Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences, fol. -

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: 0.87.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. ELLLPSIS (in Crammar) is that Figure, where-
  2. by lome Paltos Our Discourse is letr our or rerret
  3. CHCa; ad IIthe Latine Fxprestion, Paucis te volo;
  4. rieure is vety common in che Oriental Lal-
  5. Thi
  6. 6. Wner
  7. ce ehe Square oF rhe Ordinate
  8. BUaGCS.
  9. thus.
  10. in which Wecuo, verois aidgut dic sest oul.
  11. DO (= D B x DS) is equal +0BD X DF-
  12. FLLTESI, in Geometry, is an Oral Figure, tis
  13. Produced trom che Section of a Cone, by a Plane
  14. che Balc, For then ic produces a Circle) and meet.
  15. ins wich ele Base produced, asFDK F.O in chi
  16. secont sure Folloving.
  17. But Art L will sive vou DE. WVallis S Geheral ane
  18. Ceometrical Was e demonstrarins che Gener
  19. Propetis oF che Fllipse, and which he expresso
  20. e n= CCCNOP. 3.) L LCDBi to Platio
  21. COROLLARY I.
  22. Flence tis plain, Thac is rou have che RietE
  23. Lines B D and DS, yoU HaVC INC Ordinare DO
  24. OuE e contran becaule the LeS BD, DS may
  25. vary infinicely, and ver makre a Rectangle equas W
  26. DOg. Wheretore the Conick WVriters thoughE
  27. eo determine che Ordinates aocher war; For in-
  28. Read oFB D, chey rook in the SCCCC, CHC CMC
  29. A D, Or the Abscilla; and instead ot A S, etier sub-
  30. Cicured anocher Imaginary Linc, Cuppole L A
  31. (Wrhich cher called che Latus Rectam) and ordered
  32. and consequemdy ihe Latus Rectum = AF X AS,
  33. and A d
  34. e 2a 100
  35. it(0 schac ic Mould be 2 4 proportional recipro
  36. cally 10 the Lines AS, BD, and D A. S0 thac e
  37. very wrhere ic Mould bc B I X AS == D AXL A
  38. cuttins boch Sides of che Cone (bur nor parallel 10
  39. The Square os any Ordinare (TK) in ehe Fllipsis, 15
  40. equal tothe Rectanele (IL) under rhe Lacus RC
  41. ctum (P. L) and the abscissa (F. I) Less, or adia
  42. tine out of it another Rectansie made ) ihe san
  43. Abscissa P. D, and a fourth Proportionat (R S) 10
  44. the Lacus Francrersum, the Larus Rectum (D F)
  45. and the Abscissa.
  46. In the Fllipse the Squares of the Ordinates are equat
  47. 1o the Disserences betroeen to Rectaneles, os rhict
  48. the greater are as the Abscissae; the lesser, as the
  49. Squares os the Abseissae.
  50. For,
  51. r. ThC Squares OF DO, are = Rectangles BD
  52. X DS every where, because S B is the Diameter
  53. Ot a Circle.
  54. 2. Dramins then S F Parallet 10 A a, The LarUS
  55. Transversum, and producins che BSSerery where
  56. t0F; che Lines D S will erery where bc =DF
  57. FS, Where che D FS are all equal, because SF
  58. Parailet Aa.
  59. 3. Nou ill And also char che Rectangles under
  60. BD and DS (= D O 9) will bc = 10 che Rect.
  61. ansle under BD and D F, deductins chac undes
  62. BD and F S. Thac is, BD X DS = BD.
  63. DF = BD X F5.
  64. 4. AIso Becaule the D FS are all equalthe R ect.
  65. anoles BDF, wil Aill bc a5 che BDS: And those
  66. B DS, because oF che Similar Tr. angles ADB, wil
  67. Rill be as the D RS, Or the Abscissae. WVheretore
  68. ehe Rectanoles B D F will erery where bc 25 chc
  69. Ablcis A O; eohiich is ihe ProOt ot ehe tirs
  70. PAIT.
  71. 5. BuF thC SqareS BD L F S, MIIICO WOEI IIC
  72. BDS and F S5 are cvery where 25 che A D:
  73. must be in a duplicare Rario ot, or 25 che Square.
  74. et ine plscettae aB.
  75. Drav a Parallet rorhe Section, as MB, Which
  76. Nore wich B, and continue che Axis oF che Section
  77. illir meer wich rhe Diamerer oF the Base oF che
  78. Cone produced in che Poine F, and draw it On 1O
  79. i, and calI AM, c.
  80. Draw also the Latus Primarium F P, and paral
  81. el to ir N O, chrough any oiven POIME, L. Call
  82. che Side of rhe Cone, in wrhich the upper Verrex ot
  83. che Section is, a. Let che Abscissa F I be nored
  84. Nich eb. And rhen (working by che similar Tri
  85. angles BC A, and P IN, accordins corhe Rule ot
  86. Proportions, NVI will be expressed in chis Nocari-
  87. On, by ec. Let the produced parr ot theBale MC,
  88. De called d; andche Latus Transversum, Or Tran-
  89. verse Diameter F D, becalled o b: Then will ID
  90. be=
  91. Sincerhe Triangles BM C, DED, and DFO,
  92. are all Similar, Work For a fourth Proporrional 10
  93. expre(s F P, and vou ill sind ic to bc o d, and 10
  94. in this Nocarion (by che Came way ol ortins)
  95. will be od = e d
  96. Here

Cite

Lexicon Technicum: Or, An Universal English Dictionary Of Arts And Sciences, fol. - . Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/806933011:0286?run=74