of their great fubferviency to the bufinefs of geometrical investigation in general. Thefe propoftions were fo named by him, either from the way in which he difcovered them, while he was invel tigating fomething elfe, by which means they might be confidered as gains or acquifitions, or from their utility in acquiring farther knowledge as fteps in the investigation. In this fenfe they are porifmata; for og fignifies both to inveftigate and to acquire by inveftigation. These propofitions formed a collection, which was famili. arly known to the ancient geometers by the name of Euclid's porifms; and PAPPUS of Alexandria fays, that it was a moft ingenious collection of many things conducive to the analyfis or folution of the most difficult problems, and which afforded great delight to thofe who were able to underfland and to inveftigate them. Unfortunately for mathematical fcience, however, this valuable collection is now loft, and it ftill remains doubtful in what manner the ancients conducted their refearches upon this curious fubject. We have, however, reafon to believe that their method was excellent both in principle and extent, for their analyfis led them to many profound difcoveries, and was reftricted by the fevereft logic. The on'y account we have of this clafs of geometrical propofitions, is in a fragment of Pappus, in which he attempts a general definition of them as a fet of mathematical propofitions diftinguishable in kind from all others; but of this diftinction nothing remains, except a criticism on a definition of them given by fome geometers, and with which He finds fault, as defining them only by an accidental circumstance, " Porifma eft quod deficit bypothefi a theoremate locali." Pappus then proceeds to give an account of Euclid's porifms; but the enunciations are fo extremely defective, while the figure they refer to is now loft, that Dr Halley Confeffes the fragment in question to be beyond his comprehenfion. The high encomiums given by Pappus to thefe propofitions have excited the curiolity of the greatest geometers of modern times, who have attempted to difcover their na ture and manner of inveftigation, M. Fermat, a French mathematician of the 17th century, attach ing himself to the definition which Pappus criticifes, publifhed an introduction (for this is its modeft title) to this fubject, which many others tried to elucidate in vain. At length Dr SIMSON of Glafgow, by patient enquiry and fome lucky thoughts, obtained reftoration of the porifms of Euclid, which has all the appearance of being juft. It precifely correfponds to Pappus's defcription of them. All the lemmas, which Pappus has given for the better understanding of Euclid's propofitions, are equally applicable to thofe of Dr Simfon, which are found to differ from local theorems precifely as Pappus affirms thofe of Eu. clid to have done. They require a particular mode of analyfis, and are of immenfe fervice in geometries investigation; on which account they may jaftly claim our attention. While Dr Simfon was employed in this inquiry, he carried on a corre4pondence upon the fubject with the late Dr M. STEWART, profeffor of mathematics in the unipurity of Edinburgh; who, bfides entering into Bu supton's views, and communicating to him

