Leibniz Legible

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LBr. 437 · Huygens, fol. 43r

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: 0.77.

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. 44v); this page is its right half.

The machine reads it as

  1. Ctm
  2. dy. dx.: 2X4 7y sit y. x v. a, fiet
  3. ya = ex et adu = vdx + xv. quos vatores substituendo in
  4. aequt. fiet: vt vdvo d. v + v: 2 seu
  5. 14 d8.d e . v dv. dx = pa. v f3v.2 vel erit
  6. +v. dx = +34ur CBe d ed =c du era 4 2a: wr,
  7. DB: DC:: dx: dy As et = f yy: 2X 4 2X, y. sit y. x = v: a fiet ay = vx seu ady = vlx + xdv
  8. Uende ex org. 1. fit v + xdo.dx +a vira + 2aa v si xdvidx - g r. 2 - 1 v + raa. v
  9. suex e vet per compend. Unde ex sg.1 siet: adx: vax + xav = ( v. 2a + 2a: v
  10. et =) + vo + 4aa: 2av. unde +2aa vdX = Y, ve dx f, vuxdo . 4a avdx f. 4aa X dv
  11. seu fiet dx: x du, voftaa,: βaa v Y3
  12. 1P i +
  13. (
  14. ijam e L4 2 voremus B fiet o 4 vocemus B3 fit β aa vax V dx = vexdv aaaxav
  15. piu ad destro
  16. facio
  17. +2. -
  18. in
  19. Zure
  20. seuplx. X=
  21. asq V at v
  22. (1g. 9 X. u
  23. logeaa vera
  24. seu fiet
  25. jam
  26. FX: X Sav. V: paa _ v- (d: Paab .
  27. H sit E B a a = , et Z = VBB. BbC. jam momentum figmras FIG) ex
  28. e Ex axe aequilibius est Z 5∞Zav. seu bs vav: bba
  29. Et idem haberi potest per summam quadratorum GG, s demto sumua quadratorum
  30. inter GH seu summ. FG in EF, sumindo omnes FG inter FG et (F HG) inter De) G et (G)
  31. sed idem momentum etiam aliter haberi potest, nam moni 1C) mom
  32. nam mom figurae GHH) G seut suum qu. HG inter G et (G) demto momi. rectanus GH)
  33. addito momento rectanus, =1G). sed rectanguli G,B) mom = ZC in HG, = FG- in HG
  34. et rectanguli F (G) mom. = (F( in FF) in 2F+ L RF) = en FG) in (D= EF in EF + E) - LEF
  35. seu (B(G) in EF)= EF. _ jam sit EF, D, E() (1), FG,Z (5)(5) (2) et fiet
  36. mom rectanus. G(H) = Z - (2) in L vD et mom. rectanus F(G) = LZ in (VD)- vn, ergo denique
  37. fdenq i sum qu. HG. = = s uvaZ jam - vv Z + bbZ = b3 seu bP = - b: Z + bb et set
  38. sovaque = - b sAZ. Z Lb Z. (2) describatur Hyperbota LM (M) ubi HM sunt bb: Z
  39. erit spatium H (2) = bb: (aZ. Z. itaque tandem prodit talis aequatio:
  40. rn quo
  41. +2() (vV)- vn
  42. B3 (vav. Bvv = - 2 li in spat M(M) +: B Z- Z) = 2 rv Z. (E + L ((VV) - +s vV
  43. faciliore pro
  44. n ne quis enor sit admissus, instituemus comprobationem, in exemplo
  45. linem GG curva ad hibento rectam oposito SEK esse triansulm rectanus. isosceles.
  46. promentum trianguli _NFG ex axe EK est _ tianus.NVFG in EF+ LFS et similiter
  47. nom an. SiF) (G) = Manu sBG) in EF) = (F) s jam SVEChianus: L FGii FN et
  48. Fs= sit EN - e, fiet FN = e - v et d NFG = G C- D m EZ, _ sed Z= C- v fiet E A E. B = NVFG
