T R A 



tk uiimJpal ddi^s tint come before the Royal Society of 

 Loodan. TheTra 



_ Tranladiaas cootziin the fevoal dtfcorcries 



and faiftories of nature and art, made by the members of the 

 Society, or commmiicated by them from their corre- 

 fpondents, with the (e«eral expemnents, obfervatiaos, &c. 

 made hx them, or tranfmitted to them, Sec. 



They were firft fet on foot in 1665, by Mr. Oldenboig, 

 fecretirv of the Society, and were cootinaed by him till the 

 Tear 1677. Upoo has death, they «rere difoootmued till 

 Jamiary 167S, vhen Dr. Grew refnmed the pobhcatiofi of 

 them, and coatiaued it for the months <^ Decendier 1678, 

 and JaDoarr and Febiury 1679, after which they were ic- 

 tntnitted t31 January 1683. Doriag this Izft interval, they 

 woe foppbed in foroe meafore by Dr. Hooke's Philo- 

 fophical CoQedioDS. They vrere aUb interrupted for three 

 years, from December 1687 to Jannary 1691, befide other 

 unaDer interruptioas amounting to near ooe year and a half 

 mme, befiore Oaober 1695, fince which time the Tianiac- 

 tioiis ham been regularly carried oa. 



They ««e for manr Tears pnhHibed in nimibei^ and the 

 ptindag <^ them was always, from time to tone, the fin^ 

 a&s of the lefpertrre feoetaries, till the year 1752, when 

 the Society thiwglit fit that a caamnttee fiMnld be appointed 

 to recoofider the papers read beDore them, zndtofekA out 

 of tbsm fnch as they (hoold judge moft proper fior publica- 

 tioa in the fiitme Traq^a^onSL The members of the 

 cooncil rnqiltn^itf a ftandk^ ooomittee for this purpofe. 

 They meet oe the firft Thnrfday of evoy month, and no 

 lejs than (inen membeis of the committee (of which number 

 the prefideut, or, in his abiJTKy, a vioe-fHtefident, b alwap 

 to be one) are aDowed to be a qmsrmm, capabk of ading in 

 .idatian to liich papers. The qoeftioa, with regard to the 

 pnbticaxian <£ any paper, b ahrays decided by the majmity 

 of votes takoi by bafflot. 



They are pubfiihed annually in two parts, at the expeooe 

 of the Sodety, and each frik>w is entitled to receire ooe 

 copy grjlit, <d every xtAmae puhlilfbed afto* hb admifiinn 

 into the Society. 



The Plulofophical Tranftf^imn, to the end of the year 

 1700^ were abridged in three Tofaanes, by XIr. John JLow- 

 tfaorp; thole from the war 170010 1720 were alxidged in 

 two Tofames, by tir. Henry Jones; tho& from 1719 to 

 1-33 were abridged in two iiJames, by Mr. John Eames 

 and Mr. John Martyn. S>ir. Martyn coDnnoed the abridg- 

 ment of thofe from 1732 to 1744, in two nJnmes; and 

 thofe from 1743 ^'^ I'jC. in two Tolumes. 



TRANSCELLEXSiS Moxs, in jtmieai Gttgrtfhj^ a 

 mountain of Africa, near the mnnicipnm ; caOed by Am- 

 imanns^ MarrelHnns Sugabarritanmn. Tins town was fitu- 

 ated in Mauritania Czlarienfis, footh of the town of Zoc- 

 ch^ifaaii, and near the rirer Cfamalaph. 



TRANSCENDENT, or Tkaxscxxbestju, fame- 

 thing Tai£ed or ekrated beyHKid other thingj ; or which 

 pafies or tranibesds the nature and ciicumftanoes of other 

 iolerior beii^s, fo k not to be intimat^ and eflentiaDy in- 

 cluded under them. 



1*be term b particnlatly aj^hed to the objed of meta- 

 {&tSc% windi coofiders bongs in general, or tianfrendeotal 

 hemgs as God and angds, and truths confiftii^ in pure 

 fpecnialioa. 



LogiciaBS and meta]diyficians give the name of tranlcen- 

 dental terms to thote whidi are fo general, and of a fignifi- 

 cation fo estenfive and uaiveiial, that they pais thrcmgh all 

 the categories, and ^ree to all kinds of tiimgs. Such are 

 :he terms imt, mmmm, vsrsa, hmmm, m. See Exs, &c. 



