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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 167r

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: 0.80.

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. 168v); this page is its right half.

The machine reads it as

  1. si formula 10 10NX + 1X + 12 posset aequari quadrato y ponendu
  2. X: a7 = 20X X + 21 X + 22, : 30X X + 31X +3. et y: a = 40XX + g1X+ 42,:, 30+31 +3
  3. modo sit 31 = 62 130. 32, poterit A: a deinde aequard quadratot atque adeo etiam
  4. 10X3 + uxX + 12X poterit aequari quadrato
  5. +10 XX = + 10m 20. 20 74 2. 20. 21 23 + 2. 2022 24
  6. + 2b
  7. + 11. X = + ua 20. 30.. + 1. 203
  8. 1. 21. 30.
  9. + 12 = + 12, 30.30.. 42. 30.31..
  10. ocyy = B00aa, - 40. 40. 42. 40. 41.
  11. =
  12. +1. 21. 21 2 + 2, 21. 22Z8X22. 22
  13. + 1. 2B, 3L..
  14. 1. 21. 31.
  15. + 1. 21. 32 2
  16. 1. 22. 30. 1. 22. 31 . +22. 32
  17. + 2.30. 32..
  18. 4 1. 31. 31..
  19. + 2. 31. 321 + 32. 32
  20. = 1. 41. 41., - 2. 41. 92.- - 92. 42
  21. 2.90. 42.
  22. Tentemus destructitias veriticare in numeris, 00 40 1∞ 20 + n. 2030+ 12. 30 sit
  23. ngi
  24. ob terminum Z idestruendum sit 00, 40 = 10. 20 +, 114 20. 30 + 12 30, sit 10 idem quod 1 etfiut = 10 20 + 2. Si0
  25. = 102420 +2. 10. 20. 00. 50+00. 50+ a fiet 20 - 00 5i 10 13. 309, 10. 1. 30- 2. 601b. 51 et fiet
  26. 42 (00. 10) 20 = 10 10 + 4. 10 20 +00. 51 seu 40 100o -, 08. 15. 12. 30 +00. 51, 10.1. 30-6051. 0,. 5
  27. fiet 20 = 00. 58. 10. 12. 30: 10 10. 14. 30 - 2. 00. 10.50 et 160. 10) 40 = 10. 20 +00. 50
  28. et fiet 1600. 10) 40 = (90. 10. 5P - 10, 12. 30 + 00, 10. 11.30. 4 - 1. 90. (5) (2)00. 10. 59 :, 10. 1130 -2,09. 15
  29. seu Y(00.40) 40 = 107 12. 30 + 00. 10. 50 = 00. 1. 11. 30.509:, 2.00.. 51, 11. 30a
  30. Et pari jure ex ob termi
  31. et 20 = 10. 12. 30 -00. 51 :, 2, B0. 10.59- 10. 11. 30a.
  32. num ultimum, fiat 1(00. 10) 42 = 10. 12. 32 408.522- 00. 11. 32. 54):, 2. 00.52a 11. 32
  33. ergo ex Termino 2d0 fit (2.10. 21. + 1431) (10. 12. 30 - 00. 507 + (11. 21 + 2. 12 35)30 (2. 00. 10. 50aa - 10, 11. 30a)=
  34. et 22 = 10, 12. 32 - 00.527:9 2.00. 10.52 - 10. 11. 32
  35. Et ex termino penul timo fil (2. 10. 21 aa = 1a 31) (10. 1. 32 - 06. 5 a) H (ua. 21. 4 2. 12. 31)32 (2. 00 10. sraa - 1011.73a)=
  36. ita habemus duos valores ipsius 41, nempe
  37. = 2. 00aa [: 180.10) 41 (10. 12. 30. +00, 10.504a)
  38. ex priore fit 41 = (2. 10. 21 aa +HI. 31a) (10. 13. 3 5 - 00. 50 4) +I. 2a + 2.M. 31) 30 (200. 50ac. - 10. 11. 30a)
  39. = 2ouaa (: 160. 10) 41 (102, 12. 32+00. 10. 52aa)
  40. 20 aa (: 100. 10) (18. 12. 302+00, 10.50 aa)
  41. per quas duos valores
  42. ipsius 41, habebitur 21. Hinc tandem inventos valores ipsorum 20, 22, 40, 42, 41, ( ZI, substi
  43. Et eodem modo 41 adhuc semel pro 30, 32, 50, 52, ponendo 32, 30, 5, 50.
  44. tuendo in Termino merio destruendo, fit tm aequatio in qua supererunt arbitraria
  45. 50, 52, 30 et 32. Suspico Unde puto licere ponere, 32 =0, adeoe et 31 =0
  46. compendio sit 29 = 150 + 202,:, 50a +301 et 4ca = 150aa + 402, :, 50a +301 ( ut post patebit)
  47. et (iet 20 quidem et 40 ut posuimus sed 42 = 10. 22: 100. 10
  48. Unde ex termino 2do fib 2. 10ac (50aa + 202)21 + 11a (0a + 301) 21. 30 =7 00 aa (50 a a + 402) 41 = 2. voca daa + 42) et 10
  49. et Ex Termino ultimo 42 = += 22 Y10: 00 ex et renultimo. a0 Et ex penultimo fit
