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Prop. XXXVIII. Theor. If a plane be perpen- which is to the other as the axis of the first to the dicular to another plane, and a straight line be axis of the other. drawn from a point in one of the planes perpen- Prop. XIV. Theor. Cones and cylinders upon dicular to the other plane, this straight line shall equal bases are to one another as their altitudes. fall on the common section of the plaries.
Prop. XV. Theor. The bases and altitudes of Prop. XXXIX. Theor. In a solid parallelepiped, equal cones and cylinders, are reciprocally proif the sides of two of the opposite planes be divided portional: and if the bases and altitudes be reci. each into two equal parts, the common section of procally proportional, the cones and cylinders are the planes passing through the points of division, equal to one another. and the diameter of the solid parallelepiped cut Prop. XVI. Prob. To describe in the greater of each other into two equal parts.
two circles that have the same centre, a polygon Prop. XL. Theor. If there be tiro triangular of an even number of equal sides, that shall not prisms of the same altitude, the base of one of ineet the lesser circle. which is a paralelogram, and the base of the other Prop. XVII. Prob. To describe in the greater of a triangle; if the parallelogram be double of the two spheres which have the same centre, a solid triangle, the prisms shall be equal to one another polyhedron, the superficies of which sball not
Book XII. Lemvia 1.-Which is the first propo- ineet the lesser sphere. sition of the tenth book, and is necessary to some Prop. XVIII. Theor. Spheres have to one anof the propositions of this book.
other the triplicate ratio of that which their diameIf from the greater of two unequal magnitudes, ters have. there be taken more than its balf, and from the GEOMETRY (Descriptive), the name given to a remaiuder more than its half; and so on: there species of geometry almost entirely new, and shall at length remain a magnitude less than the which we owe in great asure to M. Monge. least of the proposed magnitudes.
When any surface whatever penetrates another, Prop. I. Theor. Similar polygons inscribed in there most frequently results from their interseccircles, are to one another as the squares of their tion curves of double curvature, the determinadiameters.
tion of which is necessary in many arts, as in Prop. II. Theor. Circles are to one another as groined vault-work, cutting arch-stones, wood-cutthe squares of their diameters.
ting, for ornamental work, &c. the form of wbich Prob. II. Theor. Every pyramid having a tri- is frequently very fantastical and complicated: it angular base, may be divided into two equal and is in the solution of problems appertaining to these similar pyramids having triangular bases, and subjects that descriptive geometry is especially which are similar to the whole pyramid; and into useful. two equal prisms wbich together are greater than
Some architects more versed in geometry than half of the whole pyramid.
persons of that profession commonly are, have Prop. IV. Theor. If there be two pyramids of long ago thrown some light on the first principles the same altitude, upon triangular bases, and each of this kind of geometry. There is, for example, of them be divided into two equal pyramids simi- a work by a jesuit named Father Courcier, who lar to the whole pyramid, and also into two equal examined and shewed how to describe the curves prisms; and if each of these pyramids be divided resulting from the mutual penetration of cylindriin the same manner as the first two, and 50 on: as cal, spherical, and conical surfaces: this work was the base of one of the first two pyramids is to the published at Paris in 1663. P. Deraud, Matheus base of the other, so shall all the prisms in one of rin Jousse, Frezier, &c. had likewise contributed them be to all the prisms in the otber, that are a little towards the promotion of this branch of produced by the same number of divisions.
geometry. But Monge has given it very great Prop. V. Thcor. Pyramids of the same altitude extension, not only by proposing and resolving which have triangular bases, are to one another as various problems both curious and difficult, but their bases,
by the invention of several new and interesting Prop. VI. Theor. Pyramids of the same altitude theorems. We can only mention in this place which have polygons for their bases, are to one one or two of the probleins and theorems. Thus arother as their bases.
among the problems. 1st, Two right lines being Prop. VII. Theor. Every prism having a trian- given in space, and which are neither parallel por gular base may be divided into three pyramids in the same plane, to find in both of them the points that have triangular bases, and are equal to one of their least distance, and the position of the line another,
joining these points. 2d, Three spheres being Prop. VIII. Theor. Similar pyramids having given in space to determine the position of the tri ingular bases are one to another in the tripli plane which touches them. There are also curicate ratio of that of their homologous sides. ous problems relative to lines of duuble currature,
Prop. IX. Theor. The bases and altitudes of equal and to surfaces resulting from the application of pyramids having triangular bases are reciprocally a right line that leans continually upon two or proportional: and triangular pyramids of which three others given in position in space. Ainong the bases and altitudes are reciprocally propor- the theorems, the following may be mentioned: if tional, are equal to one another.