many curious porifms, purfued the fame fubject in a new and very different direction. He pub. lifhed the refult of his inquiries in 1746, under the title of General Theorems, not caring to give them any other name, left he might appear to at ticipate the labours of his friend and former pre ceptor. The greater part of the propofitions contained in that work are porifms, but without demonftrations; therefore, whoever wishes to a veftigate one of the most curious fubjects in geo metry, will there find abundance of materiais, and an ample field for difcuffion. Dr Simfon de fines a porifm to be" a propofition, in which à is propofed to demonftrate, that one or mon things are given, between which, and every on of innumerable other things not given, but affum ed according to a given law, a certain relation defcribed in the propofition is thown to taki place." This definition is not a little obfcure, bu will be plainer if expreffed thus: "A porifm is pofition affirming the poffibility of finding fuck conditions as will render a certain problem inde terminate or capable of innumerable folutions. This definition agrees with Pappus's idea of the propofitions, fo far at leaft as they can be under food from the fragment already mentioned; fo the propofitions here defined, like thofe which he defcribes, are, ftrictly speaking, neither thes rems nor problems, but of an intermediate na ture between both; for they neither fimply cau ciate a truth to be demonftrated, nor propofe♣ queftion to be refolved, but are affirmations of a truth in which the determination of an unknową quantity is involved. In as far, therefore, a they affert that a certain problem may become indeterminate, they are of the nature of the rems; and, in as far as they feek to difcover the conditions by which that is brought about, they are of the nature of problems. We hall endea vour to make our readers understand this fab ject diftin&tly, by confidering them in the way in which it is probable they occurred to the anciest geometers in the courfe of their refearches; thos will at the fame time fhow the nature of toe analyfis peculiar to them, and their great ufe in the folution of problems. It appears to be certaia, that it has been the folution of problems which, in all ftates of the mathematical fcience, has led to the difcovery of geometrical truths: the first mathematical inquiries, in particular, mutt nave occurred in the form of queftions, where fome thing was given, and fomething required to be done; and by the reafoning neceflary to answer thefe queftions, or to difcover the relation between the things given and thofe to be found, many truths were fuggefted which came afterwards ta be the fubject of feparate demonftrations. The number of thefe was the greater, becaufe the ancient geometers always undertook the folution of problems with a fcrupulous and minute at tention; infomuch that they would fcarcely futfer any of the collateral truths to escape their o fervation. Now, as this cautious manner of proceeding gave an opportunity of laying hold of every collateral truth connected with the naa object of enquiry, thefe geometers foon perceived, that there were many problems which is cu tain cates would admit of no folution whatevi.

La confequence of a particular relation taking place among the quantities which were given. Such problems were faid to become impoffible; and was foun found, that this always happened ter one of the conditions of the problem was stent with the reft. Thus, when it was ted to divide a line, fo that the rectangle cntained by its fegments might be equal to a gres tpace, it is evident that this was poffible cay when the given space was lefs than the fquare of half the line; for when it was otherwife, the two conditions defining, the one the magni rede of the line, and the other the rectangle of its fegments, were inconfiftent with each other. bach cafes would occur in the folution of the met fimple problems; but if they were more complicated, it must have been remarked, that the conftructions would fometimes fail, for a an directly contrary to that juft now affigned. Cles would occur, where the lines, which by Leir interfection were to determine the thing mught, instead of interfecting each other as they commonly, or of not meeting at all as in in above mentioned cafe of impoffibility, would concide with one another entirely, and of courfe leave the problem unrefolved. It would appear geometers upon a little reflection, that fince, the cafe of determinate problems, the thing required was determined by the interfection of the two lines already mentioned, that is, by the ats common to both; fo in the cafe of their Coincidence, as all their parts were in common, cry one of thefe points muft give a folution, or, other words, the folutions mult be indefinite in rumber. Upon inquiry, it would be found that the proceeded from fome condition of the probkm having been involved in another, fo that, in fact, there was but one which did not leave a fufficient number of independent conditions to limit the problem to a tingle or to any determinate number of folutions. It would foon be perceived, that thefe cafes formed very curious propofitions of an intermediate nature between problems and theorems; and that they admitted of being cnunCrated in a manner peculiarly elegant and concifc. It was to fuch propofitions that the ancients gave the name of porifms. This deduction requires to be huftrated by an example: fuppofe, therefore, that it were required to refolve the following problem:

+

(2.) PORISMS, EXAMPLES OF. A circle ABC fig. 1. Plate CCLXXXIII.), a ttraight line DE, and a point F, being given in oppofition, to find a point G in the ftraight line DE, fuch that GF, the ne drawn from it to the given point, fhall be equal to GB, the line drawn from it touching the given circle. Suppose G to be found, and GB to be drawn touching the given circle ABC in B, let H be its centre, join HB, and let HD be perpendicular to DE. From D draw DL, touching the arcle ABC in L, and join HL; alfo from the centre G, with the diftance GB or GF, defcribe the crcle BKF, meeting HD in the points K and K'. Then HD and DL are given in pofition and magtude; and becaufe GB touches the circle ABC, HBG is a right angle; and fince G is the centre et the circle BKF, therefore HB touches the cirDie BKF, and HB1 the rectangle K'HK; which

