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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. bola 2 = 10 che Square OE CB, Or C F.
  2. PTo aSCtOr, (OIS ZEO = = G F, and ils
  3. Squate 2 E Woist Be erelore = 10
  4. irtich Eguarion seducect, will bC = 2
  5. Buc by che former Lemma= is equal 10 etic
  6. Sinc oF che double Angle, WHCTeOE S is the
  7. Sinc: Wherefore till be a5 Radius to Sine of
  8. double the Angle F CB, P0 is half the Parame-
  9. tet, co che Llorizontal Ranse or Distance Cought;
  10. and at the sereral Elerarions, the Ranges are 25
  11. the Sines ot che double Angles oE Elevation.
  12. 2. L. D.
  13. COROL L. A R Y
  14. Hence il FOIIOMS, That hals ihe Parameter is
  15. ibe ereatest Random; and that happens at
  16. ibe Flevation of 45 Decrees tbe Sine o)
  17. Wwhose double is Radius: Fitenvise that the
  18. Rances equally distant above and belorv 4.
  19. are equalus as are ihe sines of all double Ar-
  20. ches 10 the Sines of their double comple
  21. ments
  22. P R OP. II.
  23. The Altitudes of Projections made with ihe same
  24. Velocity, at several Elevations, are as the Ver
  25. Sed dines os che double aneles os Elevation.
  26. 15 c 1s 10 5:: 5013 = 6 B 10
  27. Proposirion 10 = C F; chat is, 25 Radius
  28. iealiotus attet ell eulleo ate Aopocat 10
  29. Clee Lco. Wheccioe inc limes aee aS EnC
  30. dineset ThC Eteration: tirso constat propositro.
  31. PROP. IV.
  32. Problem. A Projection beins made as pou please.
  33. Bavins the Distance and Altirude, or Descent of
  34. an Object throurh which the Project passes, to
  35. sether with the Ansle os Elevation, mith the
  36. Line of Directien; 10 find the Parameter and
  37. Velocitus that 15 (in L.18. 2.) Bavins ihe Ansll
  38. FG B, GM, and M X.
  39. catice siven, 10L; and as Radiusto l’alt
  40. sent ot L CB, l0 6Ml 1o L. M. Lhen LM
  41. M X in FleigHIS, OF -] MI X in De(CeHES
  42. Ox else MX MI, il the Direction be bc
  43. = BF, andVK = RV = = ihie AIi-
  44. Jour the Florizontal Line, is the Fall in che Time
  45. that the direet linpulse siren in G, ould have
  46. carried che Project frOm C LOL = L Z = CY
  47. Then by realon oF. che Parabola, 25 L X 0
  48. C Y IS 1O C F OF Y X, :: (0 is C L. 10 che
  49. Parameter (OugHE.
  50. Prop: 2. and 4, tind the Lime in Scconds chat=
  51. Bodr Wvould Falt che Space L X, and By thar
  52. diridins che Line CL, che Ouore will be che
  53. Velocitr, or Space mored in a Second (ought,
  54. uotich is alvays a Mean Proporrional between
  55. che Parameter, and 16 Fcer r Inch.
  56. PROP. V.
  57. L. Y. No by che Problem 2. Favins che Parameter, Hlorizoncal
  58. Corexoins Lemma = r0che Versed Sine ol
  59. che double Angle, and theretore it wilt Be a5 Ra
  60. dius ro Versed Sine ot double che Angle F C B,
  61. (0 an 8th oF the Parameter 1o the heighe or che
  62. Projection WK; and lo chese Hleiglus ac se-
  63. veral Eleracions, are as che laid Versed Sines,
  64. L. D.
  65. COROL L A R Y.
  66. Distance, and Fleisht or Descent os an Object, te
  67. vine CML, M X, and the greatest Random
  68. equat to hals the Parameter; to find the An-
  69. the Horizontal Distance GM = b, the AIII
  70. cude ot che Object M X = h, the Parameter
  71. =P. and Radius = r, and ic Will be 25r 10
  72. in Ascerts
  73. From bence it is plain, ehat ehe preatest AIi- C0 b c0 = = H L, and F BZ in DesCerT
  74. rude of the Perpendieul er Projection is a Ath
  75. os a earameter, or halt ihe greatest Florizon- = L. X, and = F= pB = C L. 1 = X Z R
  76. tat Ranse; ihe Versed Sine of 130 Degrees,
  77. beins = 2r.
  78. P ROP. HII.
  79. br reaton os che Parab. buc b b- 2
  80. = 61
  81. 1. 47. T. Euclid. Wheretore = pB =
  82. The Lines C F, or Times os the Flipht of n Pro- b b- - trich Equation rranspoled, is
  83. ject cast vith the same dezree of Velocity at dif-
  84. ferent Elevations, are as the Sines os the Fle-
  85. vations.
  86. b
  87. r,
  88. DF B F pB - bb, dividedt b7 bB
  89. r
  90. Aoci vor: : (015 l. = C B by che cl (i - g F p
  91. 2. Fhis Liquacion Mews
  92. oa eeleracion, so che Pacanteu le lle
  93. Line C FS Toche Lines eL arc a5 che Sines oF
  94. SOLVT1ON
  95. AS RadtiuS EO SCCaNE OF F CE B, (O CFMI the
  96. 20 fuid che reibens et c spulle, by
  97. find the Flevations of the Line of Directions ne-
  98. cessary to hit the siven Objeet; that is, TTa-
  99. Sles FC B.
  100. Texthe FanGeNE OF che Angle CouBHE BC == F

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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/806933011:0583?run=74