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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: 0.89.

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  1. Denominator or Divilor is ro be 2 a (the double) Vn.) Tochis Numeracor, il (For che Denomi-
  2. Roor ot the substracted Square) Or 2 a F c. (thaE
  3. double Roor increaled by one) checrue value (al-
  4. lins becween chele rvo; Comerime che one, (ome-
  5. time che ocher, beins nearest to che rrue value.
  6. Bur (for avoidins ot negarire Numbers) thelac
  7. ter is commonly directed
  8. The erue ground oE rhe Rule is chis; aa beine
  9. (by Construction) che srealest Incezer Square
  10. nacor or Dirisor) re Tubjoyn 30a, che Resule
  11. will cerrainly be 100 grear tor e, becaule che DC
  12. vilor is. 100 lirele: (P’or ic Mould be 3aa f 34c +
  13. ee, to sire che rrue ralue ot e.) It For theDi
  14. vilor, we cakre 3aa + 34 f 1, ic Will cerrainty be
  15. co0 lierle, becaule the Dirilor is 100 ercat. (For
  16. e by construction is lels chan r.) Ic must chere.
  17. fore (berveen chele L imiEs) be more chan chis
  18. concained in n, ris evident chace mus be sels
  19. chan e, (ocherwile noc aa, bur thesquare ot a L 1,
  20. Patrex; and cheretore rhis larrer Resiile being ad-
  21. ded to a, will pire a Rooc Whole. Cube may be
  22. or lome oreater chan ic, ould be the srearest subsracted trom the Non Cubick propoled in
  23. mainder b= 290 f ee be dirided by 2a, che resule
  24. Will be e00 ereat tor e, (the Dirilor being 100
  25. order ro anocher Rep.
  26. Buc il for the Divilor, we take 304 f 3a, (OF
  27. even lels than (0) che Resule may be t00 great:
  28. liccle, tor ic Mould be 2a F c to make che Ouori or (in case b be (mal1) it may be r0o lieele, ane
  29. enc e:) Bur il (co rectitie chis) ve diministi che
  30. Ouoriene by increatins che Divilor, addins LtO
  31. ic ic becomes 100 licele, because che Diritor i
  32. nou c00bis. Por (e beins lels chan X) 2a f X is
  33. more chan 22 =c; and cheretore t00 big.
  34. e
  35. AS For instance; IF che Non-quadrar propoled
  36. n-5, che Ercarest Inreger Square cherein
  37. concained is aa =-4 (the Square OF a == 2.) Whiet
  38. beine substracted, leaves n aa--5. 4 -- 1 -- 1
  39. 2ac = ec; wrtuch beins divided by 24= 4, sives
  40. : bur divided by 2a f 1 == 1 = 1=- 5, gires 5
  41. OFE 15 (0.)
  42. noueh, che lame Procels may be again repeated;
  43. Which comes co pals trom hence, becaule
  44. (by Construction) is less chan L; and cheretore 3aC
  45. lels chan 32; and perhaps l0 much, 25 chac che
  46. Addirion ot ee will nor redress ic. And wvhen ic
  47. (0 happens, 30a f za is a berrer Divisor chan
  48. Thac t00 ereac, and chis c00 licele for c. And
  49. cheretore che crue ROOr (a f e-= Yn) is lels chan
  50. 24 = 2, 25, bur greater chan 25 =2, 2. And chis
  51. wras ancienely choughe an Approach near enough.
