Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 69r

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: 0.77.

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. 68v); this page is its right half.

The machine reads it as

  1. itaque superest, ut tribus sationalibus atamur
  2. vlentis ipsis Z, 2,6, , fiat (a = n20 1G2 + 130 1h6 + 1230 146 + 10BV+ 10014
  3. axtiam = AES ionobV X in ayaB + uro vuna +. 2. u7o uro f. (7 12. 120 ug0 1G6 + 2. 1120. 130 26
  4. 1139. 1030V3 + 1130 10 an F 1135. 1. 31 aR
  5. 1230. 20 30 pV + 1eyo. 203) at 11 30 n. X aa
  6. 1000 a VB + 2. 100B 00IAV F 1001’aa
  7. 2, 1120. 1090aV + 2 . 1130, 101OV + 2. 122 IuaV
  8. 2. 1120, 1801 a_ 2. 1120. 1001a_ +2. 1230 1001 aa
  9. sit jam exxtaum = quadato
  10. ecitis o m et o faciam aun + aenn = 1) a 32e stit + 30 1o4, ne iti omnnia pro in eon eodem
  11. cux fat l cra an Lhnot 4 2. 32o. 2 204 Ito (ter 4) id
  12. axxtana
  13. Ex a ilerficatis teruinis irrationalibus fit 3120. 2720= 1120. 1320
  14. et
  15. 3t20 c =re 1020 AC 31B. 1. = 1120. 192)
  16. 3ro - 12C. 122 3120. 10. 20 aq. 128, 1020 3125. 10.21 aequ. 1125. 10. 26
  17. ex aeper aosit
  18. 1326, 30.20
  19. 1320.90. 21
  20. 3128. 11. 2 aequ. i12C
  21. (47) 3320. 30. 20
  22. 3125.10.26 aequ. 3120. 1120. 10.16 se et ex 45per 4) sit 3125.10d aqu. 3125. 1120. 1221
  23. 1128. B20. 32
  24. 1126. 1320. 3028
  25. 3120. 1328. 30.26
  26. ( per 17 48 fit 3120+ 9d. 3120. 1129. 1025 -3120. 1328. 3076- 1125. 1320. 30. 26,: 10
  27. 3128 aq. 3128. 12d. p. 2 = 3125. 1320 3a21 - 1128. 1323. 3021, : 11. 2
  28. (Sis 3t.
  29. 312d. 1920 3 2b
  30. uquos duos valores ex eeyg.3.3
  31. aequando inter se fiet:
  32. (320. 123. 10r 10as) - 3,26. 193 18. 30. pudd = 12. 1910. 3o b. 2d ap. (3n t. 12B. 10. 1 1) - 31 5.128. toho 28 - 11o. 1926. 10.
  33. et pari jure fere
  34. 4 fuit 3120 = 1120 209 30 - 10.31: , 1320 20 11. 38 931. Ergo 3128 = 1128
  35. Ergo Ex aeg. 46, ope 53 et 54 fieret ainn-
  36. nam etsi vellemus _3 H. 30 - 10. 31. facere ag. 0. ad hoc evitandum; tuns in inteterminatis
  37. per aqu. 43. fiet 31263328= 1320.
  38. 6 et t in indeteatis coinciderent, quod _ freci, non debere pranovi. Ergo nec hic calculus succedit
  39. 5od. n
  40. 3101 a
  41. ua vso 3iolae. 10
  42. 3302a 20 V
  43. sd jam videm hoc con valoe issus axx+ann, qualis dicitur ex ag.6 non posse comparari quia in hoc quod ex venctur
  44. occunrit v, nec vV sho, et licel tolli possit v, non tanen alterum
  45. unum ad huc superest. sit aax = 1120 1k2 + 1320 162, ut aute
  46. axX L ann Z 2 L210h + 2306, 21odF. +93 6
  47. axxrann = 2o h + 2o 5, 41 dq ran ex6
  48. qua duae aequationes sunt efficienda ) sed praeterea opatet ut
  49. Ziia nia Frustia sperabimus in
  50. sit jam
  51. + 146. Sed nonquadrat Et revera