a plane surface given in space is projected upon Prop. X. Theor. Every cone is the third part of three planes, the one horizontal, and the two a cylinder which has the same base, and is of an others vertical and perpendicular to each otber, equal altitude with it.
the square of that surface will be equal to the sum Prop. XI, Theor. Cones and cylinders of the of the squares of the three surfaces of projection, samc altitude, are to one another as their bases. This theorem is as interesting in the geometry of
Prop. XII. Theor. Similar cones and cylinders solids, as Pythagoras's theorem (Euc. 1. xlvii.) is have to one another the triplicate ratio of that in plane geometry. But for more on this subject which the diameters of their bases have.
we must refer to Monge's and Lacroix's ingenious Prop. XIII. Theor. If a cylinder te cut by a works entitled Geometrie Descriptive. plane parallel to its opposite planes, or bases; it GEOMETRY OF THE COMPASSES, a species of divides the cylinder into two cylinders, one of geometry more ingenious than profound, lately
proposed by the Abbe Mascheroni. Hitherto considered civil and religious liberty as the unboth the ruler and the compasses hare been made alienable right of mankind; and iherefore he use of in the solution of problems in plane geome. granted it to a people who pleaded no other try, and it had not been imagined that problems claim to it than the known goodness and hucould be solved or constructed without the combined use of these two instruments.
manity of his temper. Possessed of these noble
But the Abbé Mascheroni has struck out a greater number
and generous sentiments, though his accession of problems, wbich are rendered very piquant and
to the British throne enlarged his sphere of acamusing, by the new condition of employing only tion, it did not alter his plan of conduct; that the compasses in their solution. Thus: two points was uniformly and invariably the same, both terminaling a right line being given, to find either before and after his advancement to that high between those two points or exteriorly any num. dignity. In a word, it may be affirmned, that ber of points which shall be in the same right line no prince was ever better qualified to sway the with the former, and which shall be with the in- sceptre over a free people, nor any who ever terval between them in a given ratio: to draw to exercised the virtues of a great and good govera given line perpendiculars, or parallels, or lines nor with more distinguished ability, or more making with them given angles: to inscribe or uninterrupted success.” circumscribe within or about a circle, the various polygons which are constructible by plane geo- his father in 1727. In 1737 he lost his queen
GEORGE II. king of England, succeeded metry: to determine the mean proportional be, Caroline, a woman of excellent qualities, and tween two given distances; or to find third and of a strong mind. In 1739 admiral Vernon the Euclidean geometry are here resolved by the was sent with a squadron to the West Indies, simple intersection of arcs of circles, without where he demolished Porto Bello, but failed drawing a single right line. He also resolres by in his attempt on Carthagena. In 1743 George ingenious approximations many problems wbich put himself at the head of his army on the lie beyond the limits of common geometry, as continent, and gained the battle of Déttingen, those relating to duplications, trisections, &c. still June 16th. In August 1745, the pretender's employing only the compasses. The inquisitive eldest son landed in the Highlauds, and was reader will be much entertained with the work en- joined by several clans. After obtaining sctitled Geometria del Compassa, in which these curi- veral successes, the rebels were defeated by the ous particulars are explained with much perspi. Duke of Cumberland, at Culloden, in 1746. cuity and elegance.. A French translation of this In 1748 peace was concluded at Aix-la-Chawork was published in 1798, in 1 vol. 8vo.
pelle. In March, 1750, died, universally laGEOPO’NICAL. a. (yn and eros.] Relat- mented, Frederic prince of Wales, between ing to agriculiure. (Brown).
wboni and his faiher there had never been GEOPOʻNICS. s. [on and moros.] The science any cordiality. The next year an act passed for of cultivating the ground, the doctrine of agri- regulating the commenceinent of the year, by culture.
