Volume 1

A mathematical and philosophical dictionary: containing an explanation of the terms, and an account of the several subjects, comprized under the heads mathematics, astronomy, and philosophy both natural and experimental: with an historical account of the rise, progress, and present state of these sciences: also memoirs of the lives and writings of the most eminent authors. Both ancient and modern, who by their discoveries or improvements have contributed to the advancement of them ... With many cuts and copper-plates / By Charles Hutton.

  • Charles Hutton
Date:
1795-1796
Catalogue details

Licence: Public Domain Mark

Credit: A mathematical and philosophical dictionary: containing an explanation of the terms, and an account of the several subjects, comprized under the heads mathematics, astronomy, and philosophy both natural and experimental: with an historical account of the rise, progress, and present state of these sciences: also memoirs of the lives and writings of the most eminent authors. Both ancient and modern, who by their discoveries or improvements have contributed to the advancement of them ... With many cuts and copper-plates / By Charles Hutton. Source: Wellcome Collection.

    671/696 (page 643)
    Sc alfo, In Algebra, to luvolvctlie binomial a h, or raife its powers. a b - • - - ifl power, or root a b + oh + d^ + lab H- - - 2(1 power a b a} 4“ 'id^h H- 2dLr- “h d^b 4- ah^ -P ^a^b 4 b^ - 3d power 4~ ^ a‘* + ^db 4- yi'^b'^ 4 £>0“^ 4- db 4“ '^d-b'^ 4 \£^b^ 4~ d 4“ ^-dh 4- ()db 4- 4 b^ 4t]i p('!W'er And m like manner for any other quantities, what- ever the number of their terms mav be. But compound algebraic quantities are bell involved by the Binomial ’Theorem; which fee. Simple quantities are Involved, bv railing the numeral coefficients to the given power, and the literal quanti- ties ^are railed by multiplying their indices by that of the root ; that is, the railing of powers is performed by the multiplication of indices, the fame us the multi- plication of logarithms. Thus, The 2d power of a is d. The 2d power of id is I'^d ^ ^ or \d. The 3d power of '^dl'^ is Z']dh’^. 1 ,2 , 3 The 3d power of d^b^ is db^. The «th power of a” eP is V or c? . INWARD Flanhhig Angle, in Fortification, is that made by the curtiii and the razant Hanking line of defence. JOINTvS, in Architeflure, are the feparations be* tween the Hones or bricks wiiich may be filled with mortar, plaller, or cement. Joint, in Carpentry, Sec, is applied to feveral man- ners of allembling, felting, or fixing pieces of wood to- gether. As by a mortife Joint, a dove-tail Joint, Sec. Um-verfed Joint, in Mechanics, an excellent inven- tion of Dr. Hook, adapted to all kinds of motions and flexures ; of which he has given a large account in his Cutlerian I.edtures, printed in 1678. This feeins to have given occafion to the gimbols ufed in fufpending the fea compalTes ; the mechanifm of wiiich is the fame with t.hat of Defaguliers^s rolling lamp. JoiNT-/y/wj-, are fiich as continue during the fame time, or that exift together. See IuFF.-y/;;;iw/Vw. JOISTS, or JoYSTs, thofe pieces of timber framed into the girders and fumm.ers, and on which the board- ing of floors is laid. ‘‘ JONES (W illiam), F. R. S. a very eminent mathematician, w'as born at the foot of Bodavon moun- tain [Mynydd Bodafon] in the parilh of Llanfihangel tre’r Bard, in the Ille of Anglefy, North Wales, in the year 1675. liis father’s name was John George, his furname being the proper name of Iiis father. For it is a cuftom in feveral parts of Vv ales for the proper name of the father to become the furname of his chil- dren. John George the father was commonly called Sion Siors of Llanbabo, to wdiich place he moved, and where his children wmre brought.up. Accordingly our author, wdiofe proper nam.e w^as William, took the fur- name of Jones from the proper name of his father, who was a farmer, and of a good family, being defeended from Hwfa ap CyndJehv, one of the 15 tribes of North Vfales. He gave his two fons the common fchool education of the country, reading, writing, and accounts, in Englifh, and the Latin Grammar. ‘ Harry his fccond fon took to the farming biifinefs ; but Wil- liam the eldeft, having an extraordinary turn for mathe- matical luidies, determined to try his fortune abroad from a place where the lame w'as but of little fervice to him. He' accordingly came to London, accompanied by a young man, .Rowland Williams, alterwards an emi- nent perfumer in Wych-ilreet. The report in the coimtrj' is, that Mr. Jones foon got into a merchant's counting hoiife, and fo gained the eileem of his mailer, that he gave him the commamd of a fliip for a Weil In- dia voyage ; and that upon his'return he fet up a mathe- matical fchool, and publifned his book of Navigation ; and that upon the death of the merchant he married his widow’ ; that, lord Macclesfield’s fon being his pupil, fie W’as made fecretarv to the chancellor, ami one of the deputy tellers of the exchequer :—and they have a lloi*y of an Italian wedding which caufed great dlllurbance in lord Macclesfield’s family, but was compromifed by Mr. Jones ; which gave rife to a faying, “ that Macclesfiejd was the making of Jones, and Jones the making of Macclesfield.” The foregoing account of Mr. Jones, I found among the papers of the late Mr. John Robeft- fon, librarian and clerk to the Royal Society, wLo had been well known to Mr. Jones, and poifefled many of his papers. Mr. Jones having by his indufliy acquired a compe- tent fortune, lived upon it as a private gentleman for many years, in the latter part of his life, in habits of in- timacy with Sir Ifaac New^ton and others the moil emi- nent mathematicians and philofophers of his time ; and died July 3, 1749, at 74 years of age, being one of the vice-prefidents of the Royal Society ; leaving at his, death one daughter, and his w'idow wdth child, which proved a fon, who is the prefent Sir William Jones, now' one of the jiidg*es in India, and highly efleemed for his great abilities, extenfive learning, and eminent pa- triotilm. Mr. Jones’s publications are, 1. A nenu Compendwm of ihe Whole Art of Naviga- tion, Sec ; in fmall 8vo, lAindon, 1702. This is a neat little piece, and dedicated to the Rev. Mr. John Harris, the fame I believe who was author of the Lexicon Technicum, or Uiiivcrfal Didlionaiy of Aits and Sci* ences, in w'hofe houfe Mr. Jones fays he compofed his book. 2. Synopfis Palmnrionnn Maihefeos : Or a New^ In- trodmllion to the Mathematics, See; 8vo, London, 1706* Being a very neat and iifeful compendium of all tlm matliernatical fciences, in about 300 pages. His papers in thePhilof. Traiif. are the followu'ng; 3. A Compendious Difpofition of Equations for ex* hibitingthc relations of Goriiometrical Lines ; vol. 44, p. 560. 4,. A