rectange +DK-HD', becaufe K'K is bifected in D; therefore HL'+KD'DH2=HL' and LD2; therefore DK-DL2, and DK=DL; and fince DL is given in magnitude, DK is also given, and K is a given point: for the fame reafon K ́ is a given point, and the point F being given by hypothefis, the BKP is given in pofition. The point G, the centre of the circle, is therefore given, which was to be found. Hence this conftruction: Having drawn HD perpendicular to DE, and DI touching the circle ABC, make DK and DK' each equal to DL, and find G the centre of the circle defcribed through the points KFK; that is, let FK' be joined and bifected at right angles by MN, which meets DE in G; G will be the point requi. red; that is, if GB be drawn touching the circle ABC, and GF to the given point, GB is equal to GF. The fynthetical demonftration is easily derived from the preceding analyfis; but in fome cafes this conftruction fails. For, firft, if F fall anywhere in DH, as at F', the line MN becomes parallel to DE, and the point G is nowhere to be found; or, in other words, it is at an infinite diftance from D.-This is true in general; but if the given point F coincides with K, then MN evidently coincides with DE; fo that, agreeable to a remark already made, every point of the line DE may be taken for G, and will fatisfy the conditions of the problem; that is to fay, GB will be equal to GK, wherever the point G be taken in the line DE: the fame is true if F coincide with K. Thus we have an inftance of a problem, and that too a very simple one, which, in general, admits but of one folution; but which, in one particular cafe, when a certain relation takes place among the things given, becomes indefinite, and admits of innumerable folutions. The propofition which results from this cafe of the problem is a porifm, and may be thus enunciated: "A circle ABC being given by pofition, and alfo a straight line DE, which does not cut the circle, a point K may be found, fuch, 1-at if G, be any point whatever in DE, the ftraight line drawn from G to the point K fhall be equal to the ftraight line drawn from G touching the given circle ABC." The problem which follows appears to have led to the discovery of many poritms. A circle ABC (fig. 2.) and two points D, E, in a diameter of it being given, to find a point F in the circumference of the given circle; from which, if straight lines be drawn to the given points E, D, thefe ftraight lines fhall have to one another the given ratio of a to 6, which is fuppofed to be that of a greater to a lefs.-Suppofe the problem refolved, and that F is found, fo that FE has to FD the given ratio of a to 6, produce EF towards B, bifect the angle EFD by FL, and DFB by FM: therefore EL: LD :: EF: FD, that is in a given ratio; and fince ED is given, each of the fegments EL, LD, is given, and the point L is alfo given because DFB is bifected by FM, EM: MD:: EF: FD, that is, in a given ratio, and therefore M is given. Since DFL is half of DFE, and DFM half of DFB, therefore LFM is half of (DFE+DFB), therefore LFM is a right angle; and fince the points L, M, are given, the point F is in the circumference of a circle defcribed upon LM as a diameter, and therefore given in pofition. Now