  49. et LF e - (0) =, 5V(F)(G) et EF+ L EN = v + C V seu C + 2v et fiei mom itrrem
  50. et fret momi hiam N FG = Cn + L (D C v seu ( CeV erB + (V + LC(LCD + eB (1V,
  51. = L0 + V - L evr similiter mom. tianu s (F) (G) = + + (V) - = e(~Y)
  52. smoctntum spulis differentra momentora hora bragulorus seu cubim, spati F(G)d EV- (B): eop aL etV
  53. =dif inter .V + ev, et inter h(V) + es) u idem jam investigemus priore via
  54. nam idem nom est samum qu. HG= mom rectavus; G(H) F momi rectanus ((G) Jam (quad. HC
  55. sic datur. suum. qu. HG inde a K seu sDdqe seu f.dZ L. HH = B et i KusgriH) .
  56. ergo (quad HG inter G et E) = 2(p3) = = V jam um rectanus G H) + mom. rectanus. P. (G) est
  57. supia i in B( Z. Z) + L Z (BV) un sed in casu rectae q- ev
  58. et e (1), et fer - V Z (2) et Z - (Z) = (e6 ( () v, ergo fiet
  59. on Z(2) + Z (on) - vn = L (v) vV = + v) + = e(vv) - L v (VV) - = e DV (+ L P)
  60. sed non osentit itaque monenta ducrum sctangulerum denno calculemus nempe
  61. rectanus G(H) = _. HGseu v in H(H) seu in Z-(2), quod ducatur in LHG, siet rectanguli GBC) mom = : vo 2 (2
  62. sed rectamus F(5) = (8) Ae(C) (E) seu (Z) in F(F) seu in (V) - v = (Z) (B - v quod ducatur EF+ L F() seu in v+ L( B
  63. sm v seu in V + LV, fiet mom. rectanus FG) = + (2) ()- vn. iteque in eo paulo ante peccaviquod posui
  64. G.Fat
  65. Z pro (2). jam in casu rectae Z- (Z) = (Y) - v et (Z) = e - () ergo tandem fiet
  66. sum quad HG inter G et G) _ - mom rectanus G(H) + mom restum G) F = = (V). L. v- = (BrB+ : V + e V) -x v- V L (V) p
  67. seu = = V- LIV) - e(V) ut ante. itaque calculus ut correximus est probus
  68. Rursus jam suplr est inveniendu summa (dv. bbB
  69. s
  70. 4 M 1+ mVtro P+ qV+ YBZ SB 1bb + mbbv + ubbx + n v + nv + pb + quo+ rre srt: 6bB +V
  71. aderque DC + . b+v
  72. bbton = bb
  73. vobtr
  74. rubi ponendo m, n, P, Y, S, esse c et relinendo l et 9 fet 1 = - q
  75. et L. + V
  76. bb -vD 1F bbV - ∞3
  77. tatem (dBv: βaa - vV - 4 aa sodv: BBaa v - P. Et quia =
  78. Ergo + Baa aa B - 4 aa
  79. (3aab - p3
  80. ergo Y
  81. Baa- vV
  82. paat p. = ) 2a Ba 1
  83. ga
  84. bb
  85. bbv. B7
  86. Bac- bV
  87. Habemus nos ineundam summam
  88. hinc etiam -Baa
  89. BaaD- V aa- BI
  90. +L. seu 4na
  91. eaav. B3 paa- v = +aa - paa + L. sed 4 - β = + 2
  92. ud B geo b Bet la pan (4 . v. . Quod spitus tertum siet Experiei montiil
  93. ee eb ditet om 1la tar 4 t . eri er o . Br. en t e u tar dund a + Bet eitet . B0. prse. X eb
  94. cin ncb
  95. b0Baa et talecus
  96. v
  97. . P vo- 40a = f 2aa V. pr. H, v
  98. si
  99. r us
  100. E CH 1
  101. BB - 2 - yy. 1

Cite

LBr. 437 · Huygens, fol. 43r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-3595205:0085?run=74