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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: 0.83.

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The machine reads it as

  1. Ouancicres A and E, itole summ 15 Z and L
  2. etie Ablolure Number, Was the Summ ot cheir
  3. Cubes in che tormer, buc x cheDitference oF them
  4. andX che Ditterence ot cheir Cubes in che latrer.
  5. L.nd he tound allo, chac aII Cubick E quations mixhE
  6. De reduced ro one of chele two Forms; Por as Por
  7. chele 1NO, Zc 3 A Z Z. and Xc + 3 C. X
  8. Xc, Where Z and X are Nepacire Ouanciries
  9. chey omly ditter lrom cheformer, in wtich che
  10. are Astirmacive, in ehiis, ehiat here X and Z will
  11. be Weparive Ouanciries, whereas chere chey will
  12. De Posicive.
  13. So rhac all Cubick Equarions beine reducible re
  14. chiele cmo Forms, che only Disticuley remainine i
  15. etiis: Flavinque ihe Rectanele of eruo Duanticies, wich
  16. ehe summ or difference of cheir Cubes, to finst the
  17. duantiries chemselves, and consequentys, their
  18. Summ and Difference.
  19. Wstict is performed by relolvine a Ouadrarict
  20. Aiguarion ot a Solid ROOr (or one Wwhole ROOT i
  21. aCube or lome hixhee POWCT.)
  22. FOr =F. =E C. AC+ = Ac-
  23. Eo = Z, and (0 = = 4 C = A0 and 3
  24. EAC L F CZ; Wheretore (multiplvins by
  25. AC Or Ec, and chen cranspolins che Terms
  26. Acc AC= c B CC E C, wtrole
  27. RODES ace : Z +V: Z Z.95 R -
  28. And Dy che lite Process it will be sounc, rhar
  29. Ac
  30. =eX-
  31. EC E0; and consequenaty
  32. AcC X AC= C FCC + X F. C, intiote ROOI
  33. are V: i. X 9, + R 0 +. Y = Ac
  34. And etlen will ehe summ or Disserence oF cheir
  35. Cubicke Rots BC A + F = Z, and A F= X thC
  36. RoOrS Couphe in rhole cabicke Equarions: That is
  37. V6 =Z LV: 29, cFV: C, + =Z V.
  38. Cq F c A + F Z V: C + = X + V: 2 X93 F
  39. BCC XFY: + X q3 FC A F. X.
  40. Ouamay be NegacM, as -Z Or = X; ihe
  41. AS I5 plain scom bare Algebraieat Mulriplicaci
  42. on in che followine Example.
  43. 4a + 2a6 +00
  44. firom wtience ris very easie ro understand, borh
  45. ehe Componition ot any Cubick Number, and aIIC
  46. the Reason oF che Method For excractins ehe Cubc
  47. Root our oF any Number siven-
  48. Thus, luppose 28 vere provoled ro be cntred.
  49. eire is doin (0 chac chere may be so0m co rire
  50. Fixures berween cach
  51. Place; 25,
  52. 20 15 8 ct 6000, 11
  53. (wilen 15 t2) mucis
  54. wilen place orderty un
  55. Nexr Z riimes the Square
  56. Ot. 8 15 192, and thac
  57. allo ordexly, as vou sec: And lakly, the Cube o
  58. 8 i5 512, Wrhich must De wriccen dovn so rhac che
  59. trk Kixure ot ic ro che Righe Cland may Aanc
  60. ander 8; and ehen addins all cogerher vou have
  61. IP che Number eo be cubed hact conilted ot 3
  62. Nou must procced as betore ca snd eie Cube OF
  63. 28, che 2 sirst Pigures roward che, Letr.hand
  64. eetich is 21952; chen atcer char vou are 10 ac
  65. conne char Number 25 rhe Cube oE a. and B0 on
  66. eo find che orter Members as foIIOWS.
  67. and lec charbeb, and 20
  68. Non eo construet Cubicke L quarions atcer MF. sfOrC thuS, 3 tmes IBC
  69. Daters Way by che Parabola, Sec Construction os Square ot 28 is 2352
  70. Equations.
  71. Mr. Ealley (nou oux Learned Savilian Protel.
  72. males 11760 44ab
  73. EOF OF Gcometry 2E Oxon) in Philos. Fransact. N. 190, vorire chac doon there
  74. sires 2 po0d vray co exrract che Roors oF all Cubick tore as vou lec: ltien
  75. aquarions by ehie help ot rhe Tables oE hines:
  76. By che Mulciplication ot a square Numter by IES
  77. 21952=Cube ot a + B
  78. oc moie places: L5 (uppole 285.
  79. oure 5 10 Hand 2 places
  80. Roors ihen will be - 1. F- Z. and - A Tarrher corhe Riphehand
  81. b
  82. Or Ot 280
  83. mulriply d by 2 eires 334== Z abb, wtrich Wrire
  84. 21952, chetrue Cube of 28.
  85. 2
  86. 21952= a a.
  87. 24149143.
  88. 5, Which is 125 = b bb in iis proxer order, a5 Was
  89. ROOE Thus S4 is a cubick Number, and is made Memed above, and rhen addins ail rogecher, chc
  90. By mulriplxins 16 che Square oF 4, by che ROOT4
  91. In Alrebra the chird Porver in a Serieo oF Geome
  92. rrical Proporrionals concinved, is called a Cube:
  93. 25, a is cheRooE, a a che square, and a a a che
  94. Cube: And all Cubicke Numbers may be ranged
  95. Summ will bc 23149125, che Cubc oF 285.
  96. And atrer ene lame manner son mult proceed
  97. on, les che Number robe cubed benever lo large.
  98. Andctiis Mechod et etie Componiion it a Cubc.
  99. Number beine well understood, the Extraction oE
  100. Mo che form OF Cubes, 25 8 or 27, Whole Sides )etie Cube-Root ill be very eatie and incellixible
  101. erc zand 3, and cheir Bases 4 and 9
  102. by che sollormine Directions.
  103. Suppole sounere lo exract he Cube-ROOt OUF
  104. _t the Hoor, and ot z times the square ot the for Lom over elie Arit Fieure 5, and hen over e
  105. ereacer pare mulciplicd by che leller, and ot very chird Pisure atcerwards; 25 many Poinrs a5
  106. reo che desdate b de telet una schere arcus 1o many Rigures will jon trave in vour
  107. he BCcater
  108. aobt.
  109. . P inet
  110. adFLaab
  111. e act habeecdo
  112. aad+ 34a0+ 3000+ 606.
  113. aa
  114. d em 2E10
  115. db
  116. 12
  117. C
  118. 11760=3a ab
  119. 2100 3
  120. 125 = bbb
  121. Lla 3, l Cube oF 20r
  122. rimes the Square oF:
  123. by 8 Bives 96=3 a a b
  124. der che 8 25 you sec.
  125. Imaxine che ned et.
  126. Or 280, a; proccedrhere.
  127. rhick ulcixls d by
  128. N. B. IF, 25 Was Paid above, the Abloture
  129. Cay. J rimes che Square oF 5 i5 25, Which mulei
  130. COBICAL Number, is thac which is produced don as sou sec: sna lalels, eire the cubc ot
  131. ply d by 28 eires 2100=3 b ba; vrrite thac also
  132. Lbeorem. Frery erue Cubical Number prou
  133. acut a nominal Hooc consiles ot chele Parrs, oF chis Number 2314912)
  134. 8Z. Lhe Cubes ot the ereater and leNer parrs
  135. 2. Beximmine at heRiptic harid, mate a Prick

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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/806933011:0233?run=74