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[Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa, fol. 431

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.

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The machine reads it as

  1. 11D. 1.
  2. um sire
  3. B, (II
  4. node
  5. IM PaI.
  6. CH. Fil
  7. dictat
  8. distat
  9. 5V,
  10. R
  11. Ecribali
  12. IPOIC
  13. Datiu
  14. Pot.
  15. VM;
  16. ipsiuo
  17. qud 1
  18. atabo
  19. IuICI
  20. Chot
  21. uncta
  22. Bect
  23. 15 iM
  24. etet,
  25. ee
  26. S1
  27. +a0
  28. D;
  29. 10C
  30. Lab. V.
  31. aE GEOMEFELOE L. LLMF AIA.
  32. 5.
  33. hoc cA, ut S+ ad 5D: Ideoque ABad Y2 r Yr in Cubduplicata ratione
  34. SF adl 5D. O. F. D.
  35. PROPOSTTIO XXIII. LEMMA.
  36. T communi foco s describantur duae quaevis Parabolae ACD.
  37. D ECF, in quibus ductae chordae AB C~ FF abscindtant sermenta
  38. quorum vertices ce ea lee ut ductis rectis se C se praedictas
  39. chordas in DS secantibus, sit cD aequalis CH; dico a B esse ad P. F
  40. in sub duplicata ratione rectae Sc ad rectam Sc.
  41. Per C ducatur em segmenti a cB diameter, e per C recta CK
  42. Termenti L CF diameter, chordis respe.
  43. etiris in m C x occurrentes. Ilarum
  44. diametrorum parametri aequantur qua-
  45. druplis Sc, Sc, ut superius octensum;
  46. Critque (per Prop. XI IX. Lib. L. Conic.)
  47. AMg = 4 SCKCD, _ F KG = qSGLCF:
  48. Inde AMg eA adFKg SICuEq SCrCD ad
  49. 4SGLCH, hoc est (Ob aequales cD e
  50. GH) SICUE SC ad SE; _ isIEUE AM est ad
  51. F. F in Subduplicata ratione sc ad Sc. Vnde elt AB (iptuS aM du
  52. PLa) ad F. F. (ipsiuS P. K duplam) in subduplicata ratione sc ad SC.
  53. PROPOSITTOXXIV.
  54. Trea datum focum Parabolam describere; quae per data duo
  55. puncta transeat.
  56. Sit datus focus s, puncta duo data Pet qua Latavra MMCCerC
  57. dehet a _ B. Centris a _ B, distantiis aS _ BS ducantur duo cir-
  58. culi, e ducatur (per Constr. PrOp. CxVIIT. Lib. VII. P appi C ollect. Math.)
  59. recta eo utrumque continsens, in quam ex s puncto demittatur
  60. perpendicularis sF, quae bi-
  61. secetur in V. Verticer, axc
  62. VSx recta e latere recto x
  63. quali quadrupla rectae rs
  64. (per PrOP. LII. Lib. I. ConiC.
  65. describatur Parabola: Prit
  66. haeC qualIta.
  67. Ouod ssit descriptae Par.
  68. abola focus constat exinde,
  69. quod in axe Parabola di-
  70. stat ab illius vertice quartd parte lateris recti, qua est notistima
  71. foci Parabola proprictas. Ouod vero haec per puncta a e Btranseat,
  72. sic patet: Parabola axis rx ultra verticem productus c ad F, ita
  73. UE YE. Ct aequalis rs distantix foci à rertice; et per P ducta est
  74. cFD recta ad axem Parabola perpendicularis, et punctum a tale
  75. est uE aS ejus distantia a foco aequalis sIt A C, gux (Per PrOP. XVIII.
  76. Fl. II.) perpendicularis est ex a ad cD rectam: Unde (per C Orol. 2.
  77. PFOD. XIV.) Parabola Supradescripta per a trantit, et propter s
  78. miles rationes trantic exiam per B. G. L. F.
  79. Pocu

Cite

[Astronomiae Physicae & Geometricae Elementa] Astronomiæ Physicæ & Geometricæ Elementa, fol. 431. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/1040780814:0449?run=74