the

the point F is alfo in the circumference of the given circle ABC, therefore it is in the interfection of the two given circumferences, and therefore is found. Hence this conftruction: Divide ED in L, fo that EL may be to LD in the given ratio of a to, and produce ED alfo to M, fo that EM may be to MD in the same given ratio of a to ß; bifect LM in N, and from the centre N, with the diftance NL, defcribe the femicircle LFM; and the point F, in which it interfects the circle ABC, is the point required. The fynthetical demonftration is easily derived from the preceding analyfis. But the conftruction fails when the circle LFM falls either wholly within or wholly without the circle ABC, fo that the circumferences do not interfect; and in thefe cafes the problem cannot be folved. The construction also fails when the two circumferences LFM, ABC, entirely coincide. In this cafe, every point in the circumference ABC will anfwer the conditions of the problem, which is therefore capable of numberless folutions, and may, as in the former inftances, be converted into a porifm. We now inquire, therefore, in what circumstances the point L will coincide with A, and alfo the point M with C, and of confequence the circumference LFM with ABC. If we fuppofe that they coincide EA: AD::a:6:: EC: CD, and EA: EC:: AD: CD, or by converfion EA: AC:: AD: CD-AD:: AD: 2DO, O being the centre of the circle ABC; therefore, alfo, EA: AO::AD: DO, and by compofition EO: AO:: AO: DO, therefore EOX OD=AO2. Hence, if the given points E and D (fig. 3.) be fo fituated, that EOXOD=AO', and at the fame time a:6:: EA: AD: :EC: CD, the problem admits of numberlefs folutions; and if either of the points D or E be given, the other point and alfo the ratio which will render the problem indeterminate, may be found. Hence we have this porifm: "A circle ABC, and alfo a point D being given, another point E may be found, fuch that the two lines inflected from thefe points to any point in the circumference ABC, hall have to each other a given ratio, which ratio is alfo to be found." Hence alfo we have an example of the derivation of porifms from one another, for the circle ABC, and the points D and E remaining as before (fig. 3.), if, through D, we draw any line whatever HDB, meeting the circle in B and H; and if the lines EB, EH, be alfo drawn, thefe lines will cut off equal circumferences BF, HG. Let FC be drawn, and it is plain from the foregoing analyfis, that the angles DFC, CFB, are equal; therefore if OG, OB, be drawn, the angles BOC, COG, are al equal; and confequently the angles DOB, DOG. In the fame manner, by joining AB, the angle DBE being bifected by BA, it is evident that the angle AOF is equal to AOH, and therefore the angle FOB to HOG, that is, the arch FB to the arch HG. This propofition appears to have been the last but one in the 3d book of Euclid's Porifms, and the manner of its enunciation in the porifmatic form is obvious. The preceding propofition alfo affords an illustration of the remark, that the conditions of a problem are involved in one another in the porifmatic or indefinite cafe; for here feveral independent conditions are laid down, by the help of which the problem is to be refolved. Two

points D and E are given, from which two lines are to be inflected, and a circumference ABC, in which thefe lines are to meet, as alfo a ratio which thefe lines are to have to each other. Thefe com ditions are all independent on one another, fo that any one may be changed without any chang whatever in the reft. This is true in general; ba yet in one cafe, viz. when the points are fo relate to one another that their rectangle under their dil: tances from the centre is equal to the square of th radius of the circle; it follows from the precedin analyfis, that the ratio of the inflected lines is n longer a matter of choice, but a neceffary conf quence of this difpofition of the points. From & this, we may trace the imperfect definition of porifm which Pappus afcribes to the later geom ters, viz. that it differs from a local theorem, wanting the hypothefis affumed in that theorem If we take one of the propofitious called loci, an make the conftruction of the figure a part of th hypothefis, we get what was called by the ancies geometers a local theorem. If, again, in the enu ciation of the theorem, that part of the hypothef which contains the conftruction be suppressed, th propofition thence arifing will be a porism, for will enunciate a truth, and will require, to the fu understanding and investigation of that truth, tha fomething, fhould be found, viz. the circumftan ces in the conftruction supposed to be omitted Thus, when we fay, if from two given points D, (fig. 3.) two ftraight lines EF, FD, are i flected to a third point F, fo as to be to one and ther in a given ratio, the point F is in the circum ference of a given circle, we have a locus. Bu when converfely it is faid, if a circle ABC, which the centre is O, be given by pofition, alfo a point E; and if D be taken in the line EO fo that EOXOD=AO; and if from E and D the lines EF, DF, be inflected to any point of the circumference ABC, the ratio of EF to DF will be given, viz. the fame with that of EA to AD, we have a local theorem. Laftly, when it is faid, if a circle ABC be given by pofition, and alfo a point E, a point D may be found, fuch that if EF, FD, be inflected from E and D to any point F in the circumference ABC, thefe lines fhall have a given ratio to one another, the propofition becomes a porifm, and is the fame that has juft now been inveftigated. Hence it is evident, that the local theorem is changed into a porifm, by leaving out what relates to the determination of D, and of the given ratio. But though all propofitions formed in this way from the converfion of loci, are po rifms, yet all porifms are not formed from the converfion of loci; the firft, for inftance, of the preceding cannot by converfion be changed into a locus; therefore Fermat's idea of porifms, founded upon this circumftance, was imperfect. To confirm the truth of the preceding theory, profeffor Dr Stewart, in a paper read many years ago the Philofophical Society of Edinburgh, defines a porifm to be "A propofition affirming the poffbility of finding one or more conditions of an in determinate theorem;" where, by an indetermi nate theorem, he meant one which expreffes a rela tion between certain quantities that are determi nate and certain others that are indeterminate; a definition which evidently agrees with the expla

