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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. HIe (ays, tatins the Cube of each, (Wvtich he) No, wrhac is laid ol the Cube, is calils ap-
  2. does; chac che chine may be more clearty appre-
  3. hended) ic is nor necessary chac ve crouble Our
  4. selres with che Whole Cube: FOr, aa2 being al.
  5. ready substracted, For finding b-- 3aac = 3ace + ece
  6. ve have no more ro ery, buc Whecher 3200
  7. 3rec f eec be crearer or lels than b, accordins 25
  8. Wve rakee 0,0000840r0,000083. FOr c.
  9. WVhich may be convenienely done in chis man-
  10. ner: Pake 3a =c, and mulciply chis by c, (OrC
  11. by ic) so have we 3ac F ee; ro chis add 3aa.
  12. and mulciply ele whole by e, ((0 have we
  13. 394c f 3aec = eec) ro see whether chis be sreater
  14. OF lels chan b.
  15. Thar is, in che prelene Case, it we cake
  16. 0,000084, and add cochis, 34 ==6, 24, chen i
  17. 6, 240084 = 3a fc: This malciply d by e-
  18. 0,000084, 15 300 + ec ==0, 000524 +5. c0 Which il
  19. we add 344 = 12, 9792, ic 15 304 + 3ac + ce=
  20. c2.979724, erhich mulciply d again by c=
  21. 0,000084, 15 0,0010902 f, = 3440 + 34cC F ece.
  22. exhich is more chan b==0, 001083.
  23. Bur it Wve Take c 0,000083, and proceed a
  24. betore, We MaI have 3aac F 3aec f ecc=
  25. plicabie co che higher POrers..
  26. Thac ot che Biguadrare mray be omited, Le
  27. canse here perhaps ic may De rhongBE most ac-
  28. rilable ro extract rhe Square ROOE OF che PILH
  29. ber propoleu; and then the Souare ROOCOF EtAF
  30. ROOF.
  31. Buc if we vould do ic aconce, We are From n
  32. Ithe Number propoled, beins nor a Biguadrate)
  33. eo substract a (the greacest Biquadrare contain-
  34. ed in ic) e0 Aind che Remainder b=- 420- + 6a702 f
  35. 42c3 4. +, Wrtrich Remainder, il ve divide by ae
  36. the Quorient ill certainly be c00 biz For 0, (cho
  37. perhaps noc much.)
  38. IFBy 442 + 6a F 4a + F, ic will cerrainly be 200
  39. licrle (for reasons betore mentioned.). And We are
  40. couse our Dilcrecion in caking lome incermediare
  41. Number. And il ive cherce chance noc to ssicom
  42. the nearest, the Inconvenience vill De bur chis
  43. char our leap will noc be (0 great as ochervile ie
  44. mishebe, which will be rectify d by anocher b
  45. aE ThCNCXL SceP.
  46. For che Sursolid (oF ehe Are Dimensions) WBE
  47. are, trom n (che Number provosed, being noc 2
  48. 0,001077 F, wrhich is lels chan b, and cheretore pertect Sursolid) 1o substract a: (the grearest Sur-
  49. (it eve substract chac trom chis) the Remainder solid cherein contained) ro Aind che Remainder
  50. 0,00002r, will be anocher b for the nexE SceP,
  51. it ve please to proceeu Furrher.
  52. b 542C- + 1043 02 f 104203 +5401. + e5.
  53. Wrhich (a5 before) it we divide by 5a2, the RC
  54. Fricherro we hare pursued che Method most sule will be lomenhar 100 bis, (becaule che Di
  55. affected by che Ancients, in sectins a Square or vilor is 200 licrle.)
  56. Cube, land rhe like of ocher Povers) alvays lels
  57. IF by 5a2 + 1043. F 1042 F5a F P, The Relule Wwill
  58. than che just Valve, chac ic mishr be substracted certainly be lels chan che erue e. The jus
  59. From the Numiber propoled, learins b a pohcire Value ot e beins lomenhar bermeen chelé rvo
  60. Remainder, chereby aroidins Nepacire Num-where we are ro ule our Discrerion, what inter-
  61. DerS.
  62. Buc since the Arichmerick of Nepatires is (0
  63. Wvell underscood, ic may in chis (and acher Ope.
  64. rations of like narure) be adrisable ro cale che
  65. mediare Number ro cake; wrtich accordins a5 ic
  66. prores r00 grear or 100 licele, is to be rectits dar
  67. the REXE StCP.
