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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: 0.87.

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The machine reads it as

  1. R
  2. pla supereriparciens septimas, Or Subquadrupla super-) Ference. For Wtien etie lonser Radius e l Hlacte
  3. criparriens septimas.
  4. Sind char the First hach as much Creatnels orhmal-
  5. nels, in respect of ehe Second, 25 the Thira hath in f allo Will be come to 5, and will as vellas che
  6. respect of the Fourrh; thole Four Ouantities are ortiet hare delcribed a Semi-cirele: S0 chat as the
  7. called Proporcionals, and aue chus expretlec
  8. 8. 2 :: 10. 4
  9. b : : c
  10. d
  11. hat i5, A5 S comeains 2 tour rimes, (0 16 comains
  12. aTour rimes; and cheretore 8 is just as bis in re-
  13. spect oF 2, 25 16 is in respect oF 4.
  14. 7. Lte Hon chese Considerations may all the se-
  15. Fore theretore, the Rario berween the First (veral Species oF Proportion De demionstrated troL
  16. Pair, is equal ro the Ratio betreen the ottier Pair ( the Nature oF the Thing. For if
  17. ot Numbers; and consequenelr, chese Four haring
  18. then ther will noc be Proportionals: AS it instead
  19. OF 8 Vou Bould puL9 OF7, letring aIl the rest re
  20. main as chey vere; twill chen be plain, chatc
  21. hach more Magnitude, and 7 hath less in respect
  22. OF 2, WHaII 1O HaLA In TEIBCCL OF 43 FOF 9 COn-
  23. IE Wils cerrainty Pollon by Inversion, Fhat
  24. A: Z.: B. 22.
  25. Thac Is, I Z be a5 bis in respect oF A, 25 Z
  26. tains 2 abore four rimes, and 7 doch not contain ic is in respect of B; then must A DC as licrle in reo
  27. 50 otren as Tour rimes; Whereas 26 contains + ex- spect oF Z, as B is in respect ol X.
  28. actli four cimes: Wheresore these latter NVum-
  29. berS, 9, 2, 16, 4, Or 7, 2, 16, 4, dlC nOE Propor.
  30. tionals. And trrould bc the Pame, it any other
  31. Member oF ihe Arst Pour Numbers had been al
  32. cered; For the Proporrion vould neceslarils be de
  33. Rroyed.
  34. Ox it +2 Contain 3 as OFren a5 B Contains 2, then
  35. Will 3 be contained in 12 a5 oEc a5 2 is concained
  36. in 8.
  37. 8. Since Z: A :: X: B, it will follow, by
  38. Alternate Proportion, Chat Z : Z :: A: B3
  39. thatis, Ancecedent is to Anrecedent, a5 Conse
  40. quent is to Consequent: Wrhich is plain, il che
  41. Formet Fisure De ell considered.
  42. For suppose the ourer Cirele Z to be Double,
  43. Triple, Guadruple, 690. oF the inner Circle X5
  44. chen must che Ark A (or any ocher ParF OF IE) BC
  45. Double, Triple, C9c. OF the ANK B, 2 litce ParE OF
  46. the Cirele X. Therctore, Asche Whole is +O the
  47. Whole, (0 che Parrs must be corhe PAHS; that is,
  48. L: Z:: A: B. d. F. D
  49. 9. IF Vou compare che Differences (ertrich is
  50. wrhac remains when one is subrracted trom che
  51. orher) Detveen the Anrecedents or d cheir Conse-
  52. quems, With thole Consequents; another Species
  53. OF Proportion ill be found, which is called Pro-
  54. porcion by Division, and ouxhc r0 be chus exprett,
  55. Z = A: A:: Z - B: b.
  56. Non undoubredlr, is trom che wwhole Circle Z.
  57. Vou rake a OHarter, (OF anY OEHeF PATE) 2S A; and
  58. also trom che whole Circle X rou cake a Ouarret,
  59. Oc aur like ParE, as B; che remainine Three quar-
  60. tersol the ourer Circle, must be to iis orher Ouar.
  61. ter A, as theremainins Threc quarrers in the in-
  62. nec Circle ave ro its Ouarrer B. Thatis,
  63. mored orer the Fourch part ot ille Cicle L and
  64. ee Lon cis comelor, chenee LBIK) al
  65. Ldecoe c, ale dla lare soneorer a ua
  66. atant ol its Circle Z; and when eis come tod;
  67. Orcle Z is ro ans Parr ot its Peripherr, Or 25 ic is
  68. cothe Ark A; (0 will che Circle X be ro a like
  69. Parr oF its Peripherr, orto che Ark B. Thac IS,
  70. .2..
  71. Z: A:: X: B.
  72. 5. IF When Four Onantiries are considered, vou
  73. equal Ratios, are Propornals.
  74. But H ron encreasé or diminist any onc of thele
  75. Four Numbers, the Ratio ill grow unequal, and
  76. 6. Elie atinexed Tisure vill serve vers Wen
  77. explain Proportion.
  78. Lec the Radius c C DC supposdro more quile
  79. LOuI On ieS Centre C, rill the Poin c’Ce to
  80. ehie Came Place ic wras ac betore it besatt i ore
  81. etien it char Poine hare clsibeu ne Ccum
  82. at the lame rime, any ocher Poine of che Radius.
  83. 25 supposes, Wwiil also have described che Inner
  84. Circle fBGX. Dram che crvo Diamerers IIL,
  85. and ea cntrins each ocher ac Righe Angles in C, guenes rogether, and chen compare the sums wict
  86. ertrich wils diride borh Circles into Four Ouadrants. the Former Consequents; another Species ariles,
  87. erhich che outer Circle (Z,) Bears to its Fourrh Prest,
  88. (Or any ocher) PAIE A; IC LaM MLIC EC MICL
  89. Coiscte C3) beal 10. D, ale vult d lo Circum
  90. 2. = A: A:: Z = B: B. Q. F. D.
  91. 10. Oris rou acld che Antecedents and Conte
  92. ference ot a Circle, Wile set DCLa LC. eHen
  93. Tis plain trom bence, char che came Proporrion called Proportion by composition; and ris chus ex
  94. Y F A: A: . X. f B. B.

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/806933011:0668?run=74