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.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

1. ies Cnbe Roorbeins requird, ic selF DC NOt L true
2. Cube, _c. Then ris impostible eo attign, cicher
3. in nhole Numbers or Fractions, any exact ROOr
4. Ot luch Numiber propoied. And wten ever His
5. trappens; tis usual in MachematickS ro mark HC
6. required Roors oF Tuch Numbersor Guantities, by
7. pretirins betore il cheproper Mark oF Radicalliry,
8. erhichis V: Fhus V: 2 sipnities the Square ROOr
9. METACOE atrel DenOminAtOT. Thus,is redu
10. ced to V
11. and
12. ihe Radieat Sien aftects Boch Numerator and DS.
13. nominaror alike.
14. OF2 and V: 16. Or V: (3) 26. Sienises che Cu TI. F0 reduce Simple Surds, havins different Radical
15. Bick ROOEOF 16: TVhich ROOES, because ther are
16. imporsible eo be expresed in Numbers exactlr (For
17. no ettable Nuniber, cirlier Inceger or Fraction MuI
18. ciplied into it felt can ever produce 2; Or beins
19. usciplied Cubically can ever produce 16) arc
20. verr propertr calld Surd RROOts.
21. Tlere is atso anorher Way OE Noration non muc
22. in ule, Wotierebr Roorsare expressed, Wirhour che
23. Radical Sigu, Dy cheir indexes: ThuS, 28 x. ~
24. x5. 3c. Cienitie the Square, Cube, and sch Porver
25. OF X; (0 x. v X5. C9c. signitic the Square ROOT
26. Cube RCOF, C9c. OF x. The Rcalon Ot wrtrich is
27. plain enoueh, For since V: x is a Creomerrical mear
28. Proporrional between r. and x. So = is an Aich.
29. metical. mean Proporrional betveen o and L. and
30. cheretore 25 2 is che Index ot chie Square ot X,
31. Wrill be cheproper Index of iis Square ROOr, C9c
32. Oblerre allo, char for Conrenience or Brevits
33. Pake, Juantiries or Numbers erhich are nor surds
34. are otien expressed in che Form ot Surd ROots.
35. Thus V: 4. Y: = V: 27, Oc. tieritie, 2,
36. C8c
37. Bur alcho chese Surd ROOrS (Wtien cruly such,
38. are inexpresible in Numbers, eliey are ver capable
39. et drichmerical Operations (Tuch as Addirion, Sub.
40. eraction, Musciplicarion, Dirision, esc. Which hon
41. readily eo pertorm che Alhebrist oughe nor to be
42. IBHOTAHE.
43. Surds are eictrex Simple, wtich arC expresed B
44. orie sinele Perm; or else compound, utrich are
45. Formed by the Addirion or Subrraction ot simple
46. Sueds: ASv: 5 =] V : 2: V : 5 V 5. 2. O1
47. : 7 =)- V: 2: Wrhich las is calledus an Uni-
48. versal R00t: And Signities, che Cubick ROOE oF thar
49. Number wbich is che result of addins 7. 10 the Squari
50. Root ef 2.
51. The Arahmerick. ef Surds consist sof ihese princt
52. cixal Parts.
53. I. Zo reduce Rational Ouantities 1o the Form of an
54. Surd Roots assiined.
55. Cuanrier accordins ro the Index of the PouerO
56. the Surd, andchen pretixins betore ir the Radica
57. Sien oFthe Surd provoled.
58. Thus reduce a = τ0to ite Form ot V: 15.
59. :b. Voumust Squarea == n0; and prefixing rh
60. Sign, it wvill Aand ctuS, V: 4 a = ~: 100
61. ertich is in che Form oE ihe Surd desired. Se
62. also if 3. verero be bronghero the FOnm OE : 12,
63. ron must raise 3 up 10 ies tourth Pover, and chen
64. prelixins che Nore oF Radicalies t0 ic, ic Wwill be
65. if: 81. Or 81 1, which is in che Came Form vict
66. : T2
67. Siens (wtrich are called Hlereroseneat Surds) t0
68. otbers that may have one common Radical Sign, or
69. mhich are Fomozeneal.
70. Diride the Index ot che P’overs ot che Surds by
71. etcir sreacest common Dirisor, aud ser che Ouct
72. enis under che Biridends; chen lalciply chole In-
73. dexes crols mays by cach biers MoCMIo, aHd
74. betore che Produets, Per hecommen Radical Sisn
75. V: Wichis proper Index: LhetrInrolrechePo
76. ets oFrhe siven Roors Alternatelr, accordins corhe
77. Index ot cach others OuoreM, and betore chose
78. Ptoducts, pretix che common Ladical sien be
79. lore houne.
80. And ehis ay may a Simple Surd Fraction, wwhose mas pt 2 N: 72. OF3 V: 32. Or 4 V: 18. Or
81. Radical Sion reters onty ro ore of ies Terms, be
82. _.. B. Dt tedtl l). L V. L ardet lnde telleae aetas
83. chansed inso anocher, wwhich Mall saleet boch Nu. done in Species.
84. 10 V:: IVhere
85. Wrhich is pertormd By Involvins ehe Rationa
86. ToReduce V: a a and Y: bb
87. 2d:
88. Lo Reduce V: 5 amt Y: 2.
89. 25 V: 2407
90. III. Toreduce Surds 2o rheir lomest Terms possible.
91. Divide che Surd by che greacest Square, Cube
92. Biguadrate, C9c. Or any ocher higher Pover, wtict
93. rou can discorer iscontained in ic, and will Mea.
94. lure it wichour any Remainder, aud rhen prefix
95. The ROOE OF char Porver betore the OOTIeHE, OF
96. Surd s0 dirided, and ehis will produce a new
97. Surd ot che lame value with theFormer, but in more
98. Simple Terms. Thus, N: 162 ab, bY dividine
99. by 26 a a and pretixins che RoOr 4 a, vill BCrC.
100. duced tochis 4 a V: b and v: 12, willbe deprel
101. Acao2 V: 3. AIO V: cbor, vill be brouet
102. donnto bu: cr. And chis Reduction is OLGrCAE
103. Se Whenerer ir can be pertormed: Dut iF no sucH
104. Square, Cube, Bignadrare, (8c. can be Found for
105. a Dirilor; chenrou must findour all che Divilors
106. Of the Porer ot che Sure propold; and etien sec
107. Whiecher anr of them be a Sguare, Cube, C9c. O1
108. such a Porer as the Radical Sien denores; and il
109. ariy fuch can be found, lex thar be uled in the lame
110. macster as is abore Caid, ro tree the Surd Ouancits
111. in parr trom the Radical Sign. Thus, iF V: 288
112. beproposd; amons is Dirilors, will be found che
113. SGuares 4. 9. 16, 36. and 244. by which iF 288
114. be dirided, chere vill arise che Ouorients 72. 32
115. 18. 8. and 2. Wheretore instend oF V: 288, 701

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/806933011:0790?run=74