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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: 0.85.

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The machine reads it as

  1. BuriE the Number of ReRlections be even, chen
  2. che double of che grearest Retracted Angle, Will be
  3. che Diltance oF che Tris trom che sun himselF.
  4. Nou ro sain chele Createst Lxcesses, havins he
  5. Petractlon oF any Liquor, or che Rario ot che sine
  6. oF che Angle of Incidence ro the Sine oF Retracted
  7. Arisle, sou must obserre, thac che Excess OF ENO
  8. Retracted Angles, abore one ot Incidence, will
  9. BC Greatst Where ThC NIOMENLANCOUS AUBMCME OP
  10. Filuxion of che Angle ofIncidence, is precisels dou-
  11. ble to ee Momentaneous Auement ot che Retra-
  12. cted ansle. And if chere be chrec Retracted An-
  13. sles, the createst Excess, will be Wrhere the MO-
  14. mentaneols Auement of che Ansle ot Incidence is
  15. Friple ot heMoment of the Refracted Angle, anc
  16. S0 on, Which is sufficieney evident.
  17. Buc in order 10 And che Angles themselre
  18. Eles ac the Bale, ate lo oe alotiet cucs as etie
  19. Lecchere be anr RiphE Linc as A C, and let ir bC
  20. 10 dirided in D, FhaE C A may bC LO C D::
  21. according ro the Rario OI LCHALHO; ThaEIS, IM
  22. NVateF: : 25 250 i5 1O 187, OF more nicelY : : 529
  23. i5 r0 396. Then lec ic be divided acain in P, 10
  24. that C F Ball BC EO A F: : a5 Oniry is eo che
  25. Number OF Reections Which chre SolaE RayS
  26. must undergo in producins the Tris propoled: This
  27. cular draw the Larallet F B
  28. E
  29. MI. Fralley premiles che Lols Lemma.
  30. OLD
  31. ARY.
  32. Elence it follons, Lhacche Moes Otne AH
  33. langenes ot chele Aneles.
  34. Lainthe Diamerer ot any Iris, cither GeomerricallY,
  35. Ot by Calcularion.
  36. Du ehe help ot chis Lemma he Bewvs hon 1o ob.
  37. done; on che Diamerer AL lecché Semicirele ABL
  38. De described; and on the Cenere wrirh che Radius
  39. CD, deaw the Ark B D, curring chie Semi-circle
  40. A B F inthe PoinE B. Then drawing rhe RigHE
  41. CS C
  42. B, AB, ler the Perpendicular C F, be le
  43. FaII on A B produced eO F; and to chac Perpendi-
  44. he piocuc c Blopel His.
  45. Yche Ansle C B F is che Angle of Incidenice
  46. C A B is the Retracted Angle, borh required For
  47. at A; ies L egS B A and C A, ane ene BasC
  48. on Which produced, let Fall che Perpendlcular AV
  49. Chen let the Verrical Ansle B A, C bC suppo
  50. De encreased by a Ouancier infinitely sittalI, a5 sup
  51. pole by che Momene C Ac: LIn Cawins il
  52. Lines B C d, and c D, chey vill de os mmagina
  53. rils differene trom BC D and C. D.
  54. This done, JCaY, Thac if che Lessb ite Planc
  55. Friariele B A C, Cor any ocher) continuns ch
  56. tame, the Verrical Ansle be imagined Wdde en
  57. crealed by any Infinicetr (mall Moment ot LIuXior
  58. chen will the Moments of the Anoles at the bas
  59. reciprocally as the segments of the Base: Lhar ie
  60. CBc, is 20 che Momenc oF che, ASC AC B, 0
  61. ACD:: 26C D i5 10BD.
  62. For since the extemal Angle A C D == A B
  63. I- anele BAC, its Momene must allo be equat r
  64. ere Sum ot cheir Moments, Ox to C BC = CAC.
  65. buc non because che Frianole AC D is ris alls led
  66. aC D A C may bc che Diameter oF a Mcle
  67. Whose Peripherr ill pass chro A, D, C, al
  68. and consequencly chc Angles C A0, C VC DemE
  69. in rhe lame Seomene are equal. S0 chac ehie Sum
  70. ot che rvo Fluxionarr Angles C Bc, andcD
  71. (1. c. the external Angle D)cd) Will be che MO,
  72. menic oF che Angle A CD, Or ACB. Buc chole
  73. CBC, and Dc d, beins infinicely (mall, will bc
  74. o each ortier, as the Sides oppolce rochem, el a5
  75. cD Or C D isto BO: Thac is, reciprocallu ad
  76. Scgmenes ot the Balc. D. F. D. 11
  77. IFB and C had been boch Acure, rhe way ot
  78. AB
  79. Eistea BuD E MONS FR A YFO H.
  80. istoDniey; by che Construction.
  81. roche Moenoe e AL u ne sate Ra-
  82. Since chec trianeles AOE, A F B are Similar
  83. AF will bero BF e: 25 A O2OBC:: Thac is, 2d
  84. che Numbe s
  85. Wherelore the MomeneoF the Anele C BF, is
  86. rio, by che Lemma. cse hac
  87. ProOF Bchelame, all Coeledo
  88. Duc chepune osche AnsleilBL, is ro the SiC
  89. de ate And eo l dt si. Me Aeo. leauio de atere deda

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/806933011:0693?run=74