Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 25v

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. 24r); this page is its left half.

The machine reads it as

  1. po aequ. 7. compendro scrilatur W11DD + 144 4Q + 1+ D Q + 112D8 + 113DC) + 12380 2 0
  2. 2u DD + 244 4 8 f etc
  3. Collamus utrobique 8Q, et videamus an simul tolli possiti sC, ita enim residuum poterit dividi per D et habebitur valor ipsum
  4. q integer simplex. Ex 9 fint - 8 = 111DD + 114 D_ + etc.: 144 = (ex 10) = +211∞) + 21434 + etc. ,: 244
  5. et faciendo 1230244 = (12) = 223. 144, evanescet C in reducta eq. 1, et fiet divisione institula per D
  6. - 144211. = 144. 214. 144. 212 8 = 44213
  7. prodit f (ff + (b- at). (- c) h (99 + 1b - 0)h), = 99 (39H (b - 9) h). (b -a) h (ff + b - a 2), seu fFCb -c) = 9g(b - a)
  8. 22g hx- f = he 144
  9. (5 Compendio b a sit = e bac sit = K gg f +(b - a) A = sund gg Ib C) H = trq fit 144 +h et 24+ ft q
  10. 114 = 2hemm 214 = -2hkmn 123 = fstip 22 = gglq
  11. 11I = 211 = mmun +13= -ffum 112 = -5fnn
  12. tg nm gnn
  13. gg = f(H: e) 99 + b- c) h = HfF K (s Fhe): C et Z = K hf: C. Ergo 244 = hhKKS: e
  14. 223ifKktip: ee
  15. 23 = - ffmmK: C
  16. 212 = -ffnnK: C
  17. Kk- eC = (b6) + cc - 2bc ( bb) = aa + 2ba = breviter) t(5 h)
  18. mmnn 1 V: C) D Ac = 2lmn tetikK F 8
  19. +Tlikmn litie
  20. seu mranntz D + 2h mHKe (C- f)
  21. Hun trhk(K: e)
  22. tinhurp..
  23. 1C 244- 144 = hh (Kk - eC): C
  24. -frum tihk flk: C)
  25. +tctipe Aun) + HmmK (C - K) O
  26. et quia s) divisum per ek dat = (C + K) quod compendis do cabumus
  27. =pd + H Yspe C
  28. 2tenin F
  29. Ammk ltiq
  30. etk = b- a + b- c2 2b- a -c = 5
  31. +snC.. qui vator substituendis est in aquatione 9 explicata,
  32. mmun DD + hhop q 2 - 2 hema D Z - fnn D - ffmm DC + Htip 40 (0
  33. set ptke A DD (= AKKC fFmmu +) DQ (-aL K eff mnty DO + 4h kK exumun ZC
  34. +smeddDD =2mndkff
  35. +KKF DG
  36. tfm 0
  37. - 2Fmnnsfdk _.. + 2VKK fEmmnn.. 18,
  38. TeKoni DD (F AKK esfmmi). (+ AkK effmun) u
  39. si jam in aju e8 liceret esea ut canes
  40. co stegentio 18 per compendium exet scibum
  41. cam autem in rem fiet 2 tif Kffmmun (FF + 2he) = 0 seu f + che X 0 seuf = 2h (a- b)
  42. Ergo ex aequ 15. 4g. 19 pe 14 per iy fiet 7h (a - l) (b C) 9gtb. a) seu 9g h (C - b)
  43. qui consensu valsuum f et g, spem facit ob concinnitatem
  44. lmteemmim
  45. AKKemnnn
  46. auemmun
  47. EKKemmun
  48. H + 2he = hp+ pC
  49. Non autum licuiset in hoc calculo facene idie Y =0 in aeq. 17 vel. tollere seunt BR et D C intaeqius vat Z ita eantu nan
  50. in q licuisset ope et 10 simul, vel ope 7 ut 8 simul tollere et8 et O. sed vaus fuisse
  51. jam instituimus paus prima, et reperimus ducere cio non permissa, aut certe nomfaciti pirmit ergo peculi calculor quem
  52. aequatio 1B compendio ila exprimatur i _ L 20.
  53. 2000C +020DD +(C02 EQ HLIDOD + 1,OIDG HO1∞
  54. t sit 000D = 210( + 201G + 200h. Eoque vadore substitut
  55. prodibit aequatio canonica pro datis. 4. 1200 1D29. 1002 + Vd tet H2110. 2101. 2011 = _ 2110.1002 + 2101. 1020 + 2011.120
  56. fMnn 2101 = 2KKfmnRLN, ubi hN - f+ :tie
  57. et 2011 = -2rdkffmmn quos valores substituendo in aequatione canonica, fiet
