Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

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: 0.90.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. conlequently, rhe Space described by che Fall, i5
  2. hals ivhar vould have been deseribed by an es
  3. qual Morion wich che Velocier BC, in che lame
  4. time; Wheretore ehe Velociry BC ac the end ot
  5. ihe Fall, is doublo ro char Velocity, wrtrich in ehe
  6. Time AB, vould hare described che space fat
  7. len reprelenced by che Triangle A BC, ivich an
  8. equable Morion. d. F. D.
  9. Proposition IV.
  10. Al Bodies on or near the Surface of ihe F arcts
  11. in their fall, descend so, as at the end of the
  12. first Second of Time cheyhave described 16 Feet
  13. one Tnch London Mleasure, and acquired the
  14. Velocitr of 32 Feet 2 Tnohes in a Second.
  15. This is made out from the 25cH Prop. OF rHC 2a
  16. pare OF ME. TIugenius de Porologio Osoillatoria
  17. Wherein he demonstrares che Time ot rhe leaAVI
  18. brations oF a Pendulum, r0 beto the Time oF che
  19. Fall oF a Body, From rhe Fleighe oF halF che lenect
  20. OF che Pendulum, 25 che Circumference oF a Circle
  21. ro ies Diameter: Whence, 25 a Corollary, ic Fol
  22. IOWS, chac as the squares OE The Diameter EO chC
  23. Sgnare oF che Circumference, Po Hals che leneth ot
  24. he Pendulum vibracins Scconds, ro che space de-
  25. Seribed by che fall ot a Body in 2 Second oi Time;
  26. LeF AB reprelent che Time oF the Fall Ot 2 and che lenech oF a Pendulum vibrarins Seconds,
  27. Body, BC pervendicular ro AB the Velocity dc- beins Found 39, 125, Or 8 Inches, the descent in 2
  28. quired ac the end oF rhe lan, aba arau che Line Second will be found by che atorelaid Analoei 16
  29. 4 C, ehien diride che Line A Sepleleneins Boor and ore Tnch, and by che lact Prop. ihe Ve-
  30. the Time into 25 masss Cesuas Pales a5 vou locity will be double cherero; and near eo chis ic
  31. pleale, 25 b bbb, MC. a m chele Poinsdram hach been found by several Experiments, wtich
  32. ihe Lines bc, bc, _c. Parallet c0 BC; ris ma- by realon of ihe Sivifeness ot he Fall, cannOE (0
  33. nifest, thac ehe Wrtat Lines b0 reprelent che
  34. several Velociries et che talline Body, in Puch
  35. exactly decermine ies Ouantity.
  36. From chese tour Propositions, all Ouestions con
  37. dene likemise, chac e sre bC is che summ cernins che perpendicular descent of Bodies, arc
  38. OF all ehic Lines b0 catren rogether, wtrich aCCOr-
  39. many; (o chac che drea BC reprelents che
  40. casily Polred, and cither Time, Height, Or Veloci
  41. cies beins attrened, one may readily sind che o.
  42. TheF EIVO.
  43. From them litcewise is che Doctrine oE Projects
  44. suppoled infinicely many; W Su is the deducible, astumins che cuo follovins axioms,
  45. viZ.
  46. P. Thac a Body sec a movins, will move on
  47. continually in a Rishe Line wvich an equable Mori
  48. on, untels lome ocher Force er Impedimene in-
  49. cerrene, Whereby it is accelerated, or retarded,
  50. or deRected.
  51. 2. Thac a Body beins agitaced by cuo Motions
  52. ae a time, does by cheir compounded Forces pale
  53. chrough che Came Points, as ic vould do, vere
  54. thetuo Notions divided and acted suecessivelr.
  55. The Learned Mathemarician, MIr. Reil, in his
  56. Examinarion oF Dr. Thomas Burnet S Theory of ehe
  57. Carth, P. 124. proves, Thac che Direction ot
  58. Hleary Bodies is noc tomards rhe Cenere oE the
  59. Parch any evhere, bur ac FhC RGUAEOK. OP ac the
  60. Poles: Flovever chey will be all Perpendicular co
  61. cheir FTorizons, and (o chere can be no Prror in
  62. DESCLLIDLHT, a Term in Geomerry, expres
  63. the torceoine Proposion. Lton u Ln s some Line or Surtace, which by ies Mocion
  64. 2DC is hate Mhe. Lacaltelobram ABC ti, aud produces a Planc Ribule, oi a dolid. Dec Dirisenc.
  65. DESICCA.
  66. Proposicion ut
  67. The Spaces described by ihe Fall of a Body, ar
  68. a ibe equares os ehe Times from che besinni
  69. be Fall.
  70. Demonstrarion.
  71. parts OF che Time a5 Ab is ot AB; ic is evi
  72. ding ro che Mechod ot indivisibles, are intinicely
  73. Summ oF all che Velociries, becoeen none and BC
  74. Space descended in chie Time represenced by
  75. ; lo char che Spaces delcenceu in ne limes
  76. 2B, 1, arc 25 che AreasoF che Linss BC
  77. 06, Wie) ec LBTh oE the oco Lna arc
  78. 25 IC Squares oF rheir Homolozous sides AD, Ab
  79. chac 1s lolas, ete Les; Whieretore le Delcenes
  80. A B. And by che lame realon the Areas Ab C
  81. will reprelent che Spaces descended in che Times
  82. oE Fallins Bodies are as l o guars et l LC
  83. OE cheir Fall. Q. F. D.
  84. Proposition l.
  85. The Velociey mhich a Descendins Body acquires
  86. in ans space of Time, is double to that, where
  87. nith it vould have moved the Space descendec
  88. s un equable Mocion in chesame time.
  89. Dmonsration.
  90. to BC, and complear che Parallelorram AB C P, Fallings ot che Cround: And trom hense (as he
  91. AL Bevidene chac che Area chereot may reprelent (MheWs, p. 128.) ris plain, che Surtace ot che Larrt
  92. BC vould describe in che Time AB, and che corial Diameter ro is Polar 15 2569210689.
  93. hansle ABC reprelents the Space described by
  94. LHe Fai ot a Body, in che lame rime 10,107
  95. Dram EC parallet t0 A B and AF Parallel levelline oF Lines, and in Andine che risines and
  96. the Space, a Body mored equally wich che Velocity, cannor De exactly Spherical, buc the Parchs liqua-

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/806933011:0253?run=74