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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: 0.90.

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The machine reads it as

  1. Cipte oE cheir Genetis las beine Tormed trom lc. ( trich it allo, and cBCrCe F F is nOt an Asym-
  2. ciprocas selses) dle calisy prored cohare cuo A- ptote.
  3. symprotes. And ot che larter lorr we have che
  4. Conchoid, che Cissoid, and che Locarithmick Curve
  5. V. Bur à Kiphe Line may de an somptote 10 à
  6. mixe Curre thac is parrly Concave and parcly
  7. The Nacure oF which considered, as clearly Mens Conrex rowards thar lame Linc. an Instance ot
  8. thac cher hare one and no more.
  9. TII. A5 a Righr Line and a Curre may be A.
  10. simpeotical 10 one anocher, (0 allo may Curves
  11. and Curres: And here are rvo or chree Varieries
  12. to be considered.
  13. ehis ve have in che Conchoid ot Mcomedes, Which
  14. is Concave (for lome parr OF it) eO its Normal,
  15. and chen atter the Punctum Flexus, in Which rie
  16. neithet Concave nOT Convex, ic is FOr ever Con
  17. vex cowards che lame. Concernine etich Pun-
  18. I. Any OE chese Curres, that hare trom cheir ctum Flexus, see Schoten. Comment upon Cart. Ceo.
  19. ouon Nature and Construction an Asymptote, are
  20. capable ot beine Alymprorical eo one anocher.
  21. metry, L. Ib. 2
  22. VI. AII Curres thac have one and che same
  23. Thus in Conick Sections ris demonstrared, thac Common Asymprote, are allo Alymprorical c0 one
  24. Fyperbolas chat have the lame common asimptote
  25. are allo themlelres Asimptores ro cach orher; and
  26. ehis Mall atterwards be Menn univerlally ot alt
  27. Tuch Curres.
  28. Wich an Asympeote; buc even such as in cheir own
  29. nature admir ot no luch ching, may also have chis
  30. aftection. Tie Parabola (For instance) ve know
  31. has no Rectilineal asimpeote belongins ro ic; and
  32. Tame Rishr Linc, will bc ACymiprorical to cach
  33. other; as De la Fire has demonstrared, Sect. C0-
  34. nic. LIb. 6.
  35. anocher.
  36. .Noc only chole Curres, Wrhich are endowed
  37. vec cvo Parabolas, Wu est aes placed in ehe
  38. 3. Buc no Curre chat has any asimptote De
  39. longins e HE, Can ever be A(ymprorical EO ano-
  40. chier whose Narure retules a nur mp
  41. for it ic wesc supposed co be lo, then chis lalter
  42. Curre vould hare che Lympon et cn sertet
  43. Cuere For its onn Asymptote coo, wtrich is concra-
  44. ey eo cuc Lypochesis oF ies having none ac all.
  45. can neret be Alymprorical to one anocher; for
  46. ere IE (0, the Asimptote ot che LIyperbola woulo
  47. bc allo an Asimptore co che Parabola; which is
  48. imponBe, since chac Curre can have no A.
  49. V. Ho Riphe Line can ever possibly be an A
  50. simptote to a Curve, chat is every wvhere concave
  51. corvards chac Righr Rinc: Thisis very clear Fror
  52. che bare Consideration ot the Curvarure and rh
  53. Demonstrarion.
  54. Thus, for instance, a Parabola and an Hlyperbola
  55. Simptote.
  56. Tendeney of ic; and may be thus broughe inte
  57. Let the Curre ADC (vtole AX iS AF) bc
  58. concare in all ies parrs comards cheRiphr Linc
  59. F E; this Linc chen F P MaII never bc an A-
  60. L et the Curres FGH, O F R, have che com
  61. mon Alymprore AD P; thenchey MalI be AIym
  62. protical ro cach orher. Fir oE all ic is evidem
  63. thar chey continually approacti ro one anochex
  64. for instance, drawine ihc Line FD a TangenEr
  65. the Curve OR in F, r0 meer wich che Alympo
  66. in D, and producins B F rOC in the Curve L. L
  67. deaw CF a Subrense in char Curve paranel t
  68. FD, and then From HY, the Line HIKC PatallC
  69. simprote 1o che Curre AD G. Lec A B couchche, toGB; ris clear that FG =FT, andHIL IIN
  70. Curre in che Verrex A, and be imagined parallel because FD couches in F; cheretore FO L Hs
  71. hac is, the Curves are nearer to one another it
  72. EO FF; then any Ocher TaMBeNE, 25 CD sup.
  73. Pole, all, it ic be produced, meet wirh F F in che Poines FT, K, chan in F, G; and che Pame
  74. lome Poine or orher; bur because C D is a Tan- may be Mevn ot any ocher Poines taken from rhe
  75. ParES OF B, C, rowards P. Buc chen again, chet
  76. Benc, cheretore rhe Curve Line ic selF Falls be-
  77. cveen che Tangent and che Line F E; bur ir is by Curres can never postibly meer wich, or euc one
  78. che Fypochelis alto concare 10 F P in aIl its ParIS; anocher. For Imagine chey could and did in-
  79. cheretore if the TanGenE C D produced inter. cerlect cach orher, ar the Poine suppole, anid
  80. secto FF, afortiari, ihc Curre Cm sat L L, R Y bc pacallet 10 B8, HC. Hte
  81. Sorve

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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/806933011:0093?run=74