before

nations

sations above given. If the idea which is given of thefe propofitions be juft, then they are to be difcovered by confidering thofe cafes in which the contruction of a problem fails, in confequence of the fires which by their interfection, or the points which by their pofition, were to determine the problem required, happening to coincide with one ether. A porifm may therefore be deduced from the problem to which it belongs, juft as propations concerning the maxima and minima of quantities are deduced from the problems of which they form limitations; and fuch is the most natura' and obvious analyfs of which this clafs of propostions admits.

(3) PORISMS, REMARKS ON THE ANALYSES of. Another general remark may be made on the ays of porifms; it often happens that the magnitudes required may all, or a part of them, be found by confidering the extreme cafes; but for the difcovery of the relation between them, and the indefinite magnitudes, we must have resurfe to the hypothefis of the porifm in its moft general or indefinite form; and must endeavour to conduct the reasoning, that the indefinite magnitudes may at length totally disappear, and have a propofition afferting the relation between determinate magnitudes only. For this purpofe Dr Simfon frequently employs two statements of the general hypothefis, which he compares together. As for inftance, in his analyfis of the laft porim, he affumes not only E, any point in the ne DE, but also another point O, anywhere in the fame line, to both of which he fuppofes lines to be inflected from the points A, B. This double fatement, however, cannot be made without rendering the investigation long and complicated; nor is it even necessary, for it may be avoided by baving recourse to fimpler porisms, or to loci, or to propofitions of the data. A porifm may in fome ales be fo fimple as to arife from the mere coin. cidence of one condition with another, though in no cafe whatever any inconsistency can take place between them. There are, however, comparatively few porifms fo fimple in their origin, or that arife from problems where the conditions are but little complicated; for it ufually happens that 1 problem which can become indefinite may alfo become impoffible; and if fo, the connection already explained never fails to take place. Another fpecies of impoffibility may frequently arife from the porifmatic cafe of a problem which will affect in fome measure the application of geometry to aftronomy, or any of the fciences dependng on experiment or obfervation. For when a problem is to be refolved by help of data furnithed by experiment or obfervation, the first thing to be confidered is, whether the data so obtained be fafficient for determining the thing fought; and in this a very erroneous judgment may be formed, we reft fatisfied with a general view of the fub jeft; for though the problem may in general be refolved from the data with which we are provided, yet thefe data may be fo related to one another in the cafe under confideration, that the problem will become indeterminate, and, instead of one folution, will admit of an indefinite number. This we have found to be the cafe in the foregoing propofitions. Such cafes may not indeed occur in

