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

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: 0.79.

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. 168r); this page is its left half.

The machine reads it as

  1. 3022 + 31aZ + grad
  2. 1drx- V8, 10.20. + 22021 aq + 1. 20. 22 aa 2B + 2. 21. 22 àq + 22 22a
  3. lm Z - (1, 20. 30. +1. 20.31
  4. 1. 21. 30
  5. In = ln, 30. 30- +2. 30. 31
  6. (_ = lB, - 40. 40 - 29041
  7. . 21. 21
  8. 1. 20. 32
  9. +2. 30. 32
  10. -2. 40. 92
  11. -2. 91.9V
  12. - 42.40
  13. X40. 40=20. 20 20. zoml + 2. 3onl = (20. 201l + 2. 20. 5oll = 50. 5oll. fit 20 = 30. 3on - 50. 1l,:, 2.5
  14. ex terminissummnis
  15. et 40l = 20l + a sel seu 40 = 30 n (50b + (2) 50l = 30. 50m,:, 2. 5ol - 3om
  16. lebemus ergo 20 = 30n - 50l, : , 2.50l = 3om et 40 = 30n = 30. G0m + 56 l,: , 2. 5ol = 30m. Et parijure ex
  17. erinouli 22 = 32n =sil, :, 2. sil - 32m, et 42 = 3i n - 32.52 m +5 l , :, 2. 5 2l - 32m
  18. exhis 40-20 -50
  19. Ex termino secundo C2E1G (30 n - 50) + s1. 2 m. (2. 56 = 2om t (30n - 30. 1om +507) = , 41
  20. tenultimo similiter
  21. 2. 2ut (32n - 52l) + 1. 2 m (2. 52l - 32m) . ., (32n - 3 252m + seG) = 2. 41l
  22. un iturum
  23. et aequandus valore, ipsmp. H
  24. compendio sicem et 36Bn= zol et 3Cm 5n = 00 s et musiplundo per rucem
  25. p1o2. 2l. 50l52l - 3im 5OLsID: Em. 2 5ol si lF 2. 3th. 2.50lSil + asolluset
  26. Benniile
  27. Crhonrum. F. 2. E1l; 50 Ly2 Sen + 31 n 50 L3L Dm (= 21. 20 2. 50 (32 set - 2. 31 3on 25ol 3212m)- 5dH 51 5.5M 20 mn ditem
  28. Elonm) =2. EIl5OL 32n (= 31 m 3ol 32n) = 21 3om. 250l 32n) F 2.31. 30n 25ol 3in + SdUsc3En (- 30mn. 313n
  29. L5EL 5ol - 2m ) E = 2. 3m. Z alsel F2313AMEsil sot VS ySOL (E mn. 31. S0L,
  30. tr. 2ILse posem a t 3Im 52 L3osom (+ 2(.3 2m. L52(3050m = 2. 31. Ln Vsel3Von) 53 eH 21 90. som + 32 mu. 3DSom
  31. purm L. UISXLZNG3m Si 130n) = 2 32 m 2 52130n) F2. 313V R sd 3on 45, El 31. 582
  32. Htujus aeq. ope habetur 21; 31
  33. dmfror sou et astui vot)
  34. b
  35. bfoX
  36. 31 _I(32 52. 50
  37. Hma o es
  38. +2bm (130 s2
  39. retunt. 3onc.
  40. 3 Emn313on
  41. +m sit ( 21, E 5osum A. 4 (30 5iF L. 50)(m
  42. nes pamputolicere ut fuail 31. 5B 30 52 20
  43. Et hac sequatione dibisa
  44. per si32. 60- 30. 52
  45. 31, - 4. 50. sn. =2(30. 52 + 3250)hm +2. 30. 32lun
  46. 1. 50.5m
  47. R - 1. Z Z2MMA
  48. Nisi malimus esse 32.50∞30. 52 =0 seu 52350 = 32:30 quod sane etiam ex
  49. duobus valoribus praevideri poterat, quia hoc assumto duo valores ipsius 41, statim aequantur
  50. Tantemqua Et certe in a pluriam literarum saepe insigne resolvendi impedimentum es