  50. 2. 10, 2122a = 2. G1. 42a seu X. 10. 21. = f, 41 10:00 seu 41 o100) = 41 = 21 110:00
  51. Hes valores inventos ip 20, 40, 42, 41 substituamus in Termino medio destruendo, fit
  52. 21020. 22Baa (+ 10. 21. 21 aa) + 11. 22. 30a -200. 40. 92 a a L(10100) = 10. 21. 21 aa = 0 et pro 0, et 4o somendo
  53. fit 2. 10. Z2 (5oaa + 202) + 10. antaa LH 22. 30 a - 2. 22 Yp0 10) (30 aa + 402) + (1v. 2. 2, + 1. 22. 30) (0 a +301)
  54. 2I. Ct a H 1))
  55. et fiet1 = (0 1 1)) (10 - (00. 10)) E. E (50a + 301).
  56. 2.10 (50 aa + 202) C) S) F 1. 30 (504 + 301)
  57. (10 - )) (1. 00. 10. 50a - 1d. 11, 304)
  58. Sed paulo ante 210450
  59. de, 2. 10aA50 aa + 11. 30a 50 a + 2. 1030
  60. 2=
  61. 4 1. 11. 30. 301a
  62. Hoid) aa s0a
  63. = 2 1(00.10)902a
  64. = 2. 00 a
  65. 42= S2 +00. 253.
  66. 1501 300)4.30, i2
  67. +20d
  68. ita cum bis habearans 50: 30
  69. 60. Q evane s et
  70. nulla superent ex incognita
  71. s0 1900
  72. itaque oportet rebruere et 31 et 32,
  73. 2= -52 q eguo:, 52+3d
  74. Et ex temino perultiauo sis A = 2. Se 400. B) + 1 (52+ 30Z) . 32, :, 20u ( 1
  75. 0 = 150+ 0. 118 , 30c
  76. Ergo ex temrino 2do fit 41 = 2. s
  77. +100,: 50+200
  78. p no Se + 320
  79. fiat 20=
  80. et 10 Fial 20= 50+ 00 100g: 50 1500b0 40 - + (0100,27i 50+300400 2
  81. habuimus
  82. 50 100100) +
  83. pa et i
  84. undeaequando hosvalores habe
  85. + set
  86. 40 = +00. 50+00.200:, 400 50+ 60000
  87. tur
  88. no. 52+ 6O2. o
  89. p= 10052+ 0204
  90. on ra
  91. auat luli5e 600.s4 o ut
  92. e reo
  93. 2260 40. 10b700aa - 17. 3231 (320 52 400 ∞)
  94. hoeu i st notun compandi Has a el ante (2 1 vaale 15000sr1 na (. od 10 1o g t 1V. 24400 00 2 5
  95. uli 5o 1002 10 12 3000 seuove il 35
  96. Unde Z Emino 1do fil 210. 2laa - 00. 50 20B. 100) + 212 30. 31 (300 50 + 00 500):
  97. habetur t S X 1. II.31a. 00. 100, 00. 52 + 2. 12. 30. 1. 30d. 50. 00. 57 + 2. 12.30. 3100. 500. 00. 52
  98. E. tona 00. 2. 52 (00)so rrugil +2. 10. 2laa (-901000. 204 + 88. 31 a (- 00 30. 80. 27 +2. 10. 21aa 00. 10060. 204 + 153 a 1. 100. 03. 104
  99. F 2. 12. 30131200, 50, 05. 204 + 2, 12. E. 31. 90.500.08.209
  100. quasidu calors aa
  101. aqu. (2. 10. 2 a (- 00) 59. 00. 50 4 11. 31 a (= 00) 52. 00. 50 + 2. 10. 2) aa 00. 104. 00. 50 + 11. 31a od. 10+. 00. 507 21
  102. 32. 31. 310.52. 00. 50. + 2. 12. 32. 31. 00. 502. 00.50
  103. 3. 10. 2ua (=00) (5. 88. 2 + V. 31 a (00) 52. pd. 200 + 2 10. 21 ac. 00. 10 7. 8d. 200 + 11. 31 a 90. 104 00. 200 R 12. 32. 31. 320. 52. 00.20
  104. L. 31
  105. et B1. C
  106. 500, 31
  107. 1100 100. a +, 3: 12. 3
  108. 2. 10. 2150 da-
  109. 2. 10. 21. 524a
  110. 1. 71. 50. 00sa
  111. sik- 2. 10. 2. 50 00. 52 a
  112. =2. 10. 21.50. 18. 209 a4 - 11. 00. 31. 58.95. 204a
  113. ap C2. 18. 21.31. 00. 50 aa = 11. 00. 31 31. 00. 0 aa
  114. unde
  115. 8 2. 12. 30. H. 300. 31. 50 + 2. 10. 00.100. 2 + 702.31,:32 (00. 504 00. 200) = 41 E rursus
  116. 2031
  117. 100.04a + 2. 12. 32.00. 502,
  118. 320. 31. 52 42, 10. 00. 104. 2 + 722 317:) 2 (00.57 +06.204
  119. +2. 1. 30. 300. 31. 90. N. 52 aa +2. 10, 00.100. 21. 00,52 70d 31. v0. s2 aequ.
  120. +2. 12. 30. 300. 31. 50. 0. 204 aa +2 10. 08. 100. 21. 00. 204 + od. 702. 31. N. 204
  121. 42. 12. 32. 320.
  122. tr. M.3231. 1. 502. e. 20

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 167r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0333?run=74