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Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 143v

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. 142r); this page is its left half.

The machine reads it as

  1. se fortasse obtinar quaesitum potest sine obliguitale sdinutaru. Generaliter in num cursa
  2. B EB: BF = a: Y. fiet
  3. EB = aEP- L pCP, is
  4. Saatrr =s
  5. _ BC = rEP = ACP, : 5. sit 18, DBC = EF Z BC
  6. sit R ED = KR - K L et C p = CR = EL
  7. fiet, EB = aKR - akL + YCR - rEL, :S BC = YKR - rK L - a CR + a EL,: 5
  8. sit aequatio ad conicam 2a. AB + a AB = BC erit AB = EB AC seu EB - C = aEP+ r CP - e5, : 5
  9. utfint et 2a B EP+ 24SCP + 4 aa EP + a rr Cp + a aY EP. CP
  10. Fales -iaestp - raros . rrEI E - rar Ep. cp S
  11. EC
  12. sit A(A B), in circulo L() cujus radius tr sit ah (B, - (DB) = (1) C sit (BC: BC- B (B) L. BC. g
  13. et (A) (B) = AB = AG seu AB- R et fit ad circulum aequatio G- ihk + 2h AB
  14. explicemus AB per a EP + rCP = e5,: S et BCper rP. al P3. 5
  15. Ael
  16. KK + 2KAB E
  17. d
  18. t2gBC
  19. arhik = h HAess F E(seKaS EP + yht K) rS CP - aa Ep - rr Cp (= har Ep. CP
  20. =KK S
  21. g4
  22. +29rS EP +29 a5 CP rri- aa p (+ rar sp. Ep.
  23. + 2a es EP + 2res Cp
  24. AB2
  25. c
  26. -8C
  27. jam aequatio data proe minima ad conicam ducenda s est ac + a AB + + BC - af AB. BC =0
  28. hoc explitata dabit
  29. +ac S tgcaSEP Facrs CP - afb ar EP + at b ar Cp + atb aa E P. CP
  30. asess +HtSEP ( as CP
  31. + at best EP atbesa (P
  32. 150
  33. -a r Ep. Cp
  34. =0
  35. ponatur aequatio ad circulum muthiplicari per _ haec ad minimam multiplicari per m, at aequalio ad cirealur se
  36. quae in unum additae dare debent aequationem ad conicam videamus an hoc liceat. Et primum 2
  37. quo terminis fiet m. atb, ac - vY = a aY - 2aY
  38. altiornibus
  39. n(aa trI =
  40. -m atbar _- n (aatr) = q aa = vr
  41. + m atbar - n Caa + rr) = 4 rr - aa
  42. duarum posteriorum ope tollando n fiet (2 aa = rr + atb arm = q rr -aa - apb arm, seu fret carb
  43. a -brr + aarm + abrm = arr - aab = aarm - abrm, seu m = arr - ab- a + b11:, aar tabr)
  44. sed expriore aequatione fit m = aar = 2abY,:, aa - rY, a +b. ergo fiet 2aY, aaY- 2ubs = arr - aab - a +bYY, a a - WY
  45. seu r4 - 6 aab rY + at
  46. a +b
  47. 24b + aubeY - br4
  48. + aY
  49. + aabYY.
  50. t 6aab N+ 3ba bb = 936 a bb - a = 364 b - 4 d arb 9 a bb - at at b
  51. arb
  52. A(a +b).
  53. 4arb
  54. YY = (3a 3 aab taer 3bb - (a t bE
  55. a+6
  56. 4a +
  57. 3aab + aa Y8bb - aa - 2ab
  58. et debet esse 3b non minor quam a + b seu 2b major quam a 2b non minor quam a
  59. a +b
  60. seu
  61. a +
  62. aliter Y+ + 2aa rr + a = 2aa rr = Saab rr seu rYFaa = r Y raa. a +b + 6aa (atb)
  63. quae limitatio diplicet
  64. Et qude in Ellipsi semper latus tanversum ib
  65. t
  66. sed res at redit pro r absoluto ad
  67. est autem in Ellipsi semper latus tronversum b, non minus latere recto. nam latus rectum
  68. in parabisa latus
  69. est ordinatim applicata id focos est in Hyp. parab. et Ellipsi
  70. Ergo in Ellipsi cadit intra latitudinem Eblipseos, cum tamen ea sit longur qua ato2
  71. in Parabola tatus hursversem est i
  72. infiulum in Hyperbila vidiamus figuram adjunctam cum FNC) habenns constantem
  73. et longitudo sit latus transversum.
  74. simper differentian, latus rectum tansversum t sit socus FP2 + 2FVX VV) = (F)p
  75. sd (F) P= F P+ S(V) et fret (Ep) + 2EV+ VV = (Fp) + VV)2 + 2FP. V(V)
  76. seu fint
  77. seu 4FV (+ VV) T. 4FV. VIV) = (V V) + EFP. VIV)
  78. .Res igitur pro Hyperbola non est universalis sed
  79. pro Elipse, et forte Hyperbola peculianter accummodabitar iad Ascymplotos
  80. -2a4)
  81. +b
  82. P = EFV: VV) +EFV
  83. quia aequatio pro minina est ad Hypertactam
  84. LM = 5 LN- f- y
  85. LNqu + NC qu = LC qu
  86. AM = g NC = x +g fietque ff tgy - 2fy + XX + 2xg + gg = th, quam differentiando
  87. ABX BC,g gy = 2VX Hr. qux
  88. fit Zydus - pSdy + (Xax + XgdX = fydy = fr dx + Y fxdx
  89. ay: 1x = f-y :, X+9 Y+ 4X, :y fit se gy = X leex ZXX tre + g1
  90. Msy +Rgy 1HXXX AM rX + Mgr debet esse m- n = (m + n) siu fiet
  91. +ML gx
  92. A, 1 - (n: m) = + _ (r: 9) 4 (n: m )Y: 9)
  93. seu sa - r: 4b , 1+ (1. 4) = n: m
  94. si sit m=q fiet 9 - r, :, 4+r = n: m sit ergo n = q- Y
  95. =ngy. +nFXX + EurX
  96. et m = quo fiet (9+r = 9tr) gy + (9+r + g- Y) Y: 4) XX
  97. = ryy + 2rXX, habemus ergo aequationem ad circulum
  98. mor coleli scubendum ernit ay. Ap. 1aji, 5. 7
  99. vis
  100. a fit ab -be - aemab
  101. soa cu rati ma
  102. .farit

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 143v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0286?run=74