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Bernoullis being invited to Petersburgh ment of the Academy: but the violent in 1725, promised Euler, who was desir and laborious efforts it cost him threw ous of following them, that they would him into a fever, which endangered his use their endeavours to procure for him life, and deprived him of the use of his an advantageous settlemen in that city. right eye, which afterwards brought on a In the mean time, by their advice, he total blindness. made close application to the study of The Academy of Sciences at Paris, philosophy, to which he made happy which in 1738 bad adljudged the prize to applications of his math matical know his memoir concerning the Naiure and led, e, in a dissertation on the nature and Properties of Fire, proposed for the year propagation of sound, and an answer to 1740, the important subject of the tides a prize question concerning the masting of the sea; a problem whose solution of ships; to which the Academy of Sci comprehended ihe theory of the solar ences adjudged the accessit, or second system, and required the most arduous rank, in the year 1727. From this latter calculations. Euler's solution of this discourse, and other circumstances, it ap- question was adjudged a masterpiece of pears bat Euler bad very early embark: analysis and geometry; and it was more ed in the curious and useful study of naval honourable for him to share the academiarchitecture, which he afterwards enrich. cal prize with such illustrious competitors ed with so many valuable discoveries. as Colin Maclaurin and Daniel Bernoulli, The study of mathematics and philoso. than to have carried it away from riphy, however, did not solely engage his vals of less magnituie. Seldom, if ever, attention, as he, in the mean time, attend did such a brilliant competition adorn ed the medical and botanical lectures of the ammals of the Academy; and perthe professors at Basil.

haps no subject, proposed by that learn. Euler's merit would have given him an ed body, was ever treated with such force easy admission to honourable preferment, of genius and accuracy of investigation, either in the magistracy or university of as that which here displayed the philosohis native city, if both civil and academi. phical powers of that extraordinary trical honours had not been there distribut. umvirate. ed by lot. The lot being against him in a In the year 1741, M. Euler was invited certain promotion, he left his country, set to Berlin, to direct and assist the Acade. out for Petersburgh, and was made joint my that was there rising into fame. On professor with his countrymen, Hernian this occasion he enricheil the last volume and Daniel Bernoulli, in the university of of the Miscellanies (Melanges) of Berlin that city.

with five memoirs, which form an emi. At his first setting out in his new ca. nent, perhaps the principal figure in that reer, he enriched the academical collec. collection. These were followed, with tion with many memoirs, which excited a amazing rapidity, by a great number of noble emulation between him and the important researches, which are dispersBernoullis; an emulation that always ed through the memoirs of the Prussian continued, without either degenerating Academy : a volume of which has been into a selfish jealousy, or producing the regularly published every year since its least alteration in their friendship. It was establishment in 1744. The labours of at this time that he carried to new de Euler will appear more especially astogrees of perfection the integral calculus, nishing, when it is considered, that, while invented the calculation by sines, reduced he was enriching the Academy of Berlin analytical perations to a greater simpli- with a profusion of memoirs on the deepcity, and thus was enabled to throw new est parts of mathematical science, conlight on all the parts of mathematical taining always some new points of view, science.

often sublime truths, and sometimes disIn 1730 M. Euler was promoted to the coveries of great importance, he still professorship of natural philosophy; and continued his philosophical contributions in 1733 he succeeded his friend D. Ber to the Petersburgh Academy, whose menoulli in the mathematical chair. In moirs display the surprising fecundity of 1735, a problem was proposed by the his genius, and which granted him a penAcademy, which required expedition, and sion in 1742. for the calculation of which some eminent It was with great difficulty that this mathematicians had demanded the space extraordinary man, 1766, obtained perof some months The problem was un. mission from the King of Prussia to redertaken by Euler, who completed the turn to Petersburgh, where he wished to calculation in three days, to the astonish. pass the remainder of his days. Soon