  51. ae hypothesin excogitare, qua aequatio facile praestetur. Eaerum u aliquam saltem
  52. Y aequationis radicibus suppeditabit
  53. non fiat A similiter 21: 31, a 41: ut 20: 30, et 41. B1, ut 40: 30.
  54. Ex Termins medis fit. 2. 202.324-21230 (+ 20. 30. 32 lm + 21. 30. 31m ( 1. 3+L 20. 30. 32 lm
  55. Am in temino ens psterimus cedo fe relinquere 40 inexplicatam, quia continet 21
  56. 22hL 2. 20. 21 l +20. 31M +2130m + 2. 30. 3. M = 2. 40 41 l. fea fue
  57. 40 autem et 20 continent tantum 30 et 50,
  58. quibus non videmur hactenus indigere fit ergo 4+ =, et q = ∞d 228. 21. Y ∞. 32931,
  59. 2. W. 228. 32B. 31. 21 f. 10
  60. 2.20. 20. 32l + a. 21. 30 l +20. 39. 32m + 21. 30. 31 mt CB _ 20. 30. 32m
  61. + 2.30. 32N + 30. 31. 3In 240 Ace -2. 92. 40= Ait etqig
  62. = 1 2287 ,, 720. 320. 21. 31 +9 320,.317:40
  63. Unde ex duos valores aequando sit
  64. 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
  65. 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)
  66. seu 40b. 220l = 3on - 30. 50m +50l 30 +50l + 3050lm = =3dmm, : Z sol 3om = - 30mm: ,2 (t. (ol. 30m)
  67. 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
  68. 30, 20. n +2. 3on = 2. 220=635 ma) C0 em 4 4. 30 solm - (2) 3d mn, 30, 2, 25ol. 20m
  69. 404 2 4d- 220l= 30- 3056n + 58U (20F L30m) (250l- 39m), : 350l- Zom
  70. 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)
  71. quod dividendum est per qu (2.50b. 3om et mult pli candum per 4. 30 (40 - 220
  72. qu - 20 = 40+20, 40- 20. et 40 - 20 = 2. 501 = 30. 503:7 2. 50l - 30m = 50 et 40 +20 = ,39n - 30. spM,: 2. 5ol -3om
  73. Ergo 40= 20 2. 30350n -3958m, : 25c, l-30m
  74. 30. (0 - 2202) 2 2V + 3 olersqu + 30. 31 (45 2. 2d0. 320(21 l. +2 1 3T. colo 20 30m
  75. +3440 en = 32013;
  76. ubi modo caveatur ne 21 sial ad 31 seu ad 2Y 30. 32 se ut 20 ad 30, neque himiliter 41 ad 31, res est
  77. Fictantem 230 (40- 225) 2l =
  78. et 91 possumus sumere ex explicare ex Termino 2do. non
  79. explicata in eb quanitate 40, ces neq vel 20, et
  80. AB compendio 22+ 2 2ol+ 3em sit 50. Z20
  81. et 2om + 2. 30n =, 320l, et fiet
  82. posita ergo hac aequatione, 52:50 = X: 30
  83. Tantum cavendum me 2Ca et 31f
  84. 292. 40 a , 5. r1. 41H
  85. 41 = 0b. 220,. 21 + ∞5. 320.31 : 40
  86. Porro ex terminis mediis fit
  87. adeoque 22: 32 = 20: 30 et 42:32 = 40. 30, quod quidem hactenus videtur licere, modo
  88. fit 22: 20 = 32: 30 = 4h: 40
  89. 2.3 3 gent
  90. 7Z141a2f3iaa
  91. 40075

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 167v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0334?run=74