T R A 



and of tliefe three forms a general equation of the line 

 fought, from which he finds the tangent according to the 

 differential method, which fucceeds even in tranfcendental 

 quantities. What he finds he compares with the given pro- 

 perties of the tangent, and fo difcovers not only the value of 

 a, b, c. Sec. but alfo the particular nature of the tranf- 

 cendental quantity. 



And though it may fometimes happen that the fevcral 

 tranfcendentals are fo to be made ufe of, and thefe of dif- 

 ferent natures, too, one from another ; alfd, though there 

 be tranfcendents, or tranfcendentals, and a progreffion of 

 thefe in infinitum ; yet we may be fatisfied with the moft 

 eafy and ufeful one, and for the moil part may have re- 

 courfe to fome peculiar artifices for (hortening the calculus, 

 and reducing the problem to as fimple terms as may be. 



This method being applied to the bufinefs of quadratures, 

 or to the invention of quadratrices, in which the property 

 of the tangent is always given, it is manifeft not only how 

 it may be difcovered, whether the indefinite quadrature may 

 be algebraically impoffible, but alfo how, when this impol- 

 fibility is difcovered, a tranfcendental quadratrix may be 

 found ; which is a thing which had not before been (hewn. 

 So that it feems that geometry is by this method carried in- 

 finitely beyond the bounds to which Vieta and Defcartes 

 brought it ; fince, by this means, a certain and general 

 analyfis is eftablilhed, which extends to all the problems 

 which are of no certain degree, and confequently not com- 

 prehended within algebraical equations. 



Again, in order to manage tranfcendental problems 

 (wherever the bufinefs of tangents or quadratures occurs) 

 by a calculus, there is hardly any that can be imagined 

 ihorter, more advantageous or univerfal, than the differential 

 calculus, or analyfis of indivifibles and infinites. 



By this method we may explain the nature of tranf- 

 cendental lines by an equation ; e. g. Let a be the arc of 



fdx 



1 circle, and x the verfed fine ; then will a = — : 



\^ 2 .V — -v X 

 and if the ordinate of the cycloid be y, then will ji ;= ^/ 2 .v 



— XX -\- — ' , which equation perfeftly ex- 



^/ 2 X — .\" X 

 prefTes the relation between the ordinate y and the abfcifs x ; 

 and from it all the properties of the cycloid may be demon- 

 ftrated. 



Thus is the analytical calculus extended to thofe lines 

 xvhich have hitherto been excluded, for no other caufe but 

 that they were thought incapable of it. 



TRANSCOLATION, m Pharmacy, the fame with 

 filtration, or percolation. 



TRANSCRIPT, a copy of any original writing, par- 

 ticularly that of an aft, or inftrument, inferted in the body 

 of another. 



In this fenfe we fay, tranfcript of a Jine, i^c. See FiNE 

 and Duplicate. 



TRANSCRIPTO recognitionis faffie coram jujlitiariis 

 Itinerantibus, i^c. in Laiv, is a writ for certifying a recog- 

 nizance into chancery, taken before the juftice in eyre. 



tiwymainvTO peclis Jinis hiuiti mittendo in cancellarium, is 

 a writ for certifying the foot of a fine levied before juftices 

 in eyre, &c. into chancery. 



TRANSEAT, in the Schooh, Sec. a term purely Latin, 

 fignifying, Id it pafs, or fuppofe a propofition to be true, 

 without granting it. 



Hence the proverb, tranfcat, Gr^cum ejl, non legitur : the 

 phrafe is faid to have taken its rife from fome ancient com- 

 mentators, or gloffographers of the civil law, who^ not 



T R A 



underflanding Greek, pafTcd over all the words that oc- 

 curred in that language, without explaining them. 



In the Roman chancery, a nil tranfeat is a kind of oppo- 

 fition made to the feahng of a bull, or to the delivery of 

 fome other inftrument, till the parties, agaiufl whofe intereft 

 it is diredled, have been heard againft it. 



TRANSELEMENTATION, a change of the ele- 

 ments or principles of one body into thofe of another. 



Such is that which Roman Catholics contend for in the 

 eucharifl, where the elements of bread and wine, they fay, 

 are changed into thofe of flefh and blood. See Transub- 



STANTIATION. 



Tranfelementation, wherever it happens, is always allowed 

 miraculous, or an effeft beyond the ordinary powers of 

 nature. 



TRANSEPT, the crofs aifle, extending from north to 

 fouth acrofs the nave and main aifles of our ancient churches. 

 In fome churches, as in the cathedral of Saliibury, there is 

 a double tranfept, which makes it referable an archiepif. 

 copal crofs in its ichnography. 



TRANSFER, in Commerce, &c. an aft by which a 

 perfon furrenders his right, intereft, or property, in any 

 thing moveable or immoveable, to another. 



The fale or donation of an inheritance, &c. transfers the 

 property, rights, &c. of it. 



The term is principally ufed, in the commerce of ftocks, 

 for the afTigning and making over of fubfcriptions or (hares 

 therein to fuch as purchafe them of the proprietors. In the 

 South Sea Company, the Bank, Eaft India, &c. transfers 

 are made by entering the flock under the name of the pur- 

 chafer under his proper letter of the alphabet. 



A counterfeit, in this cafe, is by aft of parliament made 

 a capital crime. 



TRANSFIGURATION, among Divines, that mira- 

 culous change wrought by Jefus Chrift, in prefence of 

 St. Peter, St. James, and St. John, on mount Thabor, 

 where he appeared in his glory, in company with Mofes 

 and Elias. See the defcription of it in St. Matthew, 

 chap. xvii. 



The term is alfo applied to a feaft held in the Romifh 

 church on the 6th of Auguft, in commemoration of that 

 miracle. 



TRANSFORMATION, a metamorphofis, or change 

 of form. 



The chemifls have been a long time feeking the tranf- 

 formation of metals, that is, their tranfmutation, or the 

 manner of changing them into gold. 



Among the myflics, by transformation is underftood a 

 change of the contemplative foul, by which it is in fome 

 meafure deified, or converted into the fubftance of God, 

 and in which it is, as it were, loft and fwallowcd up in the 

 divinity, fo as not to perceive its own diflinftion from God. 



The word transformation is very liable to be abufed ; 

 but many of the myftics ufe it innocently enough ; Hjeaning 

 no other by it than what St. Paul did. Vivo ego, jam non 

 ego, vivit niero in vie Chrijlus. 



TuANSFORMATioN IS alfo fomctimcs ufed for what we 

 more properly call tranfubjlantiation. 



Tran.sformation of Equations, in Algebra, is a method 

 of changing equations into others of a different form, but 

 of equal value. This operation is iieceffary in order to 

 prepare equations for a more eafy folution. We (liall fub- 

 join fome examples of the moft common and ufeful kind 

 under this head. The affirmative roots of an equation are 

 changed into negative roots of the fame v<alue, and vise 

 verfd, by only changing the figns of the terms alternately, 

 beginning with the fecond. 



R 7 Thus, 



