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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. the Came Third Numbers, are in the Came PFOPOF)
  2. And ris cerrain, ince Z: A:: X: B, bY che
  3. Supposition, and al0Z: Z: : A: B. bY Aernate
  4. Proxorrion: Z and A together will be i0 A, 25 X
  5. and B cogether are tO B. That IS,
  6. Z F A : A .. + 1 D. D. L. C. D.
  7. :
  8. 11. le vou compare che Anrecedems vich che
  9. Difterences betireen them and their Conse-
  10. quents, anocher Species oE Proportion ariles
  11. ivtrich is called Conversion of Proporrion: And is
  12. chus exprett.
  13. 12
  14. :: 8
  15. L.A :: 2. 2L
  16. Which is very plain from che Consideration oF che
  17. Figure; for no doubr che whole Circle Z is 10 its
  18. 4 (0iZ. Z A) 25 the Wwhole lesser Cirele X is t0
  19. (ertrichis = B.)
  20. 22 3
  21. 12: IE when Z. A:: X. B, Vou compare e
  22. Conseguents A and B wich cvo ocher Ouantiries
  23. (0 a5 ro make rro Rons of Proportionals, Candine
  24. chuS. A, d : : B. Y
  25. Then will Z be 10 d:: 25 Z: L, wtich is
  26. anorter Species ot Proportion, called Proporrion bu
  27. Equalisy, Ox ex aequo ordinata: And Follos from
  28. this Figure verr plaintr, for no doube the wrtole
  29. Circle Z is Eo its Z, Wrhich is gor d:: 28 the whole
  30. Circle X is eO its 2 Which iS L. OF 6.
  31. 13. IFZ DC taken as Otren a5 LL, ex. 1. 3 L al
  32. 3X, vou may conclude, ThacZ: Z :: 3Z: 3X.
  33. OF 25 10Z 10 10 Z; Or al(0 25 12 =Z, 1O 12 =Z
  34. And (0 on in Wwhacloerer Proporrion the evo MaG
  35. nicudes Z and X are multiplied, (0 chey are mul.
  36. riplied equallr, ox thac rou rakce one 25 olten a5
  37. ron take che ocher. For then there ill be che
  38. Tame Proportion betveen the Magnicudes hus e
  39. quallr Mulciplied, as there was berweenthesimple
  40. Masniiudes, betore such Multiplications.
  41. Number is just as much encreased by Mulciplicarin
  42. on, ex diministed by Divilion, as rhie ortier is.
  43. And chese Magnitudes thus equally mulciplied,
  44. are called, Equi Mulciples, oF che smple Nagni-
  45. tudes Z and X: Hlence ve Cay, thar P. qui Multi-
  46. ples are in thelame Proporrion a5 such simple Mag-
  47. nicudes, our of wrhich ther are compounded.
  48. 24. IF Z be divided in the lame manner 25 ZiS;
  49. and ex. gr. Vou cake a Fourth part ot Z, and the
  50. like os X; or he renth, or ariy ocher parr ot L
  51. and the Pame of Z: Then will Thele PAFES DC PFO
  52. portional ro their Wholes, Z: Z:: +Z (OF Z,Z)
  53. Or = X. AII which is selF evident.
  54. 15. A Proportion is Paid to be Compounded OE 0-
  55. ther PropOrrionS, Wrhen che KXPOnenE OF THaE, IS
  56. made b7 che Nulciplicarion oF the PXPONenES OE
  57. Thele, one inco anocher. Thus, che Compound os
  58. the Treble and Double, (evhole FZponenrs are z and
  59. 2) is che Treble of the Double, (rtole Exponent is
  60. 3 X 2;) chac is, eic Sexcuple (Decaule 3X 2 = 6
  61. Which is manifestly a W ork oF Mulciplication.
  62. 16. The Products, Ox the Quorients OF any L Wvo
  63. duacicies or Wumibers Mulciplied or Divided by
  64. tion a5 che Numbers ere betore they vere MuIZ
  65. uplied, et toracu.
  66. E. or. 1. L et 8 and r2, be MpICd 68. 43
  67. then Will 8: 12.. 32. 40.
  68. 2. Tec 8 and 12, be la by 4; vile
  69. 8: 12 : = 2 : 3.
  70. The reason os whieh is very plain; vecaule onc
  71. portional.
  72. LR OBL E M 5
  73. Eo Euo Lines A and B, 10 find D a Thirc Pro
  74. Make any Riohe lined Anole, 25 0 a e. Then Pet
  75. OA in ic a d = A, and a b = B. Sec oH al(O B a-
  76. sain fcom d ro e; then join b and d, and r0 b d
  77. dram a Parallel chro che Poince, (0 Mall b0bertie
  78. Line Coughic FOF, A. B: : B. D, by 2e6 Euolid.
  79. dThrec siven Lines, AB and C; 10 find a Fourtta
  80. Provortionat D.
  81. aatC al) Lgle do ace3 then trom a; tatic
  82. ab = and b 0 = B, and a d = C, joyn b d.
  83. and chro c dra a Paralset ro b d: (0 Mall de b0
  84. che Line Coueht: FOr A. B: : C. D. 2 e6 FV
  85. at

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/806933011:0669?run=74