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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: 0.87.

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The machine reads it as

  1. caliez
  2. Caustick rouch one anocher ac rhe Poine a
  3. Corol. 3. IF che Radius oF Concavity MLC BC
  4. =0, then again a= =o, and 2=0; Trom Wtienc
  5. MF= AFF perperualIY. Thac is the POrrion OFTOlIOWS, thac the Curre AM D and che Caustich
  6. Corol. 4. IFC MI De infinite, rhen a (= = HIF) 15
  7. Corol.. 5.Tis easie t0 apply alI ehis char ha
  8. 23
  9. have 2= 2y f 4) and co Mevr vohen ne restectect
  10. Rajs will come convergine or divergins.
  11. Corol. 6. When che Curve A ML D is a Geome
  12. eriek Curre che Caustick will bc (0 100; for it
  13. AMD bC a Geomerrick Curve, the F voluta. Will
  14. be(0roo; that is, all chePoines C may De Geome
  15. ericallr derermined, and from che Evoluta, che
  16. POInES FOF che Caustick may be Ceomerrically de
  17. termined al(o. Buc farcher, ehe Caustick upor
  18. this Supposicion Mall alrvars be rectitiable 100, tor
  19. Rixhe sines may alvays be found equal 10 any
  20. Porrions OF ir.
  21. Corol. 7. Tis plain, char girins any 2 OF thC3
  22. PoinEs, B, C, F, that is, Ihe Radiatine Point, che
  23. Tex ThC POInE C DC AE the Fvolura OE the re- Point os che Evolura, and che Point os ihe Caustick
  24. Aecting Curve AM D, Or wrtrich is al one, ser che 3d Poine may be derermined.
  25. MIC bethe Radius otthe Concariry for the Poine
  26. MI; and suppolins che Arch Mm infinicely (maiI
  27. lec Bm, Cm, Fm be drawn. F’arrher, uxon che
  28. Centers B, F, lec che licele Arches MR, M1O b
  29. delcribed, and trom che Poine C the Perpendicu
  30. TarS CF, C e, CG, C5, c0 che incidene and re
  31. Aected Rays. The Priansles MIRm, MIOn
  32. are similar and equal, as was Meon betore, and
  33. MR = MIO. AIIO ihe Triangles C F M and
  34. COML are similar and equal, and (0 are Cc m
  35. and C∞ m; For the Ansles aE L, e, G, c are risHE
  36. and MLC, me are common, and F NI C-GNIC
  37. and em C=g m C (becaule MVC, m C are Nor
  38. mals ro ehie Curve by suppolicion ot the Evolut
  39. and che Ansles oF Incidence and Reflection arc
  40. egua) Theretore CF==C C, and C’e-C, ane
  41. contequencly C F. C cC 6- C5, Thar I5, F O-
  42. 56. LatIy, che TrianBles, B MLR and BF ∞
  43. aee similar, and (O arC F MO, FCS. NToW lec
  44. BMy, MF= MO=a; cheretore BNI + B F
  45. -2y - a; let RM.O M x, and F MI
  46. WHeresore F C==a 2, and ler it be required rO
  47. sind Z which derermines rhe Poine F in che Cau:
  48. sick. Then F proma and F e + M R=
  49. 2ji an, al(0 5C - ai 2i and 56 + M0- u
  50. but by what Wvas Mewn beFOTC RN== O MI, and
  51. S6= PF, theretore F.Q FR M=S6 + MO.
  52. By chis general Theorem and ies Corollaries, che
  53. Causticks ot particulas Curres aie easily derermi-
  54. s
  55. Ned, horvever the RayS 30, Convergins, Diver-
  56. Sins, or Parallel; bur e ill suppose che simplee
  57. Case ot Parallel Rays. Thus in the common Pa-
  58. rabola, il che Incidene Rays are parallel, and cur
  59. Ehe AX ac righE Angles, Thac is, are co. incident wirt
  60. che Ordinaces 10 chat AX; then we have 2- = a:
  61. (0 char cakins in cach reflected Ray che lengin ol
  62. 2 a (a being che reflected Ray incercepred Be-
  63. ecen che Point oF Incidence, and che Point where
  64. the Normal From che Fivoluta meers that resected
  65. Ray) by this means che several POinES OF che
  66. Caustick woill be derermined. The lenorh oF the
  67. Causticke Curve allo catien trom iHe Vertex OF itie
  68. Parabola (Wrhere it begins) eo any ocher Poine, is
  69. equat 10 ihic Summ ot che Iucidenr and Rerected
  70. Ray5.
  71. chac is, 21x.-. au ax and 272 Za =ga; and sCaustick, Becinnins AC che Tame POInE; non be-
  72. 2 (=- MIF) =, . 2: F: F.
  73. Corol. 1. IE The Incidene R ays are parallet, eher
  74. a. For y in chis case is infinire, and cheretore
  75. evich y.
  76. 27, che Ouanciey a ranictins il compared
  77. Coroll. 2. YE ehe treident R av BMI rouctes EHC
  78. Curve AMD in MI, chen a (=- MI F:) i5
  79. and cheretore Z (= MF) =O El(0; trem wotence
  80. FH L atEe RiPBEsIinE HE, rhaE IS FML L NZ =, ic SollomS, ehac rhc pivea CurDC A M D, aud ihC
  81. AEI L HIF F TL, and MIL IA = A +1, 11F-
  82. MF; buc AX L. F A-B MI B A, and cheresore
  83. the Porrion ot eHe Caustick AF B ML
  84. Ot che Curre A MI, is equal co rhe difterence ot Angle equal co the Angle ot Incidence.
  85. ehe Incident Raso BM, B a, added co rhe disse-
  86. rence of the reffected Rays MF AFT. Or, ca- intnice litewise, and 2 (= MF) = y; and in
  87. Porrion ot che Caustick whieh is evolved while che Arch Nm becomes a riphe line.
  88. Ray B A approdchech co a ca. incidence wirh BNI
  89. how co determime the Lvoluta oF any siven Curve
  90. che Invenrion e catacaustick trout chence
  91. the Caustick FYF formed trom ehe reslected Rays do cur ono anocher ac che Poine M, and makie ar
  92. kins any 2 incidene RayS, a5 B , B MI, thac ehis case oF che intinire distance of che POinEC, che
  93. 5= to che difference ot these Incidents. F the been said, when the Curve ANT D iS COnVeX IC
  94. difference oE rheir reRected RayS. Non knomins che Radiarine Poine B (in Wwhich cale woc Mall
  95. AS suppose A AL D voere rhc Parabola rohole
  96. Verrex and AX AK, and AFYF Were the
  97. cause cho incident and reffected Rays at ine Ver
  98. cez are equal eo nochine; thaE iS, AB = 0, and
  99. 2FF=0, cheretore iHC Curre AF F (= P M
  100. A + M F- AEL by wehac vas Memn BetorC)
  101. M+ MF.

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/806933011:0140?run=74