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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 13r

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: 0.81.

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. 12v); this page is its right half.

The machine reads it as

  1. inaequu ex
  2. sed jam video novissimum casum sic rectius exber laitie) x firii pt (a.: X) X:h. Ergo
  3. ergo et idem in eq.3 fieri pt. Ego hoc moddo h non occurret bis. Et res ita prodibit:
  4. (omo dy: dx = XiVia (edo) dy: dx = ( : X:) X. h et stio) y = (a: X ) X: t2 unde
  5. deduda aq. 6 est differentialis quadraturabilis. Sed ex eg. 2 B sequitumo X: h = y: (57
  6. et (2mo) X. H = X ay: aedx 6) Ergo (13ho) fit dy: dx = a Y. X (7) pro X: a fiat
  7. (ato)Z: a erit et X x = a dq seu dx = bu _ ex= AaC a Z dq. Ergo fit
  8. yZ: B) Et talis differentoris, aequatio erit
  9. glo dy: aq= sa: q er (qi a0 pi utabia
  10. xhine etiam dueitZ= y. ): aa _, quadvatutabili
  11. ee
  12. quadraturabilis, hac
  13. hodus curvarum positionedatarum
  14. si yz = va, fiet qy =va
  15. et habetimus a dev. 2): dq (a. 2) 2 . a v: a 18) vul (1800) (Vdz - 240). 42: d2) = a. 1 a ra
  16. Hil seo videamus an aliquid generaliis obtineri possit. Et omnia ab abintio resumum
  17. (Imo dy: dx = 1y: at; X: a2 do) _ assumta dy: dx = (X: a) ; h: a (1. unde (ytro)
  18. de
  19. pra unde ex1 et 2 fil (9: a); (X: a) = x: adithia) V unde (4Fo) y. a = (: a); ch: a) ~ et
  20. d0 = dx dec. x) (r: a); B: a) (2 et (to) d() = dh sec H) (X: a), (t: ) 2). jam
  21. 17 mo ) dy = do + (dl. Ergo d (4per 7. c. 6 fit (8vd) d asec. X) etc. + dh dsec. hete D: dx =
  22. (X: a)(h: a) seu (gno) dx (X: a) H: a) 1
  23. Desideratur jam in hac dequatione dividendo
  24. ec. X) (xa) 1) 2 = dh d bec h) X. a) dh: a) 2)
  25. cvanescere a
  26. sitome e
  27. sa
  28. (sit sit stomo) (x. axth. a( = X. h3. h; a et eodem modo
  29. sit cmo) (x: a, h: ad 2 = X (S) Xi h; a (∞) Sa sit xasta x. hB
  30. Eritus somo) X. a, h. a = X. hB, (d (ec. X) X; a; h: a (2 +( ex 1) pra, h: a. 2Y).
  31. sit (1dmo) Xia; h: cd = X; hia 3) in X. h (∞ et simill (mo) X: a; h: a 2) = x; h; a in X: h6) = (12mo) y
  32. Ergo do d(V) seu hy = (13ti0) X;h; a5. de d(ecX) Xih (O + X; h; aC) dh, assecit) X: h6, 1
  33. = Xih 63 dx A (seC X) Rihia 3) + X: hE, dh d (sec. h) X; hia 5) Ergo hoc ad Ax, ut ; h; a (3) in X. h B ad 1
  34. et (15to) dx, xihia E. d (secX) X: B5 + X. G +. (ecX) xitia 5) = Xihia 3) in xt V
  35. dh, xihia 57. d (sec. h) ih 6) + X: h(6) d (sec. h) Xihi a (5) oportat haec duo aequationis
  36. latera haber divisorem communem, per quem dividendo utrobique, evanescat litera a
  37. li
  38. Ergo firt (16to) Xihia 5 (sec. X) x. h(6)+ X: h 6 a (sec X) X,h; a ) - xihia B, in t
  39. Xihia 5) a (sec.h.) X: H6. + x: h6) d (sec. h) X; h;a 25)
  40. Kon
  41. Ex aeq. 16 fiel fiymo) Xihia 3) inritia decx) nih G + x. h ) as sec. X)a, b, a b -xih; a 5) Asec.h. ) X. h 6 x. h (2
  42. s Ergo repertum est qualis assumenda aequatio secunda, ex data ata vel3tia
  43. -xot 6, A sre. h) Rih; a V X. 13)
  44. Et ita loco aeq. 2 reperta est aeq. 13ba jago ent aq 12 et (8 t ollenda est
  45. jam literam ho tollenda est lit t litera h exprodinet aequ in quae coincidere debrult