TstAXSCEVDESTAi Ati. See Abt. 



TaASSCXVDEXTAL Pirftr^im. See PERFBtTlOV. 



T R A 



TtLASsciSBLyriAj. QuaxMkr, among Scbsalmea. See- 



QCASTITT. 



TraxscendextaI. Qmamiiua., among Gcamntnaams, are 

 iiMktenmnate ones ; or fnch as cannot be exprefied or fixed 

 to any cooftant equation. Such is a tranfcendental curve, 

 <» the Uke. 



M. Leihiiitz has a diileitation in the Ada Erud. Lipi'. 

 in which he endearours to {hew the origin of fuch quan- 

 tities ; nz. why fome probkiDS are neither plaic, foHd, nc r 

 lur^blid, nor M any ceitaia degree, but do trai^fcend ^11 

 algefarzical equations. 



He alfo fhews how it may be demoaflrated without cal- 

 culus, that an algei^aic quadiatrix for the circle or hyper- 

 bola b impoffiUe : for if foch a quadratrix could be fourid, 

 it would fiAow, that, by meass of it, any angle, ratio, or 

 logarithm, might be divided in a gi^en proponicKi of one 

 r^it line to another, and thb by ooe unirerijd caofb-ndi<M ; 

 and conleqneistly the proUem of the fedion of an angle, or 

 the inrention of any number of mean proponicwals, would 

 be of a certain finite degree. 



Whereas the di&toit degrees of algebr^cal equations, 

 and therefore the probleni, underftood in general of any 

 number of parts c^ an angle, or mean proportionals, b of 

 an indefinite degree, and tranfcends all algebraical equa- 

 tions. 



TaAXSCEXDEXTAJL Cmrst, in the Highir GeeaKtrj, h 

 fuch a ooe as cannot be defined by any algebraical equatioa ; 

 or of which, when it b expreffed by an equation, one uf the 

 terms b a variable qnandty. See Curve. 



Thefe curres are the fame with what Defcartes, and, 

 after hb example, feveral others, call wtechamiud ^-mrvei, and 

 v^uch they would have excluded out of geometry ; but fir 

 Tfaar Newton and M. Leibnitz are of another (imtiment. 

 For, in e%ct, in the oonfini&ion of geometrical problem^, 

 one curve b not to be preferred to another, as it is <' 

 by a more fimpie equation, but as it is more eaiily d^fo 

 than that other. See Geometkic^l Lic^. 



And fome of the£: tranfcendental or nn-ch a nifa l 

 are found of greater ufe than all the algebraical ones to 

 gether, except the circle. 



Add, that i£. Leibnitz, in the ASa Emditor. Lipf. 

 gires us a kii^i of tranfcendental equatioas, by which thele 

 tranfcendental cnrres are aoually dedsed, and which are 1: ' 

 an intWinite degree ; that is, are not always the iaine in ;-.. 

 the points of the curve. 



Whereas algebrai&s nle to afliime fome general letters or 

 numbers of the quantities fought, m thefe tranfcendental 

 problems ; M. Lobnitz a^umes geoeral or indefinite equa- 

 tions ibr the lines fought ; t. gr. putting x and j for the ' 

 ahfcifs and ordinate, the equation he ufes for a line fought 



b d 4- ^» + '/ + '•*/ -T f'' * T S3 ]■> ^^' ^ ^ ^y ^■'' 

 help of winch indefinite equatico, which in reahty b dm:r . 

 for it may always be determined bow far foerer it b necei- 

 fary to raife it, he fe^s the tai^ent ; and comparing thz: 

 winch refnlts, with the given property of taDgei^is, be bLc> 

 the Talne of the affumed letters a, i, t, and dios defines th:; 

 equations of the line fought. 



If the comparifon above mentioned do not proceed, he 

 pranoDoces the line fought not to be an algebraical, but a 

 tranfrendental one. 



Thb fuppofed, he goes on to find the fpecies of tracf- 

 oendeocy ; fin- fome tranfcendentals depend on the general 

 divifion or £ediaa of a ratio, or upon the logarithms, others 

 upon the arcs of a circle, and othere 00 more indefinite and 

 cmnponnd inquiries. 



Here, iheit£are, befides the fymbob x and j, he aJTomes 

 2 third, as r, which denotes the tranfcendental quantity; 



Slid 



4 