abolishing the old style. In 1753 another GEORGE I.king of England, was the eldest famous act passed for preventing clandestine son of Ernest Augustus, elector of Brunswick marriages. In 1735 war broke out between Lunenburg, or Hanover, by the princess So, the English and the French, which was at first phia, daughter of Frederic, elector Palatine, and very unpromising ; Braddock was defeated and king of Bohemia, and of Elizabeth daughter killed in North America, and Minorca was of James I. He was born in 1660, created taken in the Mediterranean), for which admiduke of Cambridge in 1706, and succeeded ral Byng, who was sent out to relieve it, was queen Anne in 1714. The next year a rebel- shot at Portsmouth. About this time Mr. lion broke out in Scotland, in favour of the Pitt became prime minister, and public affairs pretender, which, however, was shortly quelled. began at length to wear a new face under his In his reign parliaments were made septennial, active management. In 1768, a treaty was enand the order of the Bath was revived. In 1720 tered into between England and Prussia, which happened the failure of the famous South sea proved very burthensome to the former nation; scheme, by which many thousands were ruin- but the successes with which our fleets and ared. He died June 11, 1727, at Osnaburgh. inies were attended, made the people cheerful
The following character of this monarch is under ali the expences of the war. The British extracted from Allen's History of England :- Aag waved triumphant in every sea; and Geo. “ George the first was plain and simple in his II. died suddenly amidst the blaze of glory, person and address, grave and composed in his October 25th 1700 ; and was succeeded by his deportment, though easy, familiar, and facetious grandson, our present gracious sovereign. in his hours of relaxation. He is said to have “ The memory of George II. (says Guthrie), been the only prince of his time who knew is repreliensible on no head but his predilection what it was to enjoy the sweets of private for his electoral dominious. He never could friendship; a pleasure from which sovereigns form an idea that there was any difference bein general are, by the elevation of their rank, tween them and his regal dominions; and he excluded. He had given a proof of his political was sometimes ill enough advised to declare so abilities before his arrival in this island. Na. much in his speeches to parliament. We are, turally inclined to justice and equity, though however, to reinember, that his people gratified he was absolute and despotic in bis hereditary him in this partiality, and that he never acted dominions, he ruled them with all the lenity by power or prerogative. He was just rather and moderation of a limited monarch. He than generous ; and in matters of economy, either in his state or his household, he was ment was mean : he rendered it infamous. He willing to connive at abuses, if they had the accumulated wealth by the basest arts of fraud sancu n of law and custom. He was not very and corruption ; but his malversations were accessible to conversation, and therefore it was $0 notorious, that George was compelled no wonder that having left Germany, after he 10 escape from the pursuits of justice. After had attained io man's estate, he still retained this disgrace, in which he appears to have saved foreign notions both of men and things. In his fortune at the expence of his honour, he government he had no favourite ; for he parted embraced, with real or affected zeal, the profeswith sir Robert Walpole's administration with sion of Arianism. From the love, or the osgreat indifference, and shewed very little con- tentation, of learning, he collected a valuable cern at the subsequent revolutions anjong his library of history, rhetoric, philosophy, and servants. This quality may be deemed a virtue, theology; and the choice of the prevailing facas it contributed greatly to the internal quiet of tion promoted George of Cappadocia to the his reign, and prevented the people from loading throne of Athanasius.” His conduct in this the king with the faults of his ministers. In station is represented by our historian as polluthis personal disposition he was passionate, but ed by cruelty and avarice, and his death conplacable; fearless of danger, fond of military sidered as a just punishment for the enormities parade, and enjoyed the memory of the cam- of his life, among which Mr. Gibbon seems to paigns in which he served when young. His rank his “enmity to the Gods.". affections, either public or private, were never The immediate occasion of his death, howknown to interfere with the ordinary course of ever, as narrated by ecclesiastical writers, will justice; and though his reign was distracted by not probably appear calculated to add any stain party, the courts of justice were never better to his menory. “There was in the city of filled than under him."
