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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: 0.88.

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The machine reads it as

  1. tet oF ihc Lpieycle 10 che Centers oF the Worta,
  2. and orhe Lccentricke
  3. 2. When chere is an intermixture oF Ouantile.
  4. EOVA TIONosthe Orbit, is che Came wich the knovn and untenonn, in anr Equation, let all ehe
  5. Total Prostapheresis Ox Lquation Total.
  6. EODALION, in Alscbra, is a murual com
  7. Parins oF evo equal Thinss oFditterent denomina
  8. riOnS; 2535. = 36 d. 10 CFOWNS = 2 l. 105. =
  9. 505. = 600 d. = 2400 FarhineS, (9c. a = b-
  10. du 36 =
  11. 50c.
  12. The Ferms os an Equarion, are che severat Onan
  13. riries ox Parrs of wtich any lquarion is composed
  14. untnovn Ouanciries (bY Transpolicion) Oc Made
  15. 1o possels ony one side ot rhe Equarion, and all the
  16. Knorn ones another.
  17. Transposirion is alvays done by purtine cheduan-
  18. tiey over roche ocher side wich a concrary sien ce
  19. wtrat ic had betore. The Demonstrarion ot whict
  20. Rule dexends on charAxiom, Thac il to or trom
  21. Equals vou add or lubrract Equal, he SumS Ox
  22. connected roserher by the Sions-I and - A5Remainders willbe equal.
  23. in ehis Equation a = b ) c. The TermS are
  24. 2, b, and c, where ris suppoled chat some Ouan-
  25. Thus, suppose a = 34 = 60, Then a = 34- 1.
  26. 60
  27. 94. Or it a -1 b
  28. ciry reprelenced by a, is equal 10 che summ oF b (chen a = e = c - 1 d. IF 4 a = 300 = 3bb. ]
  29. and c, or ro b andc addedtosether.
  30. 4c - 4 5, chen 4 a = 300 -] 3bb-)
  31. Wtienerer any Ouection or Problem is proxosed IF36- 44 = 4 = 60, then a = 140.
  32. in Alsebra, e alvays suppole the chins soughr or
  33. requirea, r0 be bnonn or done: And then by put
  34. ting ehe Letter a, or some other Vovel (manv use
  35. phe last Lecters oF the AIphabet Z, X, 3) FOr thC un
  36. Z. FEThC hiphest Pover Ox Species ot che n-
  37. Hnonn Ouantier be mulciplied into any known
  38. Ouancier or Ouanciries, ler che wrhole be dirided
  39. knon Cuantiir, or For che Thins Couche, and by such knoun Ouanciis or Ouanrities.
  40. Consonants for wharever is Knomn ox siven, in Or
  41. der ro distinguiss one trom che orher. The Oue-
  42. Rion or Problem is first chrouxhly considered, and
  43. Thus, Is 5 a a = 30000, a a = 30000
  44. then duls staced, and aster this JudicionAr com- (IFb a -) d a = 100, then a =, 100
  45. pared, transformed and raried, by Addition, Sub.
  46. 40- 48
  47. sraction, Mulciplication, Division, Fxiraction oF IE d ee = a de = Z, chene c- F de = 3
  48. ROOrS, (90. accotdins a5 che narure sF che Thins.
  49. and the Rules oF Art direct; eill ae last che Ouan
  50. ciry sovelt, Or at least seme Porver ot il, becomes
  51. equal eo lome knonn or siven Ouancier, and s0 is
  52. it seltos consequence discorered.
  53. Afcer a Ouection is duly Cared, tis proper t0
  54. consider arhecher it De subject ro any Limitations
  55. OrnOL. Towhich end, the Wricers oF AIgCBE
  56. Bire chesc general Rules.
  57. Y. HEthe Onantiries (Oughr Or requir d are more
  58. than the number otrhe siren Equations, the due.
  59. stion is capable of innumerable AnSIVerS. SeC R er
  60. ser S Algebra, P. 301. Vol. 1.
  61. 2. Dur il che siron quarions, independane one
  62. upon anocher, are just as mans as the uanciries
  63. Souste, chenchie Ouection hach onty onc certain ane
  64. determinable nUIBCTOF ANLNCTS.
  65. IFche Duanciries Soushe er required, are less in
  66. number chan the siron Rguations, che Orection
  67. =6000
  68. This is called Lometimes Depression, aud by Vieca
  69. Parabolismus.
  70. 4. TE 2I che knoun Onanrities happen 10 be
  71. mulciplied into any desree of the untnovn onc;
  72. ler ali be brouphe down (by Dirision) cothe lowest
  73. degree chereot char can bC.
  74. AS Il aaaa= baca = ZZaa chen by Dirision
  75. OF all by aa, aa - b
  76. IE aa =) ab = ac = ad fa, then a - - b - c
  77. d - Fby Division; and a = d - b-
  78. by Fransposirion.
  79. c.
  80. IF ea ] - 90 - - 70 = 13 c- 1 - 34 0 = 10 e, ther
  81. vist c - 9 - 7 = 15 - 1 34 = 10 by Divi
  82. SiOn.
  83. And e - 2 = 39, theretore by Transpolion.
  84. = 37. This Rule is chac wrhich Vieta CallS Hy-
  85. pobibasmus.
  86. 5. IF anY One Member OF the Lquation bC 2
  87. is perimore limited, and is fometimes discorerable lSurd RoOr, aH must be raised up co char Pover
  88. tobe impossiblero be resolved, by reason oF such) and thenche Equation continued.
  89. Equarions beins inconsistene wwich each orher.
  90. Equations, in order to be Resolved, must Airst
  91. be prepared and reduced; which may be done by
  92. chefollonins Rules.
  93. T. IF the OVaHEIEY COUGHE, OE aNY PANE OF DC-
  94. srec oFic be in Fractions, let all De reduced to one
  95. common Denominarion, and then omirting the
  96. Denominators, let che Equarion be continued in
  97. Thus, iE V: b a - b = c, chen bY Transpo.
  98. sition V: a b = c = b, and by chis Rule C0-
  99. 2 b0 -] b b = a b; and by Ruse the 3d, a =
  100. C c = 2 bc - b
  101. EOTATTON (Annuat) oE ehe mean Morion ot
  102. chesun and MOOn, and oF the MoonS Aposce and
  103. Nodes.
  104. The annual Equation OF che meau Morion ol
  105. the Numerators oniy. v. 8r. d = 100 chc Sun, dexends uxon che Fccentricier oF che
  106. = B. Then siA a 1 b. 1 cd
  107. D VDGA PAE Y =
  108. 1b L cd = cB. Oeit a = b = 2 a c
  109. L B, mulciply all by d, and it ilt Atand ehus a d
  110. aB = d b. Or it a
  111. 25 = 3 bb 1 c = 5. mulcipis all by 4. etien 4 a
  112. Farchs Orbit roundhim; and i5 16 E= such parts
  113. Ot which rhe mean Distance becreen ehe Sun and
  114. the Farch is 1000: From Whence, by some, tis
  115. called che
  116. Equation oF the Cenrer; and ehis when greareA,
  117. 1 deg. 56, 2011. Thesrearest Aniual
  118. Equation oF che MoOnS mean Notion iS FYI
  119. 401 OFIES ApOgCe 20 and OF its FTode 9. 301
  120. 300 = 3bb- 4c- 48. This is called by And chese + Arnual F. quations are alvars murual
  121. Vieca, isomeria, anid b7 oihiers conversion.
  122. Is proporrienable c0 ore arocher. 30 chac vetaen

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/806933011:0306?run=74