after his return, which was graciously re with the greatest success; and it is im. warıled by the munificence of Catharine possible to observe, without admiration, the Second, he was seized with a violent such immense calculations on the one disorder, which ended in the total loss of hand, and on the other the ingenious his sight. A cataract formed in his left methods employed by this great man to eye, which had been essentially damaged abridge them, and to facilitate their apby the loss of the other eye, and a too plication to the real motion of the moon. close application to study, deprived him But this admiration will become astonishentirely of the use of that organ. It was ment, when we consider at what period, in this distressing situation that he dictat. and in what circumstances, all this was ed to his servant, a tailor's apprentice, effected. It was when our author was who was absolutely devoid of mathemati- totally blind, and consequently obliged cal knowledge, his elements of algebra, to arrange all his computations by the which, by their intrinsic merit in point of sole powers of his memory, and of his perspicuity and method, and the unhappy genius : it was when he was embarrassed circumstances in which they were com in his domestic affairs by a dreadful fire, posed, have equally excited wonder and that had consumed great part of his proapplause. This work, though purely ele. perty, and forced him to quit a ruined mentary, plainly discovers the proofs of house, every corner of which was known an inventive genius; and it is perhaps to him by habit, which in some measure here alone that we meet with a complete supplied the want of sight. It was in theory of the analysis of Diophantus. these circumstances that Euler composed

About this time M. Euler was honoured a work, which alone was sufficient to ren. by the Academy of Sciences at Paris with der his name immortal. the place of one of the foreign members Some time after this, the famous occu. of that learned body; after which the list Wenzell, by couching the cataract, academical prize was adjudged to three restored our author to sight; but the joy of his memoirs, “concerning the inequa. produced by this operation was of short lities in the motions of the planets.” The duration. Some instances of negligence two prize questions proposed by the same on the part of his surgeons, and his own academy, for 1770 and 1772, were de impatience to use an organ, whose cure signed to obtain from the labours of astro was not completely finished, deprived nomers a more perfect theory of the moon. him a second time, and for ever, of bis M. Euler, assisted by his eldest son, was sight: a relapse which was also accom. a competitor for these prizes, and obtain. panied with tormenting pain. With the ed them both. In this last memoir, he assistance of his sons, however, and of reserved for farther consideration several Messrs. Krafft and Lexell, he continued inequalities of the moon's motion, which his labours: neither the infirmities of old he would not determine in his first theory, age, nor the loss of his sight, could quell on acccount of the complicated calcula- the ardour of his genius. He had engag. tions in which the method he then em ed to furnish the academy of Petersburgh ployed had engaged him. He afterward with as many memoirs as would be suffi. revised his whole theory, with the assist cient to complete its acts for twenty years ance of his son, and Messrs, Krafft and after his death. In the space of seven Lexell, and pursued his researches till years he transmitted to the academy he had constructed the new tables, which above seventy memoirs, and above tro appeared, together with the great work, hundred more, left behind him, were re. 1772. Instead of confining himself, as be. vised and completed by a friend. Such fore, to the fruitless integration of three of these memoirs as were of ancient date differential equations of the second de were separated from the rest, and form a gree, which are furnished by mathema- collection that was published in the year tical principles, he reduced them to the 1783, under the title of “ three ordinates, which determine the Works." place of the moon : he divided into classes The general knowledge of our author all the inequalities of that planet, as far was more extensive than could well be as they depend either on the elongation expected in one who had pursued, with of the sun and moon, or upon the eccen such unremitting ardour, mathematics tricity, or the parallax, or the inclination and astronomy as his favourite studies. of the lunar orbit. All these means of in- He had made a very considerable pro. vestigation, employed with such art and gress in medical, botanical, and chemical dexterity as would only be expected from science. What was still more extraordia genius of the first order, were attended nary, he was an excellent scholar, and


