Leibniz Legible

Machine transcription of the Leibniz Nachlass

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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: 0.86.

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The machine reads it as

  1. P
  2. 2. For au Parallelorrams, mulciply etil P’expen-
  3. upon; and che Product is thie Area. Becaule alI
  4. Becaule char Line will be equat lohe heishl
  5. Such Ligures are equal ro Rllates et le Tae eta LdI.
  6. or equal Bale and Alcicude.
  7. 3. For al Plane Friancles, muloiply hale che
  8. Perpendicular ler tall trom any Ansie, by the
  9. oprolice le, or halfchac lde by che Perpendicu
  10. lar, and che Produet is che lue ea; because
  11. Trianoles are chehalves ol Paralleux rams ot che
  12. lame or equal Bales and Alcirudes.
  13. For a Prapezium, Where wo illes are Pa
  14. rallel, mulciply che dumm ol che Lalalles lde
  15. (b and a) by halt (p) che Leeat.
  16. dicular lec fall trom any side, by che side ic Falls ot each Triansle in che Polyson, and cheir Bales
  17. wilt be allo equal, because chey are sides ot 2
  18. Thus in a HexaCON, WI
  19. and ehe Distance som the
  20. ot any otche sices 10 Xards
  21. The Summ Ol C siueS
  22. Side is 8 Yards.
  23. onter r0 che Midale
  24. 6X8 = 48. votose
  25. halt is 24. Which mulciplied by 10 produces 240
  26. 5. For any other Traxezium or any Multane ula
  27. Plane Figure, resolve it Diagonally into Lrian
  28. oles; and add the Areas oF thole Triangles
  29. (Found by che 3d Problem) into onc summ
  30. ivtich will be che erue Area of che whole. Lhu
  31. suppose a Trapezium whole Sides are nol paralle
  32. divide it into uvo Triangles by a Viapota
  33. and lec fall a perpendicular trom che othor Ansie.
  34. therero; then multiply che whole Base b
  35. BalE che Summ, (or BalF che Bale by l
  36. aote ot che Perpendieutat, Lbuur
  37. Pards, che area ot che exacon
  38. 7. For all Circles, mulrixly hals rhe Circumte-
  39. rence by che Radius; because every Cirele is e.
  40. Quat 10 d heclanele L, one ot vitole Lcgo o ce
  41. Periphery, and rhe ocher ihe Radius. AS Archi
  42. medes Hac detonacca. For Practice, meature
  43. the Semi-diamerer, then (ay, 25 100O, ZTAY 3 2
  44. (0 is the Semi diamerer ro che Circumference:
  45. ewhich found, mulciply by halt che Diamerer (OF
  46. Radius) che Produet is che Area.
  47. 8. For a Sector of a Circle, mulriply che Radius.
  48. or one oF its Leos By HaIF hC ArCH, (Or BaIE chC
  49. IS ThC, ea.
  50. Base 24, ie5 haIF
  51. Summ ot che Perpend. 12, its t3lE 5, 5.
  52. 90
  53. hacius by chc whole Areh ihe Produet Biveo EC
  54. Content.
  55. che Sector Mnhuine onche arke and allo che Area ot
  56. che Trianele, and Cubtctact enal et uns
  57. 9. for au Segments of Circles, cu sred bi
  58. Erom hac ot he Sector, al LLCI Id EK Is CIC Lat
  59. OE hC Serment.
  60. 1D. For an Ellipsis, mulciply che longe Ba
  61. merer by the Morrell, and exrract the square
  62. Root oF the Product, ic sires che Diamerer ot
  63. Circle whole Area is equal eo the Area oF the FI
  64. C s
  65. lipsis; because che Diamerer of such a Circle i
  66. mean Proporrional olneen ine aclesot
  67. AI. For a Parabola, mulriply the eneire Ordi-
  68. a L Laa, 2 daxtim coloured
  69. Circle abour che Nixpte
  70. nare by the Abscissa or intercepted AX; chem
  71. double chac Prodult, and divide che holeby
  72. S. For all Repular Fieures or Polysons, mulci
  73. ly che hale summ ot aIl the Sides, by che
  74. lenech oF a Line dravn From che Centet W chc
  75. midate ot any one Side, che L SIres EHC
  76. Area
  77. the Ouollene 1InC Area

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/806933011:0083?run=74