Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

LBr. 56 · Bernoulli, Jac., fol. 68v

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. 63r); this page is its left half.

The machine reads it as

  1. M, nixuy
  2. n, mxmys.
  3. M. mxmy
  4. niuxnys
  5. px de pX =
  6. quadratum cubi est septa podtia
  7. p X, pX= pintu
  8. PA pX = pmn X
  9. pF X = p Ex
  10. quex ix
  11. de pIX = p
  12. m Yx
  13. enx, dX amnx
  14. ned X = quX
  15. X = dX. Ergo si Z - d X, fiat dr q - dx
  16. (1er
  17. Z= d X sit S Z = f sX. Nam s = d nZ et duq - d. n, dX = p- s. X
  18. Ergo (Z= SiX. Ergo Z- fr Huc Z d, fx = d, dr
  19. d, sz = Z stam sa = S ergo disz = 51 q = dqu quod atsardum. Ergo tibes erur
  20. p p. Z = pZ sed d, d Z = diZ. Ergo hic divatum
  21. ps pX = punx Nec hoc licet conpuarare respondet nam d, d X = dmonx
  22. E
  23. - duta
  24. ex pZ = ix d six (- _ s d. X) = X= A d x - (x H p - . Px - pr
  25. peilatus
  26. itaque omnibus et censis quideum differentias potius respondere multiplicationibus et summas
  27. ita ut differentia sit oelut praduotum multiplicitione per rdilatus;, summa velit quoliens productus divisione pertatus
  28. sit ergo BIXtu = n xry mo respondebit dxtus
  29. divisio autem exprimatur per 9.
  30. ili ut InsexFy: Xty hic exprimatur M Xty. qtu, vel M
  31. xty vel ga
  32. productum sis
  33. Seu m X1X
  34. a. M XI G roy I t M erys significat xege se erit n vm seu unitata
  35. esse per x9 iabus nt multipligtasi, et 9 xeus significat X MG eseu uni
  36. n viribus per dividatur
  37. sprimulliplicationa
  38. Itaque a _ m M X significat _ productum si 1 X eu Unitas multiplicetur n vicibus per A
  39. Hinc _ qua = m nX n _ N x = mhrn celis a M G = q m X = x re x qu, go siiliter s seu _ sxyseu d, dxdy = - d X d y. d Xdy r d Xdy - d Xdy ete
  40. et qx significat quotientem, si qX seu unitas multiplicetur dividatur vicibus per X
  41. similiter dX significat productum differentiatione si dX seu X, differentietur vicibus n
  42. (nX significat roductum summationis si s seumx summetur vicibus n
  43. hinc (ex = d2 x et d d X = qnon x
  44. Gn, auy
  45. NiXty
  46. m, Xy
  47. 1M X my
  48. nixmus + cmxrus
  49. IniXNyHmany t, nex m’y
  50. LDXny t3rixmyt3 mxmy +. mXry
  51. Ex his d SX = S d x = dx = sX = x
  52. dX d y
  53. 1dixdy + 1. dxdys
  54. 2dxay + 2d ply X1 d Xy
  55. d, xy dar dy
  56. d, Xy d 8x dy
  57. 1dx dy +3 dxdy + 3x y +1 dX d 7) d, xy d’ dxd
  58. Hinc generali regula: qui quid in formulis aptatis producit potest operando per multiplicationam
  59. E et divisionem; ei respondens id formul aptatis ad d producitur operando per differentia
  60. tanc ecusdem; ad d . Salor similis
  61. d. xy) ot, Cady
  62. scilis
  63. nsalliguntur
  64. Formila aptata ad m (vel ad d) est in qua quilibet terminus constat ex ductis invitem earundem literarum velut
  65. X, , affectionibus per a exper ct d) in se invirem ductis doservatat lens hamogenectum, sea ut summa ex affectionum
  66. si ex formula impertecti, X + axu seu MXNG+ 2MKM, ex trahiur rais quadralia more slito puditib sormmlaseries Xuly fot abalio. Nempe faciemus: p pa pepus pes simil d d X d5 dydV, quod non poterit
  67. Si data somila si iregularis ut (M X mIs. F. AX My + 5mX m y+0NX HG ea concipiatur ut e
  68. exponentibus sit semper eadem.
  69. si quani farmula
  70. son MF Xy
  71. uhabln , medita Emetrice, seu
  72. lasinitam, sed videndum squa an
  73. todem ro mldo di Xy. sed quit hoc ? potest ad erit
  74. infinitus quae erit latus hujo, sen quae in se ducta dat seriem datam formulam perfectam An ergo simuliter haec series infinita seut dispontatia huic in diffe-
  75. ronticlu respondens, a seme diferentati dubit, aX9 + 2 d Xdy; dulito, si it esset ros in alia finita succederes non minus. sed
  76. X LSX + g9 mltut se 2X + 3y un hoc video non esse
  77. sit dx d’y. hujus, diff est d x d’y + dxdy. oertatur
  78. in muliss aium mXm pixinus seu X + X y. cujus diff est quadratum est Xdx+ f. quod
  79. Erut. Aeontialiter est d seu mx my a mx ige mamus, et issemti liter dex dy+ Edx dyds
  80. porro ipsis ded y + qdeq est diff. est d’x d’y +2d’x d’y A_ + dx d’y et fiet
  81. aX du y 2 dXd’y + dX ay, : dy. + 2aexdy + d’x dy = LXdy, summa ipsius dxdytixdys
  82. namualcud exel. inaequale dxdus, hujus lifs. X. _y + d x d’y hujus diff. . st 2x9+ dXd+ dus medii quasi quadratum A
  83. dX dy + 2dx 8y + d XLFG, quod ficta divisum par tertium, reddit primum. experiamur in composito ex duobus dddo
  84. axdy + da dxd y. Hums diff. et d’as d dX dyt dx d’y+ dX d’ y. Et huius diff. est 3d xdy + 3d X dy + Ldyt d x d’y
  85. + dXdy + y quod si diff. medium quadraetur, et dividatur per3tim debet prodire prium. sed hoc perse idque successum facili porvidetur
  86. sit d xdy+ dedy. hujus diffid Xdy + d XdEy + did’y + dX d y et Aujusdiss ex d edius + pdX Kyt axa y+ aXKyt dxdyt dit dxaus
  87. ubi rarsus praevideo. si mediu quidintim nvidatur peristium redire pumum, nam sol
  88. none sei. Fictitia quod notandum
  89. Cum autem defficientes constantes dit
  90. el
  91. didus
  92. is quaesitis, ut tollamum
  93. erculando
  94. ex his nos
  95. mutsus
  96. differt a praecidente, quod ora enultiplicantur per du, multo
  97. e hic ullegneos penitus ad lene
  98. pogereorum, estque accuratius inspiccem
  99. ebere mutari ut si sit 1X + 2 du debet 2 includi
  100. et capilales quam suma sublatum iri verelar. Id ergo maxima superest in adaptum
  101. eot in id ja hoc calculo nihi
  102. Hecuntinibus ducum diffire atalium in se invilem, quod siet opt X et _, inde trau do ed maltiplanto deblum an liceat hdtem eas propter aequaves
  103. uoo fcm
  104. ecoloi non possunt
  105. anet differentia inte eoti
  106. nda dx m ti seta
  107. disque 22
  108. C = YX
  109. son I, atqu auda pli t atius) sentandio in idstitinsa

Cite

LBr. 56 · Bernoulli, Jac., fol. 68v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 160). https://leibnizlegible.com/page/DE-611-HS-958800:0136?run=160