possessed in a high degree what is gene- wound again, the point M, thereof, will rally called erudition. He had attentive describe another curve, A M M, called by ly read the most eminent writers of an M. Huygens, a curve described from evocient Rome; the civil and literary history lution. The part of the thread, MC, is of all ages and of all nations was familiar called the radius of the evolute, or of the to him; and foreigners, who were only osculatory circle described on the centre, acquainted with his works, were astonish- C, with the radius, M C. ed to find, in the conversation of a man, Hence, 1. When the point, B, falls in whose long life seemed solely occupied A, the radius of the evolute, MC, is equal in mathematical and physical researches to the arch, BC; but if not, to A B, and and discoveries, such an extensive ac the arch B C. 2. The radius of the evoquaintance with the most interesting lute, C M, is perpendicular to the curve, branches of literature. In this respect, A M. 3. Because the radius, M С, of the no doubt, he was much indebted to a very evolute continually touches it, it is evi. uncommon memory, which seemed to re dent, from its generation, that it may be tain every idea that was conveyed to it, described through innumerable points, if either from reading or from meditation. the tangents in the parts of the evolute He would repeat the Æneid of Virgil, are produced until they become equal to from the beginning to the end, without their corresponding arches. 4. The evohesitation, and indicate the first and lastlute of the common parabola is a paraline of every page of the edition be used. bola of the second kind, whose parameter Several attacks of a vertigo, in the be. is of the common one.

5. The evoginning of September, 1783, which did lute of a cycloid is another cycloid equal not prevent his computing the motions and similar to it. 6. All the arches of of the aerostatic globes, were, however, evolute curves are rectifiable, if the radii the forerunners of his mild passage out of of the evolute can be expressed geomethis life. While he was amusing himself trically. at tea with one of his grand children, he EVOLUTION. See ALGEBRA. was struck with an apoplexy, which ter Evolution, in the art of war, the mominated his illustrious career at seventy- tion made by a body of troops, when they six years of age.

are obliged to change their form and disa M. Euler's constitution was uncommon. position, in order to preserve a post, or ly strong and vigorous. His health was

occupy another, to attack an enemy with good, and the evening of his long life was

more advantage, or to be in a condition calm and serene, sweetened by the fame

of defending themselves the better. It that follows genius, the public esteem and consists in doublings, counter-marches, respect, that are never withheld from ex.

conversions, &c. A battalion doubles emplary virtue, and several domestic com the ranks, when attacked in front or rear, forts, which he was capable of feeling, and to prevent its being flanked, or surroundtherefore deserved to enjoy.

for then a battalion fights with a larThe catalogue of his works has been ger front. The files are doubled, either printed in fifty pages, fourteen of which to accommodate themselves to the necontain the manuscript works. The print. cessity of a narrow ground, or to resist ed ones consist of works published sepa an enemy which attacks them in Aank; rately, and works to be found in the me.

but if the ground will allow it, conversion moirs of several academies, viz. in thirty- is much preferable, because, after coneight volumes of the Petersburgh acts, version, the battallion is in its first form, (from six to ten papers in each volume ;) and opposes the file leaders, which are in several volumes of the Paris acts; in generally the best men, to the enemy; twenty-six volumes of the Berlin acts,

and likewise, because doubling the files (about five papers to each volume ;) in in a new or not well disciplined regithe Acta Eruditorum, in two volumes; in

ment, they may happen to fall into disorthe Miscellanea Taurinensia, in vol. ix. of der. the Society of Ulyssingue; in the Ephe EVOLVULUS, in botany, a genus of merides of Berlin; in the Memoires de la

the Pentandria Tetragynia class and orSociété Oeconomique, for 1766.

der. Natural order of Campanaceæ. ConEVOLUTE, in the higher geometry, volvuli, Jussieu. Essential character: caa curve, which, by being gradually open- lyx five-leaved; corolla five-cleft, rotate; ed, describes another curve. Such is the capsule three-celled; seeds solitary. curve BC F; (Plate V. Miscel. fig. 7) for There are seven species, all natives of the if a thread, F C M. be wrapped about, or East or West Indies. applied to the said curve, and then un EUONYMUS, in botany, English spir



dle-tree, a genus of the Pentandria Mono EUPHORBIA, in botany, English etigynia class and order. Natural order of phorbium spurge, a genus of the DoeDumos.e. Rhamni, Jussieu. Essential candria Trigynia class and order. Natucharacter: calyx five-petalled ; capsule ral order of Tricocca. Euphorbix. Jusfive-sided, five-celled, five-valved, colour. sieu. Essential character: corolla four ed, seeds calyptred, or veiled. There or five petalled, placed on the calyx ; caare eight species. These are trees or lyx one-leafed, bellying: capsule tricocshrubs; the smaller branches or twigs There are ninety-eight species. four-cornered; the leaves opposite; pe These are milky plants, mostly herbace. duncles axillary, solitary, opposite, one. ous, a few shrubby, upright for the most Howered, sometimes many flowered, dis- part, very few of them creeping; some posed in umbels.