  68. IE ro direet us in the choice of such interme:
  69. next greacer (in case thar be nearer 1o cheerue diare Numbers, we ould mulriply Rules orPre
  70. Value) racter rhan ene next lesser.
  71. Accordms eo This HNotioH, For rhe square ROOF
  72. OF 5, l ivould (ay, ic is (2 f) Comermhar more
  73. cepes for such choice, che crouble ot oblervins
  74. s
  75. xhem vouid be more than the advantage 1o be
  76. sained by ic. And for rhe most parr it moule
  77. chan 2, and enquire, ho much more : Bur For be late énoush (and lcas crouble) co divide by
  78. EhC Square RoOr ot 8, I vould (aY, ic 15 (3
  79. Tomehat less than 3. and inguire, hou much
  80. at. Which sires a Ouoriene Lomewhac 100 Bis;
  81. Wrhich e may cicher rectity ac Discrerion (by
  82. less. Fakins in boch Cales char which is nearest cakins a Number Lomewhar le(s) or proceed se
  83. ro che just. Value
  84. anocher b, Catrmarire or Nlesacive as che Cale
  85. Thus in ehe Cubick Rooc before us, Prake For Mail require) and (o onward to whar exactnels
  86. (in ehie las Enquirr) 0,000084, (nhere For ne pleale (Which is, tor substance, in a manner
  87. ehe nexe Aep we have b=0,000002,) rather co-incidene ich Mr. Raphson S Method, even tor
  88. chan 0, 000083. F, (Where tor the nexr Aer we
  89. Mould haDe b-=- f0, 00COTF.) In this lacter Cale
  90. ve are co divide b== +0, 60001I, by. 3aa
  91. 12,980236-, 10 find (by che Ouoriene) hon
  92. affected Rquarions.
  93. Thus, in che presene Case; if che Number
  94. proxoled be n-- 33, chen i5 a == 32, and b = 33
  95. 32= 1 = 54 C + (04 C = 104202 +54C2 + e, Wwtrict
  96. inuch is ta be added r0 0,000083. In cheorher il re diride by 5a1=5X16=-80, che Relulr
  97. Casc, we are 10 divide b= +0,000002, by
  98. 52F=0, C+25, is Comenhar t00 bis For c, buc noc
  99. 32a == 12, 980248, 20 find (by che Ouorienr) vetrat much. And it e examine ic, by cakine che
  100. is eo De abaced oF 0,0000843 (0 have We Sursolid oF 2,0125, Or OF 273, Wwe MMaIL And 2
  101. 3 20,00000085. +, 10 be added 10 Desarive b, (For che REXE ScCP) bUE nOE very
  102. 6, 240083: Or 4535585970,00000015+ 10 bC considerable. Or it we rhink ic considerable re
  103. abared oF 6, 240084: (Or ic may sustice in cirher, may proceed Further co anorher Scep, Ox more
  104. 2o divide by +2,98 F, Or cven 0) 13, Wichour chan 10.
  105. beine incumbred ich a lons LiTOF) etet O1). Lhe like Mechod may be axplyd (rich morc
  106. evhich sires us, For the Roor (oughe, 2,08008385 advancasc) in che Eligher Porvers, accordins a5
  107. proximé. True (ac che chird Srep) roche eiehrh che Compolition ot cach Porver requires. Anit
  108. Place oF Decimal ParEs. And il this be nor near sche lame Mechod may be oF ule (wich 800d Ad-
  109. enouph, the Cabe oF. ehis compared wwich che vancase) in lone DTumbers (it duly axplied) c
  110. umber proxoled, will. sive us anocher b, For ven betore e come ro che place ot Vnits, For
  111. pans ec. ane lo onnacdo ad Eac a0 e he laure roul equalls hola phere do.
  112. eo

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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/806933011:0080?run=74