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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. t
  2. che Onestion co hare tivo Antivers, and chC ROOrS ( peces inelined contcanely co che Fleracior
  3. chereot ave L P = V p P - + PB
  4. From Which L derire che follovine Rule.
  5. Divide halF che Parameter by the Florizoncal
  6. Distance, and Keep the Ouore, viZ. chen (aY,
  7. As Square of che Distance siven 2o che halt Pa.
  8. ramerer, so hals Parameter . double Z Deseene
  9. 10 che Square OF ihe Secant = P P + 4
  10. +
  11. b
  12. he Fangenre ansiverins t0 chat Secant, Wvill be
  13. l PP, F 4 P -1 oErr: 50 chen che Sum
  14. and Disterence oEche atorelaid Onore, and chis
  15. Tangent will BC. the ROOES OFThe Rquation, and
  16. the Pangents oF ehe Elerations (OngHE.
  17. Nore here, thac in Delcents, if the TangenE
  18. exceed the Ouore, as it does wvten ph is
  19. more then b b, the Direction of the lorver Flera-
  20. tion ill De belo che Hlorizon, and it p h == bb,
  21. ic must be directed TTorizontal, and the Tan-
  22. Sent oE che uprer Fleration will Be: Nore,
  23. likervise, That it + b b - ] 4 p B in A(CCNES, OF
  24. +bb = 4 p B in DesCentS, De equal EO P p, There
  25. is but one Plerarion thac can hir the Object, and
  26. us Fangentis; and it 4bb -F + p B in A
  27. SCens, anil 4 bb = A p B in DesCenES, do ex
  28. cecd pp Etic Object is Withouethereach OF a PFO-
  29. ject calt wirh chat Velocur, and so chechinsim-
  30. poltible.
  31. From chis Equarion + b b -L = 4 P h = p P arC
  32. derermined the urmost Limirs of che reach ot any
  33. Project, and the Fisure astigned, Wherein are
  34. all the Flcistus uxon cach Florizontal Distance
  35. berond wrtich ic cannor pals; For by Reduction
  36. Ot chac L. quarion, h ill be found equal a P =
  37. in Feighes, and - - = p in DesCentS:
  38. From Whence it sollous, That all che Poinrs B.
  39. are in che Curre ot the Parabola, whose Focus
  40. is the Point trom Whence the Project is cast, and
  41. wrhole Latus Rectum, OE Paramerer ad Axem is
  42. Filcevile From che lame Equation, m2z
  43. ihe least Parameter or Velocier be found capable
  44. 10 reachthe Object proposed; For bb = = PP. Y
  45. Ph beins reduced = p will be = sbb. Bh -= h Follons tro thC L GuaLIOH, Cstat L MLaL M Cd (aY
  46. in AScens, wtich is the FTorizontal RangC AE
  47. Forey Are Deorees of Elerarion that vould just
  48. reach che Objcet and the Flerarion requilire wrill
  49. Be casily had; for diridins che (0 found Semi-
  50. Darameter by che Hlorizoncal Dictance siren b,
  51. The Ouore into Radius wil DC che Tangene ot
  52. the Elevation COnoHE.
  53. This Rule may be ot o0od rise co all Bom-
  54. Barders and Cunners, nor only thac they may
  55. nomore about ic.
  56. To determine the Foree or Velocity of a Projeet in
  57. everys Point os the urd et cferts.
  58. TOCIHS WE HIECaHO OTHeF Praecormtaus BHIL OTI)
  59. the Third Propontion, viz. That ehe Velocity os
  60. ule no more Porder rhan is necessarr, ro cast Falline Bodies, is double to that mhich in the same
  61. cheir Bombs incoche place altiend, bur charcher time vould have described the Space fallen by an e-
  62. MaY MOOE WITH MUCH MOTE CCFFAInEY, FOK thac a
  63. quable Motion: For the Velocier ot a Project, ic
  64. (maIl Frror commirred in che Filerarion oF the componnded oF che constam cquas retcus ol
  65. peice, rill produce no sensible Ditterence in the the Impressed Morion, and che Velociry ot the
  66. Fall ot che Shor: For which Reasons ehe French Fall, under a siven Anele, viz. che Comiplemenc
  67. tincinects in cheis lace Dieses harc uled Morras.(o rhe Elevacion.
  68. ocas
  69. proporcionins cheir Charse oE Porder accordins
  70. eo theDistance of the Object cher incend ro Arike
  71. on chetTorizon.
  72. And ehis is all chat necd co be laid concernine
  73. Ehis Problem, oF Strooring upon Fleighis and De-
  74. (cents. Bur it a Geomerrical Construction there
  75. oF be required, Pchink I have one chatis as ea
  76. he as any thar can be expected, wrhich l deduce
  77. Eeishe (trom Toresoins Analycical Soluion, viz.
  78. pP-I pB = bb
  79. and ris chis.
  80. a a ne C L a, Fig. 3.
  81. makre D A, D F = p, Or grearest RanS, D
  82. =b che Hlorizontal Distance, D B, DC=
  83. 1
  84. the Perpendicular heighe ot the Object; and
  85. dram GB, and matce DP. = thereto: Them
  86. rich che Radius A C and C enere L siveep an
  87. Arch, Wrhich if che ching be possible, will Inrer-
  88. (ectthe Line A D in HI; andthe Line DH beins
  89. laid boch vars trom P, will gire the points R
  90. and L, to wrtich draw the Lines GL, OK:
  91. lar the AIneles L.GD, K G D arethe Elerations
  92. regue IOE MCS OscLD. A VCIOW MC
  93. FTorico iIs DelCenEDC =DB must be la
  94. From A, (0 aS t0 have A C = AD-) V
  95. Nece litevise, thac if in Descents D H BC
  96. Sreater than F D, and (OR FaII BeloW D, thc
  97. Ansle CD Mall bethe Deprestion belou che
  98. FOTIZON. Non this Construction (o naturalls
  99. PKO P. VI

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/806933011:0584?run=74