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: 0.88.

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The machine reads it as

  1. DDD. Thacis, Spheres are eo cach orter as che
  2. Cubes oF rheit DIaMeTETS. D. L. D
  3. 2. The Coliditz oF a Sphere is equal ro che Sur-
  4. Face mulriplied inFO OF Ehe RaciuS; 25 is proved
  5. FrOM COr, L. OF PTOP. 4. in thc Word Cylin
  6. der.
  7. 3. A Sphere is equal t0 = oF a Cylinder, havine
  8. the Diamerer oFus Base and is Axis equal r0 thar
  9. OEche Sphere, 1. c. 2 Sphere is = OF ihe Cplindet
  10. circumseribed: And che Surtace os the SpHere and
  11. the curred one of the Cylinder circumsetibins it
  12. isthe latme in Ouantity; a5 is proved in Cylinder
  13. Prop. 4. atid Corollaries; 2s also very brieAts under
  14. the Word indivisibles.
  15. 4. The Surtace DF che Sphere is equal EO FOUF
  16. rimes che Area OC a oreat Circle. Sec Cylinder
  17. Prop. 4. Coroll. WVhetetore add ro the Curve and
  18. Surtace OF che Cxlinder ies aro circular Bales, and
  19. chac Willmalce six great Cireles of the Sphere: S0
  20. thac che Surtace OF che Sphere is buE Z oF chc
  21. erhole Surtace oF the Crtinder. Sec allo Cylin-
  22. dor,
  23. anentire Sphere os Glass ill unite the Parallet
  24. Rays oF any Object ac che Distance oF near iES
  25. Semidiamerer Behind it. Molyneux Dioptr. P. 93
  26. SPFTERE of Activity, Ot anv Body, is chac de
  27. terminare Space or Excene all round abour il, 10
  28. extrich, and no Farcher, the Fstuviums continualls
  29. emicted trom chac Body do reach, and where they
  30. opetate accordins co their Nature. Thus ve sec
  31. Ehc Magneticat Fstuvia have cerrain Bounds and
  32. Limics, berond Wvtrich chez will have no InAuence
  33. Eo turn or to attract ehe Necale: Bur Where erer
  34. a Acedle be placed, (0 25 thac ic can be moved by
  35. a Lodd. Aonc, it may be Caid ro be wichin ehe
  36. Sphereos Activity oF the Stone.
  37. SPHERTCK Geometry, Or Projection, is ChC AEE
  38. oF Delcribing on a Plane che Circles of rhe Sphere.
  39. Or any Parrs of them in cheir just Policion atid Pro
  40. Porrion. and of Meaturins cheir Arks and Anples
  41. Wvhen Projected.
  42. A5 an mcroduction co ivhich, rou must under-
  43. Atand.
  44. For let L BC i LCacC OL IC Cteulat Dale
  45. then ist A L BC The Axis; and it che Cone be cul
  46. by che Aris, the Section AB C will be 2 Frian
  47. SIC. Lec c5, che Diamerer oF che Section, bc
  48. drawn, curtins che Axis in i, Wheretore e f che
  49. Diamerer ofthe Section Will be parallel 10B C, HC
  50. Diamerer oF che Bale.
  51. And consegueneis,
  52. Whetctore, by Inverse Proportion, and ex aequo, 25
  53. C: FB: : 18: ic.
  54. ard A B and A C must De Rixtr Fines, because
  55. che Surtace ofche Cone will be described br cirtier
  56. otchem; Wheretore che Section AB C is a Fri
  57. atisle. 2. F. Id.
  58. II. Y a Cone as A B C be eut by a Piane Parallet
  59. 10 ies Base. the Section ese h will be a Cirt
  60. ta L a C 1. 5 18, 3 2C: a
  61. 25 AF: FC :: A 1: 15.
  62. BucBF = F C, chercloree ; = 18.
  63. S: her place) cali ic V. lHCTCIOTC = radd. Z rDDV.
  64. rydda =ryDDD. BAE = ryddd. 1).. aua
  65. ANa CC Tae COMLCGUEHCE WI aIHC I VOU Tate
  66. o and K, any evo ocher Poines in che Bale ana M
  67. the Section; FOF K i being parallel t0 0F, and
  68. a o F beins a Frianglc. AF: 0F :: A I: B i
  69. buE 25 A F: F B :: Ai: I e. Wheretore ex
  70. aquo dF: + D.. 1 1. 1c. Andcheretore R I
  71. and i’e are equal also, and consequener che Se.
  72. ction is a Circle: For i is a Point trom whence
  73. more chan evo Righr Lines deawn co the Curve
  74. e h8 Fare equal; Wheretore char Curve must bc
  75. Cirele. L.L. .
  76. P R O POSITIONS.
  77. 1. a Cone, as AB C, be eut by a Pla
  78. eichet by the Axis, or ehiroush the Vertex, et
  79. Sectior Well be a Triansle.
  80. For the Point R is the Verrex ot thie Conc, and
  81. quist De CooEche Trianple, and B C is a Riphe Linc
  82. because tis he Diameter otche Circle or ite Base

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/806933011:0758?run=74