  58. YK fErCE hh= ArrSSKKfLMENEKKfEMurhH = ArrSdHKF m ntt Hk fEnt, ama ktismu rtikfhi, atif nuretlinmntlia
  59. dividatur hac aequatio per rrt F 2m BnS. prodit f hhA + 2rhICDS 5 = Y5554 + T8SF4 + AhtNNCM, et pro h substituendo valorem, fit
  60. fahit +2Y8 f F 4rsshess = (2r58f 4 (atit o ft stst + atihs hhee + ahtia heff, et dividendo per 4he, fit
  61. r6Sff = s eA F hhs f. Est autem thx = 4KHC + rds - +etd ego (rss = 4Ht + rodhe - aCKShe. + 2t t e rdd p. t et S
  62. quae aequatio dividi potest per e. in reliquo pro tr subsituatur valor A+he, fiat 0 = 4hHHt _SSt5 + tr ode - 4hR KS + AKKIF - 4KSf
  63. de 2K - d = 2b- 2C - C: k = 2b - 2C - b + a - b+ C = a -c. 4HK +d AHS Haec aequatio dividi potest per 4Fk + 58 - 4kd
  64. seu per qu (a-c), et fit ff +he = 0. quod sper paginam primam) non licet
  65. sufficere, ut t, 2, + t C, D, e sint intigria simplices, sed ,
  66. ) et F modo ss sic explicatur, ut utruque in iis coefficientes psirs d
  67. illud adhuc considerandum superest,
  68. sed sufficere ut Q, et qui ab eo pendent 7 s sint rationales
  69. coincidunt nemp ud sit quia gnes erit gg ss, et hil quia jaca hebet esse hHt he = tit
  70. si sit = f et n -0 fieri potest ut coincidant
  71. si esset b f( + he = 0, fieiet munus- 2hemnt +homn6 + henne
  72. ggt hki -o fieiet mmn) - 2hk mu + htinmo + hk nn 8 X
  73. et tollendo VB sit E t h (C- K), - nn Z = nn O + n C = 0 sed ita sit mmnns
  74. + 11344 D8
  75. 13. 244.
  76. 4 172
  77. Generalissima ratio sine omni suppositione soret, ut terenus , ft per aeq. 9 et 10. fuit 4= 22F
  78. (144. 214 = 114. 244) 5
  79. Videamus an liceat s+ h(b. a) QG (Hi +b- a) h) t Hm BD + fpht ED aequade quadrato, ita enim ceque s fiet extrahita
  80. icu licet sit 178 + m O4 + a ODABCFD. siat Z- YC +5Q + LS, sist lde+ lsier LitB +. 1150gt 2LHtOGlst ED +mOEm CD1YE fiat m-Alrs n=- Elet.
  81. et o= - 4 l5t. et res succedit, hine autem quaerendae Y, S, t, quae hateri possint fit ns = - m: gl rE = - n: 4, st = - p: AC irgu t - n - n: aEr = p: _ 4(5
  82. Erus n5 =rp, seu S = rp. H. sed runus f= -m: AY, fiet rep aL al rrp = nm. seu ry= -va ma: 41p Et eodem modo B -- Ip: alm et HL - - np. 4m
  83. juniiam vioeorem nonsumdere, seu ad CC; F, inio jurendeo rem non
  84. a qu(C + +4) a fri sic disse tutam inter duo quadrata, nn frpomia, in quibus quadeato nominum
  85. posse contnere tres biniones sed tantum duas ita hic opyseset tollere coe, quid esset recidenem priora. Sed si ope duar aegu.) et 8 vola
  86. et fiit mndt bib. a) (70+sC _tD) = il. r.
  87. procedere seu non posse
  88. Ed ita duae prodeunt aequatione in quibus C) C D inteo sela servant
  89. Sit _ 140bI9 L 2P L 1301 3ZF 1X2075V + 1202 y) 2 + 1211y v Et 1121 9 1Z
  90. aliquet ex dinionibus, lv.g. 1Q notent talis haber aequalio, quae sic fiat extraribiis
  91. +112yVIZ + 1022 vrZ Z. 20 fiat v = 17 FukB,: ~ 2= 2oy + 2h, : on hablnu 9t, 93, 37, 5,3) attoque 414. quique, sed literassoturo 4
  92. dais geneitatem inde cam determinatur atius quod non est licilum

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 25v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0050?run=74