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Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 85v

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. 86r); this page is its left half.

The machine reads it as

  1. pro tollendo ZB respecta aequntionis 1, erat 2. 14. 31. 42 + 15. 31. 42 - 0
  2. 2. 19. 41. 42 15. 32.41
  3. quae a queatro manet permutanda a2 et A adeoque 4 et 4 5 et 3 adesque 4 et. 9
  4. s Ex hac aequatione fit similis pro tollendo ZV respectu aequ. 2, permutando 4, et 20
  5. Et fit 2.24. 31. 92 + 25. 31420
  6. 2. 29. 41.42 25. 32.41
  7. tins quaeramus 32 et 42, fict Eips d fint 3+ = 2. 19. 31. 32 4 2. 19. 41. 42 a th. 31. 42, , 15. 41
  8. Ex 11fit 32 = 2.24. 31.37 42. 29. 41. 42 - 25. 31 42,, 25. 41
  9. Quas duos valores aequando fit 2. 14. 25. 31. 4Z YH + 2. 35. 19
  10. Hinc quaeramus 32 et 42. A eF aeq. 8 sit - 32 = 15. 31. G2 +2.19. 41. 42, 14 131 + 15. 4+
  11. item 31. 41
  12. Cq t
  13. et ex aeq. l - 32 = 25. 31. _t + 2. 29. 91. 9t pi, 24. 31 + 25. 41
  14. 25. H1 + 2. 431
  15. quos duos valores aequando fit 1g. 24. 3 A +
  16. 2. 24.15. ∞. 31 (42) 31 + 2. 24. 19. 41 (97315+ 25. 15. 51. A2. 41) + 2. 25. 19. 11 (12)41 =
  17. 2. 14. 25. 71 (42)31 . + 2. 14. 2941(9731 (+ 15. 25. 7342. 41+ 2. 15.29. 11 (42)4
  18. Et fit -3
  19. 22. 1. 2 seu 14. 19.25 41. 41 Bl. 141 29. 31. H 4+ 24. 15 - 31. 31 =0
  20. =1. 29....
  21. 2C+2.1924
  22. + 24. 19
  23. quae n aequatio manet eadem, si permatrntur 41 et 31, itrm 09 et. 4
  24. lxX + myy + n GX -0
  25. seu AxX + lmyy + lnXy =0
  26. fit Uxet InHy +. anyy = _ ua
  27. aequ. nngus - 4 lmgg: 4
  28. fit IX + Zny = Ly +Cun-alm)
  29. seu p. -nft Con. aems al
  30. lxx + amX + aan = 0
  31. Exaequo. 12 fiet 41. 1B) 4 14. 37
  32. Ex aequ. 6 fit 40 =
  33. quae duos valeret
  34. -14. 25
  35. 42 ) ex priore permntando. A et .9
  36. 21pr 3 126 F00. 12. 3
  37. triy (00.3
  38. 1. 15. 4IfL1.25. 315
  39. (224. 31 2 D9. 49)
  40. L1. 25. 41521. 15. 31)
  41. 225114.29
  42. ioth it 9
  43. +21 224. 334 00. 22. 31
  44. = (ex eq. 9) 1. 25. 4130t00 23.41
  45. 2. 2941+25. 31
  46. 2+9 30731. 31 p f15. 30231. 41 +4. 1. 29. 30 pr h1
  47. aequando fit 2521. 00. 2
  48. (2. 14. 31) (2. 2941 18
  49. Uxx tamlxtaaln =o
  50. +YCqu ( 35
  51. 2, 124. 15
  52. p 1. 15. 4100 00. 13.
  53. 2. 19415. 31
  54. 22 D0 29231. 4.
  55. J. 1. 230
  56. 1. 00. 13.25
  57. 22. 312 (219. H1 1- D1. 31752. 29. 91Y) v0
  58. 28415E15. 313 E 1. 41521. 25. 31))
  59. Hic valor, sidem manet, si permutentur 1. et 2.
  60. et tent valor ipsius 40, per mutand 3. et 4., item 12 et . 3.
  61. aequ. 16) ex aefn. 15
  62. 40, et 30
  63. Uxx tam HXrEaamm C Htabemu ergo +1
  64. adeeque + et. 9
  65. verb. gr. n paraboa.
  66. =aamm- qualus ia quia in omni eonica polli simul potest V et Z; idet etsi praejodicio harmo
  67. niae toltemus in omni vero Conica potest tolli NZ, et altera simplex velut av,
  68. tx lxa am a smmlu)
  69. et terminus absolutus; ideo id potius sequamur
  70. seu X = D- m 4l (an- a ln)
  71. e
  72. pxX +, aq taar=s
  73. IexXKI
  74. = - q + seaqu apr
  75. aequentur
  76. R. 19 +LYq=
  77. itaque omissis aequ 6 et 9 adhibebimus ipsas 7 et 8, item 10 et 11,
  78. Et quidem ipsis 8 et 1 jam defuncti sumus, earumque ope invenimus
  79. 42: 32
  80. ope aeq9. 13 et 14
  81. : 31 et
  82. 1s - p s. = A qmp Addamus jam aequ. 17 et 18, quae sunt
  83. mpet prDa
  84. Ha t OD = qu (lq- mp) 144. 30. 30 + 15. 30. 40 + 12,00. 30 + 10. 00.00 -0
  85. 13,00.40
  86. a AtLO
  87. 24. 30. 40 4 25 ∞p. 40 + 22 00. 40
  88. 19. 40. 40 + et bolt
  89. Et 18 fit ex 17.
  90. permnfando 1a et 2.
  91. (0. 38+ (1. (00. 30 + 5200.00 =0 60. 38 +61 00. 30 462.00.00 =0
  92. aapD - 4(1qu mu) 4 _ Ep aequ. 18 fiD
  93. +nalo
  94. +. et 158. 6Z = qu (450. 62)
  95. 29. 40.40
  96. Inp -qs d 1O + PD) Iu sed hoc loco 50 = 14 v0. PK 15. 40+ 12.00 et 00. 0052 = 19. 40. 40 + 1300. 10 + 10. 100 00
  97. .61602. 1
  98. 60=24
  99. + 14525.40
  100. 00. = 25. 40 + 22. 00 et 00.0062 = 29. 40. 40+23. 410420 0000
  101. 15.4075 29. 40.4
  102. (t 12.603 2e
  103. c22. 9032
  104. -l25.402 [19. 40.40
  105. od 212. 00F l (22.005 13.00. 4
  106. 10000b
  107. C29.40.40
  108. F+19
  109. A0. 0u l 20. 0000 qu.
  110. 24(19. 40.40
  111. 13. 00.40
  112. 00 vol 10. 004c
  113. f.13. Er. 19
  114. m7
  115. 19+ (mp .l91) -t0- pp D
  116. scuquetemp. lus) Hotins fet
  117. taque in m. 13et 8 P1 tg
  118. Er a4.4. 25 + 1524 d etrt
  119. etle quad vatu)
  120. et ordinande + 14. 15. 25. 294
  121. 14. 19. 2525
  122. - 19. 192
  123. 24 (15. 402
  124. 8d. by +14. 15. 23. 25. ∞0 :14. 1). 25. 15
  125. 13. B, 24. 2C
  126. Zr. 15. 24. 49 12 19.24 25
  127. - 1.4. 14. 29. 29
  128. 6. 15. 2425 12.14. 24. 19. 29.
  129. 19. 22. 24
  130. uiq
  131. +13. 14. H. 10
  132. i idi

Cite

Leibniz-Handschriften zur Mathematik LH 35, 15, 5, fol. 85v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068207:0170?run=74