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Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 64v

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: 0.82.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 73r); this page is its left half.

The machine reads it as

  1. IImo) e = O1
  2. xtum = Oe xinn -∞D
  3. fit xelle xrtam, xrim = g2
  4. ui aequando rrimum valorem cummedio sis F
  5. 2do) Hinc X = O =l = 0 tum = D- an q Hinc C, D. Gset m et similiter
  6. aquando ultimum valorem cum medio fit Z, D- O) pinmm. Unde sequitur tertia aequando primum
  7. et extremum valores inter se, sed sufficit nempe CD. Il=2D-n. sufficit ergo duas
  8. priores aequationes praestapi. ita ut C et et D, prpractentur eadem modo et l atque n
  9. itidem eodem modo; sed D et m, mediae quantitates a reliquis distiagventur
  10. O = 12 Lvy + 113 IrZ + 123 fyZ + 100 p
  11. P= 212 1yy +213Y07 +223Yy2 + 2009
  12. F = 3I Woy + 313 YvZ + 323 VyZ + 300
  13. 9= 413. 523Z Nvy + Am2. sez y l02
  14. Et eodem modo labebita
  15. unm cujusque numeri pone
  16. veluti
  17. sessit F1Z. id desopeetoggu2
  18. 123. S12. 323. 7e2 caeferis f125, 25 sus
  19. 2+ 33n = 1
  20. = l12 135
  21. F112. SB = WX3(A1I. Sez = 51223 et ita porto SuE siiis. at . m. jujis a seinvilem agg 3 et fieta Auferatur etiam aequ. 1. ab aq. 3 fit V13 sua ( m9 (71 Y51)S3 +(BHCE 11)313. 712
  22. + 12. S = 1ig1) + = Co2sB et ita porro ctatt
  23. 1312. q = dutos = 3uem - 31 2s s +s 1r. 11 - 3 u1
  24. L aequales fit . 100. 512p + 12 500t + lr13 Z= 0 100. 513p + 113 500F. + 11 23 y = 0 100. 523p. +. 123, 500F + l 213 V = 0
  25. compendio scribamus uA P F 12L +137 =0 2ip + snt + 23V =0 et sip + 3it + 33y =0
  26. Significant Sir I12 12313 S3
  27. Ex duabus prioribus aequationibus inveniamus valores ipsarum p et t
  28. FI1. 21 p) + 12. 21F + 1. 2Z =0 fit .t=
  29. Es pari jure in notis dextris numerorum permutando L et 2 fif p = + 12. 23 Y,:
  30. omissis intermi 100 et F
  31. soo quia semperre
  32. ouo sutlt intelligi
  33. 12. 23V: +12. 21
  34. quibus valoribus substitutis in aequatione tertia 31p + 32t + 33y 20 fis -12. 23. 31V 4. 11. 23 32V + 12. 21 g9 20
  35. 413. 22.31Z = 13. 21. 322
  36. em ipsorum 11, 12, etc. substituendo valores in aequationibus 1, 2, 3 hujus articuli
  37. velu B: Suc3. Unde permutandu 1 et 5 sit 5e0F = S12. 11h12
  38. 13. 123137 nam ta t tr13, permn
  39. nam l2g13 vel lau permutatis, 1 et S manent, sed S1223 vel similis) permutatis 1 et 5 mutatur in = 51223
  40. + si2. linvi:, Si quibus vatoribus substtutis
  41. A3 523 11313 Z
  42. =112. 513..... - 123- 512
  43. + 523121. y0 vel y = Sir D +515131Z, : Si2 231
  44. (2) +712. 3129: .712 etce
  45. et 72133V +713233Z 472313y= quam equationem conjungendo cum aeq. 6 articuli
  46. et pcum Y, et t cum W, fit Bo Y= +343. 319
  47. praecedentis ut tollatur Y, fiet + Sirrl. 723123 D + 513221. 723123Z (+ Saur I. 70u3V
  48. =GagEl. 71273 V - 52312(. 7132337 - 523121. 7131 231)
  49. Unde quidem haberi posset v: Z, sed quia hoc non licet, neque enim eorum ratio debet esse data, alio qui
  50. 1VZ non foret irrationalis in indeterminatis, contra intentionem. ideo hanc aequationem oportet
  51. (6to) 523,3t. 712293 - 51222l. 72413
  52. 1009- 100 P seu
  53. pro quibus substituendo valores, ex aequationibus 4 et S articuli 6, et aeque 1. et 2 articulia 7, prodibit aequatio (M. 51, S1223. W SEC. SIB231 = u2 H 2h. 5+32(+13.
  54. adtem haber o deprassio. Ham mulliplicetur a q. 7 per aiti c. praced. per aiqu 4 aniculi Eum
  55. 8. 512. l1213. I122Z V = 523, lgg3. 71223 Z = 312. 3121B. Suues V. + 31. 32313. Si23 Z =)- 112. 1.213 fin2, Vel13. 12sis. In23Z + 3ahug siu, . 79tus. Sicese) et edem modys 123. 523. 51227. (2 131 9
  56. ppermutando 12 et 23, fiet 122+ 522 um si i. ca. sed 52
  57. 32313, 51223. seu 123. 32313. 71223 + 523,12313.71223 -323.32313. 5123- 723. 32313. 51223
  58. autem habena prisstio. tam mullislictur aq. pr ic. pacud. per aequaata
  59. fid Erres He(7mo) Sc2I(si: 72233Ct1)
  60. quam aequationem rursus divellendo in duas, ut destruantur V et Z ne determinetur v: Z, fiet ideo ut tollatur Y
  61. 112. 1121Z. 71223 +512- 11213. 7.223 = 312. 31213. 51223 -712. 31213. 51223 60 seu 112 +512 ) 3icg. S1213
  62. 12
  63. et) ut patet ex artic 3. seu 2009= 100 p + 700 W, ut patet ex artic. 6. itaque fit 500t + 300r= 100 p + 700W.
  64. jam considerandum 500C esse 2009-300Y. seu
  65. et et similiter ut tollatur
  66. ope harum aequationum
  67. pari jure destruendo irrationales in D, -O, ex permutando initenles latd; cum 3167.
  68. seu Si Sin3l. D + 51323I. Z
  69. fietg (610)51213l, Jng.
  70. in aq3 hujs articuli fis denique ex aeq. 3. explicatis 11, 12, ete fit +r23. 513. 12313Z + 11Z S12 ln13V 4. 112. 52(y = 9
  71. Itaque tandem, = 4 123. 12313 2
  72. F 11. 813 = S12131
  73. 6T jam in aequ’artii destruamus irrationales ponendo coefficientes eorum nihilo
  74. aant in halor ipsis d, P.
  75. = 11. 21 p) = 11. 22. + - 11. 23V
  76. Bo = a + . 123 Z
  77. divellere in duas
  78. ergo fit 123 +523
  79. (5) in hoc aequatione primum destruamus omnes crrationales, faciendo coefficientes learum niilo aequeles e. peruntando 100p cum 300r
  80. et compendii causa faciamqus
  81. +112. 523,312.723 = 171223
  82. +112. 523. 312. 723 = 711223
  83. saudu s
  84. 51323. l = - 52313)
  85. B - 12t + 3
  86. = Hll bitur ∞, D- 0, tantum pra 1 vet 5) et compendiose scribe

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 B 5, fol. 64v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068255:0128?run=74