Alexandria a place in which the heathen priests GEORGE (St.), or GEORGE of Cappa- had been used to offer hunian sacrifices." This docia; a name whereby several orders, both place, as being of no use, Constantius gave to military and religious, are devoininated. It the church of Alexandria, and George the took its rise from a saint or hero famous bishop gave orders for it to be cleared, in order throughout all the East, called by the Greeks to build a Christian church on the spot. In Meyadona; lug, q. d. great martyr. On some doing this they discovered an immense subtermedals of the emperors John and Manuel raneous cavern, in which the heathen mysteries Comneni, we have the figure of St. George had been performed, and in it were many armed, holding a sword or javelin in one hand, human skulls. These, and other things which and in the othera buckler, with this inscription; they found in the place, the Christians bronght
P out and exposed to public ridicule. The en 0, and thercin a little A, and reürioc, heathens, provoked at this exhibition, suddenly
took arms, and rushing upon the Christians, making o arios reoprios, holy George. killed many of them with swords, clubs, and He is generally represented on horseback, as stones: some also they strangled, and several being supposed to have frequently engaged they crucified. On this the Christians proceedin combats in that manner. He is highly ve- ed no farther in clearing the temple; but the nerated throughout Arinenia, Muscovy, and heathens, pursuing their avantage, seized the all the countries which adhere to the Greek bishop as he was in the church, and put him in rite ; from the Greek, his worship has long ago prison. The next day they dispatched him; been received into the Latin church ; and Eng- and then fastening the body to a camel, he was land and Portugal have both chosen him for dragged about the streets all day, and in the their patron saint. Great difficulties have been evening they burned him and ihe camel toraised about this saint or hero. Ilis very exist- gether. This fate, Sozomen says, the bishop ence has been called in question. Dr. Heylin, owed in part to his haughtiness while he was in who wrote first and niost about him, con- favour with Constantius, and some say the cluded with giving him entirely up, and friends of Athanasius were concerned in this supposing bim only a symbolical device; and massacre; but be ascribes it chiefly to the inDr. Pettingal has turned him into a inere Basi- veteracy of the heathens, whose superstitions lidian symbol of victory. Mr. Pegy, in a paper he had been very active in abolishing. in vol. i. of the Archæologia, has attempted to St. George, the patron saint of England, and restore him. And finally, Mr. Gibbon (Hist. of the order of the Garter, is much revered in yol. IIp. 404.) has sunk him into an Arian Russia, and his figure occurs in all the churches. bishop in the reigns of Constantius and Julian. He is represented as usual, riding on a horse, The bishop alluded to,
and piercing a dragon with his lance. This GEORGE the Cappadocian, was sosurnamed, same device also forms pari of the arms of the according to our author, from his parents or Russian sovereign, and is observed upon several education; and was born at Epiphania, in Ci- of the coins. As most persons endeavour, it licia, in a fuller's shop. “ From this obscure possible, to derive erery custom and allusion and servile origin he raised himself by the talents from their own country, some of the English of a parasite : and the patrons whom he assidu- historians have conjectured, that Ivan Vassile ously flattered procured for their worthless de- vitch the Second, being presented with the pendent a lucrative commission, or contract, Garter by Queen Elizabeth, assumed the to supply the army with bacon. His employ- George and the Dragon for his arms, and
ordered it to be stamped upon the current To monarchs who madding, around their money. But this supposition is erroneous, as round tables, it by no means appears, that the Tzar was Preferr’d, to conversion, their fighting and creaied a knight of the Garter; and it is cer
fables : tain that the sovereigns of Moscow bore this When soldiers were many, good Christians device before they had the least connection but few, with England; for the arms of Moscovy are St. George was advanc'd to St. Gregory's thus described by Chanceler, the first English
due. man who discovered Russia, as being aifixed to One may be mistaken-and therefore would a dispatch sent in 1554, from Ivan Vassilevitch beg to Queen Mary :-" This letter was written in That a Willis, a Stukely, an Ames, or a the Muscovian tongue, in letter much like to
Peorge, the Greeke letters, very faire written in paper, In short, that your lordship, and all the with a broade seale hanging at the same, scal
fam'd set, ed in paper upon waxe.
This seale was much Who are, under your auspicies, happily like the broad scale of England, having on the one side the image of a man on horseback in In perfect good humour-which you can incomplete harnesse fighting with a dragon." spire, Hackluyt, vol. 1. p. 255.
