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Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 10v

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: 0.78.

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. 11r); this page is its left half.

The machine reads it as

  1. Compropemus fiet - deo = dd vdz) Y. 2 dzde se d2d2
  2. q dudo
  3. lco( (aabico deosto 3+ 2sdco A; (= (1 + 5d 1)) X 4=
  4. ec
  5. osaa
  6. 2dv (d1+ sico 7. aa
  7. seu -deo = - du + suo)) (+ 2do (it st) et habitur successus. Est
  8. (10) (asdao acot joco
  9. ed cd (1+ Sa)
  10. ergo -deo = dd de d d 2 dedy duddz: deed
  11. et invenimus ergo -ddv: ddZ = (23) deodo - 2d2dZ, dv: d2
  12. ) dq ddv - 2 dodezue, dz c: dodvddz
  13. atque ideo
  14. ia postra aggredi (ad comprobationem
  15. uersa
  16. novae Methodi) estroblema differentale tangentium
  17. olvi possi
  18. t quia ergopesteus 2 est y. a = aaque bidx et per aequ. + est
  19. X. a, =
  20. adque do
  21. inde per aeg. 3 est dy: dx = do: dz. Ideo hos valors substitnem
  22. = seu 3 = log X - 12) utione
  23. quam pea
  24. fiet dy do = sadZ: de Cle seu d dvidy = (X. 9 xod
  25. ye-dy
  26. in aequatione 5,
  27. pu substituendo
  28. fiet dz: do (25) (Sdd Z. dv: (ddz. d) - 5dZ do, seu fie t
  29. dZ. du) seu dx. dy = ax seu Ay axdus), qy = x: a substrimendo quantum
  30. opus est, et quando opas est fiet y (d Zd) , a-y = fddq: de vell (d Zd) et differentiando
  31. ae agradus ( (. d) F
  32. ddo dv) (9: a) (d2 do)
  33. 1 13) an9)) + (B a. 7) (dv daz dZ ddv: dudo)
  34. : 1 - (y: a)
  35. =a fadz: dx. Unde different audo fit
  36. (. ladss se via avdur dudae - dar
  37. 1-gia
  38. sex Aequatio jam solvenda laugentialis est 15, nempe dxidu = ax Xyi ays
  39. (8) eet
  40. sst seu velo dx dxidus, gry. a,: 1 - y. 4 = x: a, quae si differentietur, fiet
  41. d x, y. a + dx ((D) d
  42. dus 1- y:a
  43. IX 9: xa disperentiando fit
  44. seu dy -2
  45. seu (dx de ayyd
  46. dx ydy, +
  47. a 2) qu u.3
  48. dx ( 8)
  49. +yia dau =
  50. X 5o sdeo t dx = deo, 1+ Sd: c0 et d
  51. du ddx dxtaZ
  52. ady: dibus du ded: co, sed
  53. n esberum oportet ergo erratum esse
  54. gia fiet coscevico t sdco cor lnsaedico
  55. x= r X = dy 1 B3. a,
  56. u r
  57. de (p(d pen (Z (.2
  58. a) qu. (1- 2
  59. - seu
  60. aydus
  61. asd etd =a dev: co et ddus = adodioic
  62. seu dus dux: dx = ddus. dus, quod est verum nam
  63. dus as agaa
  64. et ) deo adgidus ddx: dx = deo co + cosdco: co
  65. Differentietur XQ
  66. differentiee
  67. ya d
  68. adco cadico + s o: cd)
  69. a (31) dx
  70. a pyia
  71. dZ. du. scomprobatio ded it sig-aud . t do. 2) taio corcoso
  72. que + sceoico
  73. quia dz. do per 19) = co + Co silco : - a) cendeet erit az: dv) deo + du + deo auviuo
  74. A- corespeociope nempe prota r. a
  75. e
  76. ponendo d
  77. et fiet deo, qu (1 + Sdco: c) = du + 2 deo Sde + qu Sded quod est verum calculus ergo succedit)
  78. =dq -_lo, 2tsiaim ex aeq. 31 tellantus inveniamus et fiit y nempe explicite fiet est sibt
  79. (1 29: a + yy: aa = 3ye (aX, + (y: a - gy: aa) a d d d (d8. dy)
  80. seu fyy: ca) (+ L a (dz: d) (2 + a d (a dv))9. a et divisis omnibus per y; a
  81. fiet dx, - 2 + y. aB (1 - y: a) a d (aZ: dy) adeoque y iet ) (a c (d 7. d1) + 2) ex i adt car. 40) 41
  82. ex ea dule
  83. adeoque y: a (33) a d (dx. dy) + 2dx,: a d (dY: dy) + dx comprobemus fiet
  84. - (dco: 10 = -g(l ad): _ 2 + Sdao: c0) + Idco) (, +. sdco : C0): - a (Lcd.: 4) (2 + solco: co) + deo (1 + sdco: co
  85. seu - sdco: co = C(-2 (= falio: cd (F 2) + sdev: C0) + sdlaoi co, : - D (- 1) - sduoico (+ Bt Sdae : c0)
  86. quod succedit. )jam aequ. 33 pro y: a, dx: a, dxidus substituamus valores
  87. per dZ, du, daz: ddv, uet per aegg. 1, 2, 3, et fier sddz.d-od ef c
  88. jam d (dZ: dv) = deddz - dz ddo: dudo
  89. et fiet sadz. d7 = 5), doddz-dzddx + 2 d vddz,: doddz- dzddv + dvddz, seu erit
  90. (ddz: dz = d (d Z: dv) + 2 ddz: dv,: d ( Z: dv) + daz: dv
  91. (ddz: d3 = 3 dvadz - d Z ddv,:, 2d vadz - dz ado sedquia haec aequatio iterum differentianda
  92. est, ideo jam tone descendatur infra ddZ et dao, opus est adz: ddo tolli ope ipsius doo
  93. constantis inque eum finem posset deo assumi pro arbitro per de sume pracc ddz: ddo
  94. assumi pro arbitrio per dx az: ded et do: deo, sed quia alius posset nisi priorem ipsius
  95. illo valorem jam cognitum assumeremus, alia prodiret quantitas cd, et per eam valor ipsum
  96. ipsorum Z, v, X, o quam assumsimus, Redeamus ergo ad valorem dav: daz jam
  97. ex aeg. 35. rursus quaeramus vel ex aeg. (32) inter explicata quae et
  98. iterum quaeramue valorem ipsius dav: idZe, fit autem ((32) aequatiotalis ex plicata aequatio talis
  99. inventum aequ. 24
  100. 3V) ( = y:a) (dv adque = d Z ddx: dv av)) seu -d dv. dlZ - (36) dv, 2y: a) - 3,: dZ (1 - y: a)
  101. comprobemus: q o Eos, 3 +2(dco: o: Co H (1+ (d v. C3) = A a dl Cd ud (1+ Sdco: 1)) (= 2 salo: co - 3
  102. ad :dB) B.
  103. adcetiad) sit sacdic scccedit
  104. aalo clat cor et stiono vesera . 2 Salivico 23
  105. et pro leporea

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 27, fol. 10v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068072:0020?run=73