are leafless; stems angular or tubercled, EUPAREA, in botany, a genus of the or more frequently cylindric or columPentandria Monogynia class and order. nar; unarmed, or in the angular sorts re. Essential character: calyx five-leaved; sembling the upright cactuses; armed corolla five or twelve petalled; berry su with prickles, which are either solitary perior, one-celled; seeds very many, ad. or in pairs, placed in a single row on the hering to a free receptacle. There is top of the ridges. only one species, viz. E. amoena, a native EUPHRASIA, in botany, English eye. of New Holland, and Terra del Fue. bright, a genus of the Didynamia ingiosgo.

permia class and order. Natural order EUPATORIUM, in botany, English of Personatæ. Pediculares, Jussieu. Eshemp agrimony, a genus of the Syngenesia sential character: calyx four-cieft, cylinPolygamia #qualis class and order. Na

dric; capsule two-celled, ovate, oblong: tural order of Compositæ Discoideæ. lower anthers have a little thorn at the Corymbifera, Jussieu. Essential charac. base of one of the lobes. There are nine ter: calyx imbricate, oblong ; style clo. species. ven half way, long ; down, plumose; re EURYA, in botany, a genus of the Doceptacle naked. There are forty-nine decandria Monogynia class and order. species. The species native in the Unit.

Essential character: calyx five-leaved, ed States are twenty-six in number, of calycled; corolla five-petalled; stamina which the E. perfoliatum, or bone set, thirteen; capsule five-celled! There is is a valuable medicine. These are most. but one species, viz. E. Japonica, a native ly tall, growing, perennial, herbaceous

of Japan. plants. The greater part are natives of EURYANDRA, in botany, a genus of Norh America; many, however, from the Polyandria Trigynia class and order. South America and the West Indies ; se Natural order of Coadunatæ. Magnoliæ, veral are found wild in the East Indies, Jussieu. Essential character: calys five. and one only in Europe.

leaved ; corolla three-petalled; filament EUPHEMISM, in rhetoric, a figure much dilated at the tip, with twin dis. which expresses things, in themselves joined anthers ; folicles three. There is disagreeable and shocking, in terms im. only one species, viz. E. scandens, a naplying the contrary quality : thus, the tive of New Caledonia, Pontus, or Black Sea, having the epithet EUSTACHIAN tube, in anatomy, be. abcvos, i. e. inhospitable, given it, by rea- gins from the interior extremity of the son of the savage cruelty of those who tympanum, and runs forward and inwards inhabited the neighbouring countries, in a bony canal, which terminates with a this name, by Euphemism, was changed portion of the temporal bone. See Anainto that of Euxinus. in which signification nobody will deny its being a species EUSTEPHIA, in botany, a genus of of irony : but every euphemism is not the Hexandria Monogynia class and or. irony, for we sometimes use improper and der. Corolla superior, tubular, cylindrisoft terms in the same sense with the pro- cal, bifid ; nectary six cavities in the tube

of the corolla ; filaments tricuspidate, dis. EUPHONY, in grammar, an easiness, tinct. There is but a single species, viz. smoothness, and elegance in pronuncia- the coccinea. tion. Euphony is properly a figure, EVSTYLE, in architecture, a sort of whereby we suppress a letter, that is building in which the pillars are placed too harsh, and convert it into a smoother, at the most convenient distance one from contrary to the ordinar rules: of this another, the intercoluminiations being jist there are abundance of examples, in all two dianieters and a quarter of the colanguages.

lumn, except those in the middle of the


per and harsh.

