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Chambers, Ephraim, 1680 (ca.)-1740 / Cyclopædia, or, An universal dictionary of arts and sciences : containing the definitions of the terms, and accounts of the things signify'd thereby, in the several arts, both liberal and mechanical, and the several sciences, human and divine : the figures, kinds, properties, productions, preparations, and uses, of things natural and artificial : the rise, progress, and state of things ecclesiastical, civil, military, and commercial : with the several systems, sects, opinions, &c : among philosophers, divines, mathematicians, physicians, antiquaries, criticks, &c : the whole intended as a course of antient and modern learning

C - Capillary, pp. 137-152 PDF (20.2 MB)

Page 141

4A- Lj CALATRAVA, a MilitaryOrder, inffituied in x 5B, by Sancho III. King of Caftile, on the following Occafion: The l Moors going to attack the little City Calatraw, and the l Tem lers, whoheld it, furrendering it up to the King, on l a Suficion of their Inability to defend it, Diego Velafquez, I a CiA ercian Monk, but a Man of Quality, perfuaded moed Abbat of Fitera, a Monaflery of Cijiercians, to beg Calatrava of the King. He obtain'd it; and Raimond l nd !iego put themfelves in it; being follow'd by a great number of People, who join'd 'em out of Zeal, for the De- fence of Calatrava. The Moors abandoning the Enterprize, many of thofe who came to the Defence of the City, en- ier'd the Order of the Cijiercians; and that under a Habit more fit for Military than Monaflic Exercifes. According- ly, they began to make Excurfions on the Moors; which l vas the Rife of the Order of Calatrava. The firnt Grand Mafler was Garcias; under whofe Government the Order was confirm'd by Alexander III. in II64. In 1489, Ferdinand and Ifabella, with the Confent of Pope Innocent VIII. re- mitted the Grand-Maflerlhip of Calatrava to the Spani/h Crown: So that the Kings of Spain are now become per- petual Adminifsrators therecof The Knights bear a Crofs Gules, fleurdeliz'd with Green, Fec. Their Rule and Ha- bit was originally that of the Ciflercians; but their Drefs was a little lhorten'd on account of their Exercifes; and in procefs of Time they were permitted a fecular Habit. CALCANEUS, in Anatomy, the fame as Os Calcis,- or the Ifeel- Bone: It lies under the Afiragalus, to which it is articulated by Ginglimus 5 behind it is a large Protuberance, which makes the Heel, and into which the Tendo a.chillis is inferred. CALCANTHUM, is Vitriol Rubify'd. Some maintain Calcanthum and Colcothar to be the fame Tfling: but Po- met is of another Sentiment, and takes Calcanthum to be nothing elfe but Vitriol. See VITRIOL, and CHALCITIS. CALCINATION, the Aaion of calcining any Matter; i. e. of reducing it into a CaIx, or a very fubtile Pouder, or even only into Allies, by Fire; fometimes alfo termed Chymical Pulverifation. Calcination is the next degree of the Power of Fire beyond that of Fufion: For when Fufion is longer continu'd, not only the more fubtile Particles of the Body it felf fly off, but the Particles of Fire likewife do infinuate themfelves in fuch Multitude, and are fo difperfed and blended throughout its whole Subftance, that the Fluidity which was firft caus'd by the Fire, can no longer fubfiul: From this Union arifes a third kind of Body, which being very porous and brittle, is eafily reduc'd to Pouder. For the Fire having penetrated every where into the Pores of the Body, the Particles are both hinder'd from mutual conta&, and divided into minute Atoms i fo that they are eafily reducible into the finefi Pouder. Chymifts, Goldfmiths, and Founders, diflinguifh two Kinds of Calcination; the one call'd Actual, the other Potential A&ual Calcination, is that eifealed by a~ual Fire, of Wood, Coals, or other Fuel, rais'd to a certain Heat, according to the Nature of the Subfiance to be cal- cin'd. Potential Calcination, is that procur'd by potential 'viz. by Waters, Drugs, Etc. which have, as it were, rce of Fire; as Strong Waters, Corrofive Spirits, Tec. is calcin'd in the Fire of a Reverberatory, with Mer- and Sal Ammoniac. See GOLD. Silver with common nd Alkali Salt. See SILVER. Copper with Salt and ur; Iron with Sal Ammoiniac and Vinegar; Tin with iony, Lead and Sulphur; Mercury with Aqua fortis: aft, alfo, with moft other Minerals, calcines with fire without any other Ingredient. LCINATION Philofophical, is when Horns, Hoofs, cgc. ang over boiling Water, or other Liquor, trill they loft their Mucilage, and are eafily reducible into er. LCULATION, the AA of computing feveral Sums, ding, fubtraafing, multiplying, or dividing. See A- vtETIC. An Error in Calculation is never prote&ed ar'd by any Sentence, Decree, &c. In flating Ac- s there is always underflood, falvo errors calculi. Vord Cakeuls is us'd in this Senfe, in allufion to the :e of the Antients, who us'd Calculi, or little Stones, king Computations, in taking Suffirages, and in keep- ccompts, 5c. as we now ufe Counters, Figures, &)c. ,CULATION is particularly us'd to fignify the Compu- s in Aftronomy and Geometry; for making Tables of ithms, Eclipfes, Ephemerides, Fec. See ECLIPSE,&c. LCULATION of Clock and iWatch-Work. See CLOCK fATCH- WORR. LCULUS, in Medicine, the Difea& of the Stone in adder, or Kidneys; See STONE, LITHOTOMY, SC. Bladder 'tis ufually call'd Lithiafs; and in the Kid- qepJbritis; which fee. The Term is pure Latin, and es, literally, a little Pebble, or Flint. Whence alfo, rtM Calculation. See CALCULATION. 