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Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 3r

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: 0.83.

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. 2v); this page is its right half.

The machine reads it as

  1. A _ 5: v - B s L - 42
  2. Trax - a XX = qu
  3. 2F syqq
  4. 1
  5. Elliphin
  6. Parallelogramma omnia circa eandem seltiotam conicam conscripta
  7. se sunt inter se aequalio
  8. placet
  9. sit curu A Est Gei Elli
  10. demonstratum est, sed patet idem investigare calculo sit centrum C, vertex
  11. set primarius A, oppositus V. a set rectagla ABV, esse proportionalia quadratis BG.
  12. ergo ABY ad AB sit X, BGy. a essentia latus rectum a, transversum
  13. seu bi _G b q patot esse 2aX + a x - ys et adx 4 axdx = ydy.
  14. seu dy: Ax:: a + ax,: y:: A: BGse Ergp BP = a + 2 X et
  15. CF sitCA jam CA = 4 fit pC = q 4d jacd PF: PC:: PB: P
  16. pG= 2ax fa xx + a + 2a x + a X. et pe qu sit qu a = e. fiet.
  17. a.
  18. Ex et pC Ceaq . q et PC= C)
  19. +5ax +3
  20. et p a 4 2aqX + a: qu. X. Ergo +5 Nmet B a Ergo PF = a + x. e + ax: +a +sax+
  21. et p + GF = p PG+ PF EA Fit autem parllelomamni Area ductr
  22. ijus t quartae partis parallelogramum circumscripti integri, seu parallalasiammi GeK
  23. irea exductu ipsius GF in CK. Hanc ergo CK quaeramus. Et primum quidem CM et MX
  24. jam ob triangula similia GBP et CBK CMK sit CM: MK:: GBGBseu
  25. sit AM m, et NX, Mk, _ K fiet ram + a M = K: et q M: K:: C
  26. ergo k q gm + n O = ram + a m, et m- Et 9 - m = OK. etm-
  27. et m = 4 - BK. Ergo fiet 2a9 - +OK + 2 q - 29CK + O2X = X hoc
  28. est ft: quia + = - firt +4aq +2O2K2 = k. seu K = Aaq: 1 ∞
  29. ∞ jam CM = q - m Ergo = OK. Et firt CK = O K + K = K (1+ O at H
  30. GB continuata ipsi Koc
  31. Ergo CH = ageq Y aq. 1+ C: 1 - 0
  32. fint GA fiet BM BA. BC:: O G GB continuata ipsi Ck occurxat in N
  33. siet Gs BA. BC: O Be CB: BA.: O: 1. seu BA - CB: O
  34. GB: BP:: O: 1. Ergo GB + BY e seu PG: BD:: O + 1,: 1. seu pG = BP (0+1
  35. e e PC: PF:: PG : PB Erg:O2+ 1: 1. Ergo pF = PC. 10+1
  36. BC scribatur Y = a + a x. erit O = y: v. et PC = _ v - BP.
  37. it E GF = pG+ PF = BP (O +1 + PC: 1B2+,
  38. seu pG + PF = BP. O2+1 + PC F seu = BP, O + BC: O = GF
  39. jam Bp = a + a X = v et BC = 9 - X. et O2 = Y: v
  40. Et BPO = 5 + y: v = rax F a x7: a + ax et DPO BC = (2a2 (+ a X) + ag ( av f a x ( 9X).
  41. postat ut inveniamus
  42. D F 1-O = rax + a + rax + X - 2aX + qX,: v
  43. Parallelogramma ommnia circa eandem Ellipsin descripta esse inter se aequalia
  44. ex scriptoribus constat, placet autem veritatem ejus theorematis investigare, calculo.
  45. sit Ellipseos AGEVK vertex A, e oppositus V. centruum C. latus rectum a, transversam
  46. seu AC, 4 acissac ABC Voidiuata BC . diametri conjugatae GG, Hk, ex puncto G et ex
  47. puncto K in axem AV ducantur ordinatae A, GB, XM, eut AG, X. BG,y. es AM m, MK, K
  48. a)2
  49. + quin GY perpen-
  50. Ex puncto G sit perpendicularis GF in coningatam diametrum ek, secans AC in RP
  51. ptt Y. patet parallelogram mum AC X, fieri ex ductu GF in CK. investigemus ergo utramque
  52. quia BR edX. GB seu y: BP:: dr: dy seu C: 1 et aequatio ellipleos est rax a X = 9,
  53. dicularis ad tan
  54. ventem in G
  55. erit ejus differentialis adx - a xax = s y. seu du dy.: y: a- ax: q ergo fint BP = a gr. q.
  56. tan u sit Aet = m et MK = X. firrq. m: K :: (3: 1 Kusu Ta Shra et ram - amg = KK
  57. A, + CM, qum
  58. Ex aeq. S est m= q. Op quo substituto in aeg. 5 fit: 2KO = aq- d. 9 R ∞( qost HK
  59. (2aq( 2aOB - a: 9 RD ( 29OV +8K = K seu aH+ a K = a9
  60. seu K = ag: Saq + aa 6 = CK. Rursus ut inveniamus GF, patet esse
  61. O2+1: 1.
  62. CM +H = 1
  63. 12 1
  64. est GF =GP + PF, ex GR. BP jam quia GB: BP:: O: 1 fine GB + BP,: BY
  65. seu GP Bp O1. Bursus DC = sit BP, v. fiet GP = V (O2 1-BC sit C
  66. euit pC = c - v. rursqus, pPCA: PF:: GB. BPs: VOH: 1 fiet pF - C. v: 50+1 = Cv. Syrd. = 1. 2
  67. Ergo GF = v.O +1 + c= B: YO +1. seu v O (+∞) + cCY,: (O+I et explicando
  68. erit GF = _ y + vC. Ly + v et CK ~ aq. Saqet aa
  69. seu GF = GP + PF = sy + v + c v v: ss +0 = y+ V) + Cv Cv; sy v. - G1
  70. at K ela seu CK - aqu: SaquV + aa Est autem y + = 2aX = aX: 9 + a -2a x. 9 + a . 99
  71. seu a + 2ac = aX. g: 1- a. 9
  72. LH XXXV X 7
  73. BL. 3
  74. X= 1: V2
  75. im 21 = 1.V
  76. e

Cite

Leibniz-Handschriften zur Mathematik LH 35, 10, 7, fol. 3r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068160:0005?run=74