As I know by experience—would please to Many writers are of opinion that the history enquire, of St. George is an allegory; others maintain To search this one question, and settle, I that the device is borrowed by the Christian hope, church from the ancient story of Perseus and Was oli England's old patron, a knight, ut the sea-monster, of Bellerophon and the Chi- a pope? mera, or of Apollo and the serpent Pithon, or In opposition to these opinions, several aufrom some Egyptian hieroglyphics, or from thors have entered the lists; particularly Heycharms and amulets worn by thé Pagans; lin, Selden, and Fuller; and lately, Mr. Pegge others have traced his legend from the history endeavours to rescue this saiut from annihilaof George of Cappadocia, the Arian archbishop tion, and to prove, at the same time, that he of Alexandria. Amongst the authors who was a different personage from St. Gregory. have written upon this subject with the great- But unfortunately for the arguments of the est success, must not be omitted Mr. Byrom learned antiquarian, Mr. Byrom’s treatise, (Miscellaneous Poems, vol. i. p. 100), who which he opposes, is written in verse with so has composed a metrical rhapsody addressed to much ease, humour, and whimsical rhyming, lord Willoughby, president of the Antiquarian that the reader is almost divested of his judgSociety, in which he endeavours to prove that ment, and with difficulty is presented by the St. George is a corruption of St. Gregory; and most weighty reasons from siding with the to use his own words:
poet, who, instead of dull and dry disquisi
tions, treats us with much wit, couched in an Now, my lord, I would ask of the learn'd
easy flow of doggrel meire. and laborious,
George. s. (Georgius, Latin.) 1. A figure If Ge-orgius ben't a mistake for Gregorius? of St. George on horseback worn by the knighis In dames so like letter'd it would be no
of the garter (Shak.). 2. A brown loaf (Dry.). wonder,
GEORGE (Fort Si.). See MADRAS. If hasty transcribers had made such a blun
GEORGE (St.), one of the Azores, inhabited der;
by about 5000 persons, who cultivate much And mistake in the names by a slip of their wheat. Lat. 38. 39 N. Lon. 28.0 W. pen,
George's ISLANDS (King), are two islands May, perhaps, have occasioned mistake in in the Soutlt sen, lying in W. lon. 144.56 S. the men.
lat. 14. 28. They were first discovered by That this has been made, to omit all the rest, commodore Byron in 1765, and have since Let a champion of yours, your own Selden been visited by captain Cook in 1774. Comattest;
modore Byron's people had an encounter with See his book upon titles of honour-that the inhabitants, which proved fatal to some of quarter
the natives ; but captain Cook was more fortuWhere he treats of St. George, and the nate. A lieutenani and two boats well armed knights of the Garter.
wers sent on shore by captain Cook, and landed And again :
without opposition. As soon as the gentlemen
landed, the islanders embraced them by touchThis, my lord, is the matter--the plain sim- ing noses, a mode of civility used in New Zeaple rhimes
land, which 'is 900 leagues distant, and the Lay no fault, you perceive, upon Protestant only place besides this where the custom has times:
been observed to prevail. Notwithstanding I impute the mistake, if it should be one, this ceremony, however, very little real friendsolely
ship seemed to take place on the part of the To the pontiffs succeeding, who christen’d islanders. wars holy;
GEORGE TOWN, the seat of justice in a disrict of the same name in S. Carolina. Lat. principal rivers are the Savannah, Ogeechee, 33. 20 N. Lon. 79. 30 W.