1.') CALCULUS, or Methodus Differenrialis, in Mathema' ticks, is a Method of differencing Quantities; or of finding an infinitely fmall Quantity, which being taken infinite times, lhall be equal to a given Quantity : or, as others define it, the Arithmetic of infinitely finall Differences between variable Quantities. The Foundation, then, of this Calculus, is an infinitely fmall Quantity, or an Infinitefimal, which is a Portion of a Quantity, inco parable to that Quantity ; or that is lefs than any affignable one, and therefore accountedas nothing: the Error accruing by omitting it being lefs than any affignable one, i. e. lefs than nothing. Hence two Quantities, only differing by an Infinitefimal, are equal. The better to con- ceive the Nature of an Infinitefimal, fuppofe, that in mea- furing the Height of a Mountain, while you are looking thro the Sights, the Wind blows off the fmalleft Grain of Dufi; the Height of the Mountain is, then, lefs by the Dia- meter of the Dufi than befose: But as the Mountain is fili found the fame Height, whether the Dull be there or not, its Diameter has nothing to do in the prefent Cafe, and paffes for nothing, i. e. is infinitely fmall. Thus, in Afiro- nomy, the Diameter of the Earth is an Infinitefimal, in refpea of the Diffance of the Fix'd Stars: And the fame holds in abfiraat Quantities. The Name Infinitefimal, therefore, is merely refpedive, and involves a Relation to another Quantity; not any real Ens or Being. Now Infinitefimals are call'd Differentials, or differential Quantities, when they are confider'd as the Differences of two Quantities. Sir Ifaac Newton calls 'em Fluxions; con- fidering them as the momentary Increments of Quantities; v. g. of a Line generated by the Flux of a Point; or of ; Surface by the Flux of a Line, Cc'c. The differential Cal- culus, therefore, and the Doarine of Fluxions are the fatle thing under different Names: The former, given by M. Leibnitz, and the latter by Sir Ifaac Newton ; each of whom lay claim to the Difcovery. See FLUXIONS. There is, indeed, a Difference in the manner of expreffing the Quantities, refulting from the different Views wherein the two Authors confider the Infinitefimals ; the one as Incre- ments, the other as Differences: Leibnitz, and moft Fo- reigners, exprefs the Differenti.alsof Quantities by the fame Letter as variable ones, only prefixing the Letter d; thus the Differential of x is call'd d x; and that ofy, dy: Now dx is a pofitive Quantity, ii x continually increafe i negative if it decreafe. The Englijb, with Sir Ifaac Newton, inflead of d x write x (with a Dot over it) for dy, j, &c. which Fo- reigners objea againi*, on account of that Confufion of Points, which they iinagine arifes, when Differentials are again differenc'd; btfides, that the Printers are more apt to overlook a Point than a Letter. Stable Quantities being always exprefs'd by the firfi Let- ters of the Alphabet da - o, d b = o, d c = o; wherefore d (x +y-a) =_ d x + dy, and d (x-y + a) dx-dy. So that the Diftiurencing of Quantities is eafily perform'd, by the Addition or Subtradion of their Compounds. Lao differef:ce keantities that mutually multiply each other; The Rule is, firfl, Multiply the Differential of one Fador into the other Factor, the Sum of the two Fadors is the Differential fought: thus, the Quantities being xy, the Differential willbhex dy+y d , i.e. d(xy)=xdy+ydx. Secondly, if there be three Quantities mutually multiply- ing each other, the Faaum of the two miuff then be mul- tiply'd into the Differential of the third: thus fiuppofe v xy, let u x = t, then v xy = ty; confequently dv xy)= tdy + ydt: But d t = vd x + x dv. Thefe Values, therefore, being fubfilituted in the antecedent Differential, rdy ydt, the Refult is d(vxy)=vxdy+vydX + xy d v. Hence 'tis eafy to apprehend how to proceed, where the Quantities are more than three. If one variable Quantity increafe, while the other ydecrea- fes, 'tis evidentydx-xdy will be the Differential of xy. To, difference kuiantitics that mutually divide each other: The Rule is, firfi, multiply the Differential of the Divifor into the Dividend, and, on the contrary, the Differential of the Dividend into the Divifor; fubtrac& the laft Produc& from the firfl, and divide the Remainder by the Square of the Divifor ; the Quotient is the Differential of the Quan- tities mutually dividing each other. See FLUXION. CALCULUS Exponentialis, is a Method of diferencing exponential Quantities, and fumming up the Differentials or Fluxions of Ex'ponentials. By exponential ktiantity, is here underftood a Power, whofe Exponent is variable i v.g. .x x XX ax. To, difference an exponential juantity: There is nothing requir'd but to reduce the exponential Quantities to Lo- garithmic ones; which done, the diferencing is managed as in Logarithmic Quantities: Thus, fuppofe the Direren tial of the Exponential Quantity xy requir'd, let 00XY el. CIA L

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