  52. sehod
  53. qaon fiun ib in simplaibus seu
  54. ducentibe
  55. quod igo prodatii
  56. coposit, debent pruducere quadratum, eprimus sit xd aequo a
  57. sit p+d = quadrato a e a Quod per se habetur, ex assunto valore , ipsius, ad
  58. + b X+C, H+1 a h+B
  59. Hinc sam X + b et X+C debet uunumquodque aequari te multiplo conti per coem. sed pat, et
  60. 8. + 16 non posse ( 1E+, 1 + vor posse aequari altiori quam est quadritum quin
  61. id quadrptum est simplicissinum Em debet X - X+d = quadrato a.. + 148
  62. quodrato ergo si ergo xad simile C goto a 1+ S6 sed x +b debet esse simuile to
  63. fecto ex consto in coem ergo Xrb simil est oto ab a S st ducto insimilesto asti+ +E
  64. sed ita seriper non nisi non srafuinatis composita
  65. 162
  66. et X+C similiter x+d -. vv + v. A6
  67. X+b = ybo a lG+ 1d dust. in Da hoGC, et X +C allexi pto a 1t + 6, ducto in h+ HG6
  68. occunl. Ergo faciemus X+d- + 8 HZ, a A
  69. Quio si x habeat et dvisoram in constantem, ut si sit X+d = ov + b +tio: v+4 tai L enim
  70. id saltem obtinebimus nesit nesit ne b, et c, solum quo discrimen faciunt in sola infimu rejiciantur
  71. nad- xet mox emr api 13 sib:, i v coravs vraa X+ d == () Yt _ + 162:, v+ xia
  72. et ob ita etam ad hic nova albiliara lubramum
  73. X4 bE f4 +629q0vr q1a oy
  74. et debet esse
  75. t2 + 02 2 4 v. a 14 (7 roE+ rn, 2ooetioia + 2130, seu, 1 otu av + ua + X. 200 + 2. 2a G X
  76. 30. 20 30. 2
  77. avaia
  78. 2b0. 23. 404 2ba i.
  79. sunt comparabitia t horum
  80. Y L7 -82 - d 10 +4.
  81. 15. 10. 200VV + 110. 10. 201 a b + 110. 14 201aa L 2no. 130. 20SV. A F ~ l10. 30 uB1 a ps
  82. B∞. 30. 200 ∞Y 136. 30. 20l d v 135. 36. 201aa 110. 2130. 10 +HD. 230. 1a
  83. calentem rollaa = 2. lr. 130. 20l, : , 110. 11 + 130. 31
  84. 3yoc a. 3ia monra
  85. producta
  86. 110. 1X 200a V
  87. 16 quoad
  88. d vi ton occurrit in ratonbus t
  89. tem ad ratis aoles. At pia ibi ilum go ctat, hoculanm, s ab ds fiet
  90. 2IaL na_ et Esta
  91. 4a41 = 20104, 110. 1p + 130.31
  92. el = 11. 20 + 30. 21 + 31. 20, C
  93. duam comparationem) B(2(1
  94. t asi eta
  95. fur pag.
  96. bi it laculus desceritm
  97. athoquia
  98. a 2061 15. 10+13030 -20aa 1043
  99. 1 4B 40. 4) 4, 100. 11D. 1V+ 38. 30 - 20aa 10130, 201. 116. 11 +138. 31- 21a. 1F
  100. 110. 100+ 1do 1
  101. omnis reducta est ad
  102. od seli ad torjo.aa
  103. 1oCBS
  104. . ao our ca
  105. et ror et ly hair
  106. diod faegoHitio
  107. ti aui doun ai
  108. eoradi
  109. (per
  110. at traracta
  111. accommodar
  112. deoque
  113. aereia
  114. 10. 130 M. 31 = 23108) ol e)
  115. ita
  116. torci

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 69r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0137?run=73