  52. IEchis Approach be nor nou choushie near e
  53. 3a4 f 3a =F, COr even Comewhat lels than ei-
  54. Cher.) Buc because it doch noc alivays (o hap.
  55. pen, (Though for the most part ic doch) che
  56. Rule doth racher direct the ocher; as wrtrich
  57. doch cerrainly sire a Roor sels than che rrue va-
  58. luc, Whole Cubemay always be substracted trom
  59. the Non. Cubick propoled. The delion beinsre
  60. have, such a Cube a5 (beins substracted) may
  61. leare anorher b ro be ordered in lihe manner for
  62. a new Approach. Buc for rhemost parr zaa may
  63. be Patelr taken for che Divilor: For chouoh che
  64. Resule will then be Comehac 100 bis, vet the
  65. excels may be (0 (mall as ro be neglected; Or ar
  66. A, 84 a (nou conue a5 an Inceper in che leas, e may chence casily judse irhar Number
  67. second place ot Decimal Parrs) ehis substractea
  68. From 5,00. COl, Wisel che lamc, 0. 84, ThC ex
  69. cels et ehis Squale above the Former, From 1
  70. orhich tras chettene Lemainder,) lcares a neur re
  71. dires 4. 45-=53= -0. 65636 f, t00 much: Bur divi
  72. ded by 2a f 1 = 4. 5 IE Bives 450225=0,0355
  73. F, c0d lucle. Iie ulle ralue (borween chese
  74. ivo) being 2. 256 proxime, Whosc Square i
  75. rhar e00 bis; but 2, 236067 F would be muct
  76. (ComeWhar lels chan ir) may be sately caken ;
  77. and il ve chance ro cakce ic Comenhar r00 bis
  78. ehe Inconrenience will be buc chis, thar b For che
  79. nexe Rep will De a Nepacire; ot Which Case e
  80. Mall speake anon.
  81. Thus for instance; il che Non Cube propoled
  82. be g=n: che prearest Inceper Cube cherein con-
  83. rained i5 8- aaa (Whole Cubick ROOE 15 a =2.
  84. Wtrich Cube substracted, lcaves 9. 8-- 1 -B.
  85. 3040 f 340c 7 eec. This dirided by 3aa == 12
  86. sives 13=0. 08333 f, 100 bis For es bur che
  87. Came divided by 3aa f 32 = 1 == 12 f6 f 1= 19
  88. eives 23=-0,05263 7, e00 licrle; or it bur by
  89. 3aa f 34== 12 f 6- 18, IEgiVes, 3 960,05555+
  90. vet roolicle. For che Cube ot a f0, c6, 2,06
  91. is buc 8, 742, which is More oF 9: And (0
  92. much BOrE ot ie, thac we may Pately rake 2, 07
  93. a5 nor e00 bis; Or perhaps 2,08, (Wrhich il il
  94. chance eo be roobis, ic will noc be much c00 big
  95. (25 MaII be Farther Bewn:) And uxon eryal ie
  96. will be found noc r00 big; For the C ube OF, 2,08,
  97. 15 8,998912
  98. IF ehis Scep be nor near enoueH, this Cube
  99. substracted From 9,000000, leaves, a new b
  100. 0,001085, Wtich divided by 39a =- +2,9796.
  101. Dires 0,000084, Which vill be Comentat 100
  102. big bur noc too much (For e is nou (o (mall, 25
  103. chac zac may be Pately neglected (and ee muctu
  104. From che Non Cubicte proxoled, (suppole n) miore;) (0 rhar it t0 2.08, Wve add 0,000084.
  105. the RelulE 2,080084 will bc r0obis, bur 2,080085
  106. vill be more r0o licele; (a5 will appear it We
  107. cake rhe Cube ot each,) (0 char cicher oF chem
  108. at etie econd Scep, sives the erue RoOE wichim
  109. an Onire in che siniti place oE Decimal P r1S.
  110. and rhar as oc as is choushr necessary.
  111. Lake non For a, 2, - 2,. 2, Whole Square is
  112. mainder b= -0, 16; Wtrich divided by 2a = 4.4
  113. 4. 999696
  114. Ethis DC nOE chouxhe near enouxt, substrae
  115. ehis Square From 5. 000000: The remainder b
  116. 0.000304, divided by 24 == 4. 472, Or by 2a f Y
  117. A. 473, Sires (cicher way) 0.0000683 Wrhict
  118. added 10 a== 2. 236, makes 2, 236068, Tome
  119. moretoo licele
  120. And by rhe lame method, it be chouehenecd.
  121. Tul, we may proceed furthet.
  122. Ie ere eatie ro compound the Proce(S OF L
  123. or more Sceps intoone, and sive (tor che Rule
  124. ihe ResulE oF such CMPOnEION, Wrtich evoulc
  125. Which gires us the Square RoOc oF 5, adjustec
  126. 10 the sixch place oF Decimal ParrS, at chree Aeps
  127. make it leem More seau ante mysterious, re
  128. amule the Reader.
  129. tick) ehe Rule is this:
  130. substract the greacest Cube in Incegers cherein
  131. concaind, (Cappole aaa) che Remainder (sup-
  132. Pole b= 3aac f 3acc f eec) is to be che Numera-
  133. Tor ot a Fraction for delignine l Value ot e
  134. In the Cubick RooF, (contonane to the Ouadra-
  135. (che remainins parc ot che RoOE Conelc, a + e

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/806933011:0079?run=74