face, before and behind, which are three aae not parallel; in opposition to concendiameters distant.

tric, where they are parallel, having one EWRY, in the British customs, an offi common centre. cer in the king's household, which has the EXCENTRIC circle, in the Ptolemaic syscare of the table linen, of laying the cloth, tem, the very orbit of the planet itself, and serving up water, in silver ewers, af. which it was supposed to describe about ter dinner.

the earth. EXAGGERATION, in rhetoric, a kind EXCENTRIC circle, in the new astronoof hyperbole, whereby things are aug. my, a circle described from the centre of mented or amplified, by saying more than the orbit of the planet, with half the axis the truth, either as to good or bad. as a radius. There are two kinds of exaggeration, EXCENTRIC place of a planet, is the very the one of things, the other of words. point of the orbit, where the circle of inThe first is produced, 1. By a multitude clination coming from the place of a of definitions. 2. By a multitude of ad- planet in its orbit, falls thereon with right juncts. 3. By a detail of causes and angles. effects. 4. By an enumeration of conse EXCENTRICITY, in astronomy, is the quences. 5. By comparisons. And, 6. distance of the centre of the orbit of a By the contrast of epithets and rational planet from the centre of the sun, that is, inference,

the distance between the centre of the Exaggeration by words is effected, 1. ellipsis and the focus. See ASTRONOMY By using metaphors. 2. By hyperboles. table. 3. By synonymous terms. 4. By a col. EXCEPTION to evidence, at common lection of splendid and magnificent ex- law, is the same as a bill of exceptions, pressions. 5. By periphrasis. 6. By which is a formal exception made in writ. repetition. And lastly, by confirma- ing, to be signed by the judge, when any tion with an oath ; as for example, “Pa evidence is improperly refused or rerietes, medius fidius, gratias tibi agere ceived, and is a record of such matter, gestiunt.”

which the judge is afterwards called upEXACUM, in botany, a genus of the on to acknowledge in court, and then Tetrandria Monogynia class and order. being made part of the record, it is arNatural order of Rotaceæ. Gentianæ, gued in the same manner as any other Jussieu. Essential character : calyx four- point of error appearing upon the record. leaved ; corolla salver-shaped, with an in This proceeding is founded on the Stat. fated tube; capsule two-furrowed, two of Westminster, 2. celled, many-seeded, bursting at the top. EXCEPTION, in law, is a clause, whereby There are ten species.


party contracting excepts, or takes a EXANTHEMA, among physicians, de particular thing out of a general thing notes any kind of efflorescence or erup- granted or conveyed, and it must be tion, as the measles, purple spots in the something which is not inseparable from plague, or malignant fevers, &c.

it. It must not be the whole thing grantAccording to Dr. Cullen, it is an order ed, but part thereof only, and must be in the class pyrexiæ, and includes all conformable, and not repugnant, to the contagious diseases, beginning with fe. grant, for then the exception is void. It ver, and followed by an eruption on the must also be described with certainty. skin.

EXCHANGE, in political economy. EXCELLENCY, a title anciently given The reciprocal payments of merchants to kings and emperors, but now to em are made in bills of exchange, the amount bassadors, and other persons, who are not of which is expressed in the money of qualified for that of highness, and yet are the country upon which they are drawn. to be elevated above the other inferior In calculating the par of exchange, the dignities. In England and France the ti- coin of different countries is supposed to tle is now peculiar to embassadors, but contain that quantity of gold or silver, of very common in Germany and Italy. a determinate purity, which, agreeably to Those it was first appropriated to were the regulations of their respective mints, the princes of the blood of the several it ought to contain. Thus, an English royal houses; but they quitted it for that guinea is supposed to contain 5 dwt. 6 of highness, upon several great lords as gr. troy of gold, and a Spanish dollar 17 suming excellency.

dwt. 6 gr. of silver each, of a certain deEXCENTRIC, in geometry, a term ap- gree of fineness. plied to circles and spheres which have When a bill of exchange upon Lisbon not the same centre, and consequently can be procured in London for the same VOL. V.


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