m = 2. 21. 6 + 12. 42 = 252 e 504 = 73p
  19. s 5. 516 18-6+0 + 150 = -46
  20. 5.6053460 601305 3.3. 2 -3.G.4
  21. et fiet 756(4(32 + 430 () 6b,: (-462 = 41. 6, 1on 15b. 132 +930. 66 = 2. 6, 462. 4
  22. cilas smbemus (2 AG t rg M) 1 ( 2 + Z. 3m) - q00 gyl , At. 462, -. 31 66132 = 99 l, quia 4un
  23. sed video i concenti simus abjectione Underaria, e aoveraria spunt, poe aqidem rolinquit quod s4
  24. 66, 22 sive abjicias goue 1
  25. inec veros nnmeio ipsos velumus, posse nos contentos esse omlitere l vogu
  26. 4 fiet q 6 2 5. 91l = 135436 (2. 21 l+ 1.31m) + q 66. (2 m + 2. 311) n = 4OE pro-
  27. is posito tusquod succedet in Abjectionibus fingendo l= 6, n = 2, m = 42et 31= 12 5544
  28. 32 = 12. unde 2.21lF 1.31 m = 75b et 1. 2A 2. 31 ∞ = 930.
  29. 22= 2. 1233 = itaque in probatione numer ab
  30. 441+ 2. 1. 42 53 42+ 63 421. 13.4874
  31. B 120a1 61 1
  32. 16 = 0 = be a vdi Ha
  33. uo unq
  34. Ergofiet 2. Ergo quaerendus numerus qui per Novenarii abjectione in relinquat per H denati, 4
  35. F. 2 30. 32n, + 31. 31n 2. 40. 40β2.30)1-41. 4il = ita. ubi extra comprobationem per numeros
  36. c pro 41 subsumendus valor nuper inventus. Est autem 91. 41 = 132 (4. 2 (+ 4, 21. 3.m. + 3V mm)
  37. +662 (21. 2Imp + g. 21. 3IM 4. 31 nn) + 2. 132.66 (2. 21+ 2m, um+ 2 2nBB: (1 462.l
  38. is vator substituendus in aequatione propime praecedenti. unde odra
  39. secundum 2 fol t4 36462. + 4. 30, A62M. 21 +4 463, 20.3
  40. 3817 2 I - 4. 307. 132 Um . + . 46, 2. 20l. Z2W
  41. -7. 1grbb. Im - 2. 36.13 bb. H
  42. 2. 38. 132. 65, 31. Mm
  43. F4. 469. 20 32. 3o lrit
  44. +91964 f. 2. 20. 32n
  45. +4. 465. . 30. 32 In
  46. 4 . 465- 2. = 3opnA2 3dsolp t3 8. 5o lu t 38. 1 o ni. 2 30n0 ba s8I - 965. h. 40
  47. 4, =it (imib sm) + iESIL (32M + 2 b6n)
  48. =0- + 62.00
  49. -. 13E. 4 303
  50. 6622
  51. 2. 176+66. 42 = 99 fiat at 2. 1al +66m = gga. 17222t 2.l6. 2
  52. P. 13265. 2. 4)
  53. pro po
  54. fiat 132m +266n = 660a. Ergohabenus a1= 99. 2a +5609 462 Ergo 32 = 31: 230, Ergo per 1008647
  55. et 4(ll= 99. 21aa+ 2, 99. 660. 21. 21a1 7060. 42aa, 462.
  56. 2. 20 β1. 2. 30) ll421Il + 20. 61. 2070 m
  57. hanc aequationem habebitur
  58. tur saec aequatio per 402. 2.30 ut 29
  59. +21. 3lm + 30. 20(31 2.30)) m +2. 30. 20 β1. 230) b +35ln-2402
  60. 8(99. 2taa + 2y9. 660. 21. 31 aa 4560. 317 aa 3: 462) =0
  61. l + X. 38.463. 31. 21lm
  62. peracta Fiet autemEt - B 30.31 (40 m, 2. 220. 320 +((30. 3l qu (40 m - 2. 2o. 320l) - 4. 30 (40- 220) (2. 90. 32 (2 20 l + 20. 30 r t238 2)) Seu 2
  63. y (40H - 3 2ol) 31. 30
  64. sed 4ul + 220l = + 2( (357- 305om + 50l). + = 38mm, : 2.50l- 30m. igo 40l - 22oll = - 2. 30 mml (30 n- 30. 50M + 56 ) - L 30hr,: 7 qu (2 3o l. 30m)
  65. sit 202 10 60n 40 - 20 = 14000.4
  66. f238. 465. 214 = 0. 130. . 21 (32 + 30) 30 = eo. 18. fiet
  67. X. 49. 666. 31. 2t a Y. 36.99. 2iaa
  68. eoia
  69. 4627-99F 00. 990aa
  70. 30864 99 150 = 200. 9900aa
  71. Eit 0ogquaa 21 + 2. 00. 9900 aa. 21. 31 + 00. 121 462, l. N = X 30. 462. 00. _
  72. 00.14 462 lB)
  73. eqpuolt si nrit. a t ( D L. 20. 36. 462 In 31
  74. 2. 20( 2. 40l + 203om +2. 30n = f2, 30. 500 30. 50m = 30. 50lm (435. 50ln = 303mn, :, 2. sol - 3om = 267 24030.3an + 40. 31. 30 = 2. 40. 38. 9 2n +2. 40. 30 nM
  75. am 30.20
  76. Termini medid
  77. 3.9. gi =6
  78. =. 668. 6... mm - 4. 30, 31. mp
  79. : (- 3 At nt + 2. 30. 50 I (= 50
  80. jam ob Terminum medium est
  81. (X. 20.46
  82. 404 2 4d- 220l= 30- 3056n + 58U (20F L30m) (250l- 39m), : 350l- Zom
  83. iin adde 320 l. 31. 30 fiet a 2. 30. 32 (50t mm 5. 39. 503 nn - 2. 30. 50) n + 16. 30. 50 llnn -8. 3035olmn 30 mn) + I. 40. 30. 32n (4. 50 l ( 4. 3050lm) 4 30 mm)
  84. 1609- 1359+90
  85. Hin an b
  86. Is numers est 125. itaque fiet aequatio, 2. 20 (3∞. 30)l+ 1. 21l + 20. 32m + X1. 3(M+ 2062. 30
  87. Z = 3. f. Xp - 25. 849, :, 2. 5. 2.4- fon seu
  88. siet enim 31 = 24 12 sed si 32 faciamus 27 fiet
  89. 30 -58 = 9. 2p = 25.69 = 15p - 1509 = 132
  90. =20.32:30 id est in numeris
  91. Hinc ex C quatione
  92. 12. 2 + 12. 12.2 = 2. 7.286 =41. 41. 6 =0 seu
  93. ehice error
  94. 40- 20 = 50(40+20)
  95. CL prrgessent + fieut m 122 unde habebumque
  96. 122 20∞ 1 156- 18 = (3
  97. Ergopro Ab scribumque
  98. Erutum in eoquod b debursi
  99. orimrsi
  100. abjectionibus contentisimue
  101. W 12).3
  102. in numer
  103. be q goq ut X 14 + 288∞ - 275
  104. teu
  105. 192, et 30,5079, 5 30 =3 et 50=5,
  106. 31 = 2 Y40.50
  107. v
  108. 130.660. aa. 3
  109. 1a
  110. abjectionali habeatur
  111. o

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 168r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0335?run=74