if

any of the practical applications of geometry; but there is one of the fame kind which has actually occurred in aftronomy. Sir Ifaac Newton, in his Principia, has contidered a small part of the orbit of a comet as a ftraight line defcribed with an uniform motion. From this hypothefis, by means of four obfervations made at proper intervals of time, the determination of the path of the comet is reduced to this geometrical problem; Four ftraight lines being given in pofition, it is required to draw a fifth line across them, fo as to be cut by them into three parts, having given ratios to one another. Now this problem had been conftructed by Dr Wallis and Sir Chriftopher Wren, and alfo in three different ways by Sir Ifaac himself in different parts of his works; yet none of thefe geometers obferved that there was a particular fituation of the lines in which the problem admitted of innumerable folutions: and this happens to be the very cafe in which the problem is applicable to the determination of the comet's path, as was firft discovered by the Abbé Bofcovoich, who was led to it by finding, that in this way he could never determine the path of a comet with any degree of certainty. Befides the geometrical there is alfo an algebraical analysis belonging to porifms; which, however, does not belong to this place, becaufe we give this account of them merely as an article of ancient geometry; and the ancients never employed algebra in their investigations, Mr Playfair, profeffor of mathematics in the univerity of Edinburgh, has written a paper on the origin and geometrical inveftigation of porifms, which is published in the 3d volume of the Tranfactions of the Royal Society of Edinburgh, from which this account of the fubject is taken. He has there promifed a 2d part to his paper, in which the algebraical investigation of porisms is to be confidered. This will no doubt throw confiderable light upon the subject, as we may readily judge from that gentleman's known abilities, and from the fpecimen he has already given us in the first part.

PORISMATIC, adj. Of or belonging to the mathematical doctrine of PORISMS. (1.) PORISTIC, adj. the fame with porifmatic; belonging to porifms.

(2.) PORISTIC METHOD. n. f. [ogisixos.] In mathematicks, is that which determines, when, by what means, and how many different ways a problem may be folved. Dict.

(1.) PORK. n. f. [porc, Fr. porcus, Lat.] Swine's fleth unfalted.-You are no good member of the commonwealth, for, in converting Jews to Chriftians, you raife the price of pork. Shak. Merch. of Venice.-All flesh full of nourishment, as beef, and pork, increase the matter of phlegm. Floyer.

(2.) PORK. See Sus. The hog is the only domeftic animal that we know, of no ufe to man when alive, and therefore feems properly defigned for food. The Jews, however, the Egyptians and other inhabitants of warm countries, and all the Mahometaus at prefent, reject the ufe of pork. The Greeks gave great commendation to this. food, and their Athlete were fed with it. The Romans confidered it as one of their delicacies. With regard to its alkalefcency, no proper experiments have yet been made; but as it is of a ge

latinous

tinous and fucculent nature, it is probably less fo than many others. Upon the whole, it appears to be a very valuable nutriment. The reason is obvious why it was forbidden to the Jews: Their whole ceremonial difpenfation was typical. Filth was held as an emblem or type of fin. Hence the many laws refpecting frequent safhings; and no animal feeds fo filthily as fwine. Mahomet borrowed this prohibition, as well as circumcifion and many other parts of his fyftem, from the law of Mofes. But it is very abfurd to fuppofe, as fome do, that Mofes borrowed any thing from the Egyptians.

*PORKEATER. n. f. [pork and eater.] One who feeds on pork.-This making of chriftians will raife the price of hogs; if we grow all to be porkeaters. Shak. Merch. of Venice.

* PORKER. n. f. [from pork.] A hog; a pig.Strait to the lodgments of his herd he run, Where the fat porkers slept beneath the fun.

Pope.

* PORKET. n. /. [from pork.] A young hog. A porket, and a lamb that never fuffer'd fhears. Dryden. * PORKLING. n. f. [from pork.] A young pig.Shut up thy porklings thou meaneft to fat. Tufer. PORLAIT. See PORLOYD.