  46. (81) = dy
  47. cum q3 cum aequ Hec intthodus esset (actuoen s et promtior si Xhia S) idopanstet quid pade do
  48. Aliavia st) e quemus duos valores ipsius dy: dx ex aeq. 1. et ex equ 18, et fipt 9. a, Xia aihi; a V H sc. X) et, ut in aeq. 8
  49. ubi pra y substitu enda valirem ex aeq. 12; quod eo facilius quia subosti butuo tantum facienda in datis; superent
  50. aequatio 3I, in qua solum X, h, a quae debet esse identica. compendii cansa faliamus X hic 5) LI)
  51. et X: h6, = f2d0) D) a hic sigto) giasria= e d (c.X) D + V dsse cx) a -a ec. s) v-D d sect) ae
  52. it pihi = bino, (d. seu Esto yla d(scc x) Da -D d (sec. h) v_ = X: a; BaeL
  53. cuEsto) d (SecX) va = co d (sec. h) Ba = _ L; Ba , vel (sto) Aster x) vN - X: a; v_: aa l,: A ecti) vae
  54. = X: h(2 seu co, vel (27mo) d (dec. X) X: h6). x;hial = X: a; X: h (6, Xihic Bdat: d (ec ) N. R6. X. 1, a D = x. 7)
  55. vel si malimus hypothesi aeq. u. carere sufferert: 28 v) Affer. _) Xih; a 3) - X: a; X; hia 2L: A (sect) 2, h, a 2) = X: L 12)
  56. Retumamus ab initio. data Emo) ay. d = g X: L; y: a (2do) ese alsumenda () dy: ax = X;tia es unde (91) Xa; yc a =
  57. Xihia V. seu ato (4H) y= Xihia 3 assumenda jam (5t0) du = d0 + de) et L = (6to) eld (ec. X) val. g eY
  58. (ymo) do = d ssech) val. y. Et fit dy: dx (8v0) =di d Bec. X) X; hia 2) ) dh a bec ) Xi hia 2: xn fay. de- Irtiab
  59. compendii carsa X, X; hia vel copendii causa ex ec. X) val y + dh. d (sec Li) val. y = bomo ) val. dy: dx intelliquane erloe
  60. per X, h, a - Ergo _. fit dh d sec. h) val. y = (mo) dX, ( val (dy: dx) - + (sec. X) val y). oportet iam
  61. seu db = (12mo) val (di. dx) - d (seC. X) val. Y quod o portet ese = (13tr0) X. F 2). seu oportela divide
  62. tem et nominatorem per
  63. numera
  64. munem sivisorem evanesere
  65. et fiet (14to) dh: dx = x: h2Z quae est quadraturabilis. jam ex aeq. 13. fit (15to) val d ec) cly x. h B. A sec h. vol y +d cxd
  66. a ec. k) val. 9
  67. val. dg: dx) seu = X; hia L habemus ergo qualis ex assumta caq. 4, fit assumenda aequ 2.. AC proinde loco a 12.
  68. ex aeg. 15 scribemus, () 16to) dis. X. h d ec. h) val y + dbec X) val. y = dy: dx. sed exer unde per aeg. 1.
  69. fit (ermo) xh ∞ dsec. h) val y + d (sec. X) val. y = X: a; y. a, vel _ in parte dextra hujus aequationis pro y substituenda
  70. dxJa; val. y seu fiet xhes X. a, val.L
  71. X: 14 X,a; val. y. (sec. X) val. y,: d. (Nec E) val. y. Ergo valor y in aeg. 4. seu X ihi d ) sic assimi
  72. peratorem et oominatorem per communem
  73. Xih; a 2 esse = (20mo) X. h16, X: h, aS) vel per comp
  74. ad = (21 mo) V de, posilo v - x. h16, et
  75. val. y = v abec. h)ae + a d (sec. h) V
  76. jam balorem y e
  77. ergo per 2, 23 se ex +g. c9 fiet X: h(B = X; a; vaV = V dsec. X)a = a d (sec X) v, L: V 2bec. h) ae + a + ec. h) V
  78. multiplicatae itanta m per a vel ejus potentiam. in g. M19 etiam
  79. consdorandum, quia a (sec. h) valor. y non immutat X ideo posse facilique conferri cum xia; val.
  80. is
  81. an
  82. Ex aeq. 19 patet non licere fucere val. y = formulae per X et p,
  83. u
  84. ae e ta
  85. i me ne

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 13r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0025?run=74