Alatamaha, Turtle River, Little Sitilla; Great GEORGIA, a country of Asia, called by the Sitilla, Crooked River, St. Mary's, and AppalaPersians Gurgistan, anci by the Turks Gurtshi. chikola. The winters in Georgia are very mild It is one of the seven Cancasian nations, in the and pleasant. Snow is seldom or never seen. countries included between the Black sea and The soil and its fertility are various, according the Caspian, and comprehends the ancient to situation and different improvements. By Iberia and Colchis. It is bounded on the N. culture are produced rice, indigo, cotton, silk, by Circassia, on the E. by Daghestan and Schir. India corn, potatoes, oranges, figs, pomegravan, on the S. by Armenia, and on the W. of nates, &c. Rice at present is the staple comthe Cuban, or new Russian gorernment of modity; but great atiention begins to be paid Caucasus. It is divided into nine provinces. to the raising of tobacco. The whole coast of Of these, five are subject to Heraclius, and Georgia is bordered with islands, the principal form what is commonly called the kingdom of of which are Skidaway, Wassaw, Ossahaw, Georgia; and four, which are subject to David, St. Catharine's, Sapelo, Frederica, Jekyl, form the kingdom or principality of Imeretia. Cumberland, and Amelia. For more on the This country is so extremely beautiful, that subject of this state, see Cruttwell's Gazetteer. soine fanciful travellers have imagined they had GEORGIA (New), or South GEORGIA, here found the situation of the original garden an island in the South Atlantic ocean, about of Eden. The hills are covered with forests of thirty leagues in length, and ten in breadth. oak, ash, beech, chesnuts, walnuts, and elos, It abounds in bags and harbours, but the proenriched with vines, growing perfecily wild, digious quantity of ice on the coast renders it but producing vast quantities of grapes. From inaccessible during a great part of the year, and these is annually made as much wine as is even at other times floating masses of ice render necessary for their yearly consumption; the re- the anchorage dangerous. The appearance of mainder are left to rot on thevines. Cotton grows the land is the same throughout; the lofty spontaneously, as well as the finest European mountains towards the south are divided into fruit-trees, Rice, wheat, millet, hemp,and Hax, numberless parts, and appear like Aames of fire. are raised on the plains almost without culture. The coasts are bounded with high perpendicular The valleys afford the finest pasturage in the rocks of ice, large portions of which frequently world; the rivers are full of fish; the moun- break off and fall into the valleys or into the tains abound in minerals; and the climate is sca, where they are tossed about by the waves, delicious ; so that nature appears to have lavish- and resemble small detached islands. The ined on this favoured country every production terior country is not less savage, the summits that can contribute to the happiness of its in- of the rocks are lost in the clouds, and the valhabitants. On the other hand, the rivers of leys are covered with eternal snow; there is Georgia, being fed by mountain torrents, are neither tree nor shrub. The only vegetables always either too rapid or too shallow for the discovered were a kind of coarse grass, a species purposes of navigation; the Black sea, by of burnet, and a plant like moss. The rocks which commerce and civilization might be in- are composed of a kind of slate, of a blueish troduced from Europe, has been till very l.itely grey colour, disposed in horizontal beds: many in the exclusive possession of the Turks; the shining fragments of which cover the strand, trade of Georgia by land is greatly obstructed by and appear to have no mineral in the composithe high mountains of Caucasus; and this ob- tion. In all the coast there was found neither stacle is still increased by the swarms of predla- river nor fresh-water spring. Lat. 54. 30 S. tory nations, by which those inountains are in- Lon 37.0 W. habited. The inhabitants are Christians of GEORGIC, a poetical composition upon the the Greek communion, and appear to have re- subject of husbandry, containing rules therein, ceived their present name from their attach- put into a pleasing dress, and set off with all ments to St. George, the tutelary saint of these the beauties and embellishments of poetry. countries. Their dress nearly resembles that The word is borrowed from the Latin georgiof the Cossacs ; but men of rank frequently cus, and that of the Greek you pšixos, of yy, terra, wear the habit of Persia. They usually dye earth, and pyesores, opero, I'work, or labour, their hair, beards, and nails with red. The offyov, opus, work. Hesiod and Virgil are the women employ the same colour to stain the two greatest masters in this kind of poetry. The palms of their hands.
moderns have produced nothing in this way, Georgia, the most southern of the United except Rapin's book of Gardening; and the States of N. America, bouvded on the E. by celebrated poem intitled Cyder, by Mr. Philips, the Atlantic ocean, on the S. by E. and W. who, if he had enjoyed the advantage of VirFlorida, on the W. by the river Mississippi, gil's language, would have been second to and on the N. by N. and S. Carolina, being di- Virgil in a much nearer degree. vided from the latter by the river Savannah. It GEORGINA, in botany, a genus of the is about 600 miles long and 250 broad. It is class syngenesia, order polygamia superflua. divided into 11 counties, namely, Chatham, Receptacle chaffy, downless; calyx double, the Effingham, Burke, Richmond, 'Wilkes, Li- outer many-leaved ; inner one-leaved; eightberty, Glynn, Camden, Washington, Greene, parted. Three species; all natives of Mexico. and Franklio. The capital is Augusta. The GEORGIUM SIDUS, the name given by