(1.) PORLOCK, a parish of England in Somerfetshire, containing about 110 houses, many villages and hamlets, and about 600 inhabitants. It exhibits much romantic fcenery, fteep and lofty hills, interfected by deep vales and hollow glens. Some of the hills are beautifully wooded, and con. tain number of wild deer. The valleys are very deep and picturefque; the fides being fleep, scarred with wild rocks, and patched with woods and foreft fhrubs. Some of them are well cultivated and ftudded with villages, farms and cottages, although agriculture here is very imperfectly under ftood. Most of the reads and fields are so fteep, that no carriages of any kind can be used; all the crops are therefore carried in with crooks on horfes, and the manure in wooden pots called doffals. (2.) PORLOCK, a fea port town in the above parifh, 6 miles W. of Minehead, in a very romantic fituation, being nearly furrounded on all fides, except near the fea, by fteep and lofty hills. Many of the inhabitants are employed in fpinning yarn for the Dunfter manufactory. It has 3 annual fairs, and had formerly a market on Thurfday. It is feated on the Bristol Channel, and has a good harbour: 14 miles N. by W. of Dulverton, and 167 W. of London. Lon. 3. 32. W. Lat. 51. 14. N. PORLOYD, or PORLAIT, a river of N. Wales, in Caernarvonshire.

PORO, an inland in the Gulf of Engia, near the coaft of Greece; 22 miles W. of Cape Colonni; anciently called Calauria. See CALAURIA. Lon. 41. 28. E. Ferro. Lat. 37. N.

* POROSITY. n. f. [from porous.] Quality of having pores. This is a good experiment for the difclofure of the nature of colours; which of them require a finer porofity, and which a groffer.

Bacon.

*POROUS. adj. [poreux, Fr. from pore.] Ha ving fmall fpiracles or paffages.

Of light the greater part, he took, and, plar'd In the fun's orb, made porous to receive And drink the liquid light. Milton

* POROUSNESS. n. f. [from porous.] _The quality of having pores; the porous part.-They will forcibly get into the porousness of it, and pas between part and part. Digby.

PORPESSE, an erroneous fpelling for Pox POISE. See DELPHINUS, § II, N° iv.

* PORPHYRE. See PORPHYRY, N° 1. PORPHYRISATION, n. f. See DIVISION, PORPHYRIUS, a famous Platonic philofopher born at Tyre in 233, in the reign of Alexande Severus. He was the difciple of Longinus, ant became the ornament of his fchool at Athens from thence he went to Rome, and attended Pl tinus, with whom he lived fix years. After Pl tinus's death he taught philofophy at Rome with great applaufe; and became well fkilled in polit literature, geography, aftronomy, and mufic. H lived till the end of the third century, and died i the reign of Dioclefian. There are ftill extant book on the Categories of Aristotle; a Treati on Abftinence from Flesh; and several other piece in Greek. They were printed at Cambridge, 1655, 8vo. with a Latin verfion. He also coma pofed a large treatise against the Christian religion which is loft. It was answered by Methodia Eufebius, St Jerome, &c. The emperor The dofius the Great caused it to be burnt in 338.

(1.) * PORPHYRY. PORPHYRE. z. f. [from ~ gruga; porphyrites, Lat. porphyre, Fr.] Marble of a particular kind.-I like beft the porphy white or green marble. Peacham.-Confider the red 2 and white colours in porphyre. Locke.

(2.) PORPHYRY, in the old fyftem of mineralo gy, was a genus of ftones ranked in the order faxa. It is found of feveral different colours, green, deep red, purple, black, dark brown, ard grey. See MINERALOGY, Part II. Chap. IV. O-d III. Sect. III. Gen. VII. There is a great number? of different kinds. M. Ferber describes 20 varieties under 4 fpecies, but in general it is confidered with relation to its ground, which is met with of the colours already mentioned. When the ground is of jaiper, the porphyry is commonly very bard the red generally contains felt-fpar in fmall white dots or fpecks; and frequently, together with thefe, black spots of fchoerl. The green is often magnetic, and is either a jafper or fchoerl, with fpots of quartz. Sometimes a porphyry of one co lour contains a fragment of another of a different colour. Thofe that have chert for their ground are fufible per fe. The calcareous porphyry confifts of quartz, felt-fpar, and mica, in feparate grains, united by a calcareous cement; and the micaceous porphyry confists of a greenish grey micaceous ground, in which red felt-fpar and greenish foap-rock are inferted. The porphyry of the ancients is a moft elegant mass of an ex tremely firm and compact fructure, remarkably heavy, and of a fine ftrong purple, variegated

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