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physiology, to which he made a happy application of his mathematical knowledge; and he also attended the medical lectures at Basel. While he was engaged in physiological researches, he composed a dissertation on the nature and See also:

PROPAGATION

propagation of See also:

sound, and an See also:

ANSWER (derived from and, against, and the same root as swear)

answer to a See also:

PRIZE, or PRIZE OF WAR (Fr. prise, from prendre, to take)

prize question concerning the masting of See also:

SHIPS

ships, to which the See also:

French See also:

Academy of Sciences adjudged the second See also:

RANK (O.Fr. rant or rent, mod. rang, generally connected with the O.E. and O.H.G. bring, a ring)

rank in the See also:

YEAR

year 1727. In 1727, on the invitation of See also:

Catherine I., Euler took up his See also:

RESIDENCE (Latin residere, to remain behind, to dwell, reside)

residence in St Petersburg, and was made an See also:

ASSOCIATE (Lat. associates, from ad, to, and sociare to join)

associate of the Academy of Sciences. In 1730 he became See also:

PROFESSOR (the Latin noun formed from the verb profiteri, to declare publicly, to acknowledge, profess)

professor of physics, and in 1733 he succeeded Daniel Bernoulli in the See also:

CHAIR (in. Mid. Eng. chcere, through O. Fr. chaire or chaiere, from Lat. cathedra, later caledra, Gr. xaOi3pa, seat, cf. "cathedral"; the modern Fr. form chaise, a chair, has been adopted in English with a particular meaning as a form of carriage; chaire

chair of mathematics. At the commencement of his new career he enriched the academical collection with many See also:

MEMOIRS

memoirs, which excited a See also:

NOBLE, SIR ANDREW (1832- )

noble emulation between him and the Bernoullis, though this did not in any way affect their friendship. It was at this time that he carried the integral calculus to a higher degree of perfection, invented the calculation of sines, reduced See also:

ANALYTICAL

analytical operations pure mathematics. In 1735 a problem proposed by the academy, for the See also:

SOLUTION (from Lat. solvere, to loosen, dissolve)

solution of which several eminent mathematicians had demanded the space of some months, was solved by Euler in three days,but the effort threw him into a See also:

FEVER (Lat. febris, connected with fervere, to burn)

fever which endangered his See also:

LIFE

life and deprived him of the use of his right See also:

eye. The Academy of Sciences at See also:

Paris in 1738 adjudged the prize to his memoir on the nature and properties of See also:

FIRE (in O. Eng. f j'r; the word is common to West German languages, cf. Dutch vuur, Ger. Feuer; the pre-Teutonic form is seen in Sanskrit pu, pavaka, and Gr. irup; the ultimate origin is usually taken to be a root meaning to purify, cf. Lat. purus)

fire, and in 1740 his See also:

TREATISE

treatise on the tides shared the prize with those of See also:

COLIN, ALEXANDRE (1526-1612)

Colin See also:

MACLAURIN, COLIN (1698–1746)

Maclaurin and Daniel Bernoulli—a higher See also:

HONOUR (Lat. honos or lwnor, honoris; in English the word was spelled with or without the u indifferently until the 17th century, but during the 18th century it became fashion-able to spell the word " honor "; Johnson's and Webster's Dictionaries stereoty

honour than if he had carried it away from inferior rivals.

In 1741 Euler accepted the invitation of See also:

Frederick the See also:

GREAT

Great to See also:

Berlin, where he was made a member of the Academy of Sciences and professor of mathematics. He enriched the last See also:

VOLUME

volume of the Melanges or Miscellanies of Berlin with five memoirs, and these were followed, with an astonishing •rapidity, by a great number of important researches, which are scattered throughout the See also:

ANNUAL

annual memoirs of the Prussian Academy. At the same time he continued his philosophical contributions to the Academy of St Petersburg, which granted him a See also:

PENSION (Lat. pensio, a payment, from pendere, to weigh, to pay)

pension in 1742. The respect in which he was held by the Russians was strikingly shown in 176o, when a See also:

FARM

farm he occupied near See also:

CHARLOTTENBURG

Charlottenburg happened to be pillaged by the invading See also:

RUSSIAN

Russian See also:

army. On its being ascertained that the farm belonged to Euler, the See also:

general immediately ordered See also:

COMPENSATION (from Lat. compensare, to weigh one thing against another)

compensation to be paid, and the empress See also:

Elizabeth sent an additional sum of four thousand crowns. In 1766 Euler with difficulty obtained permission from the See also:

king of See also:

Prussia to return to St Petersburg, to which he had been originally invited by Catherine II. Soon after his return to St Petersburg a See also:

CATARACT (from the Lat. form cataracta of the Gr. Karapplucrgss, a floodgate, or waterfall, properly something which rushes down)

cataract formed in his See also:

LEFT

left eye, which ultimately deprived him almost entirely of sight. It was in these circumstances that he dictated to his servant, a tailor's apprentice, who was absolutely devoid of mathematical knowledge, his Anleitung cur See also:

ALGEBRA (from the Arab. al-jebr wa'l-mugabala, transposition and removal [of terms of an equation], the name of a treatise by Mahommed ben Musa al-Khwarizmi)

Algebra (1770), a See also:

WORK

work which, though purely elementary, displays the mathematical genius of its author, and. is still reckoned one of the best See also:

WORKS

works of its class. Another task to which he set himself immediately after his return to St Petersburg was the preparation of his Lettres a une princesse d'Alletnagne sur quelques sujets de physique et de philosophic (3 vols.,. 1768-1772). They were written at the See also:

REQUEST, LETTERS OF

request of the princess of See also:

ANHALT

Anhalt-See also:

DESSAU

Dessau, and contain an admirably clear exposition of the principal facts of See also:

MECHANICS

mechanics, See also:

OPTICS

optics, See also:

ACOUSTICS (from the Gr. &eobav to hear)

acoustics and See also:

PHYSICAL

physical See also:

ASTRONOMY (from Gr. &arpov, a star, and v ,usiv, to classify or arrange)

astronomy. Theory, however, is frequently unsoundly applied in it, and it. is to be observed generally that Euler's strength See also:

lay rather in pure than in applied mathematics.

In 1755 Euler had been elected a See also:

FOREIGN

foreign member of the Academy of Sciences at Paris, and some time afterwards the academical prize was adjudged to three of his memoirs Concerning the Inequalities in the Motions of the See also:

PLANETS, MINOR

Planets. The two prize-questions proposed by the same academy for 1770 and 1772 were designed to obtain a more perfect theory of the See also:

moon's See also:

motion: Euler, assisted by his eldest son Johann See also:

Albert, was a. competitor for these prizes, and obtained both. In the second memoir he reserved for further See also:

CONSIDERATION (from Lat. considerare, to look at closely, examine, generally taken to be from con-, and the base seen in sidus, sideris, a star, the word being supposed to be originally an astrological or astronomical term)

consideration several, inequalities of the moon's motion, which he could not determine in his first theory on See also:

account of the complicated calculations in which the method he then employed had engaged him. He afterwards reviewed his whole theory with the assistance of his son and W. L. See also:

KRAFFT (or KRAFT), ADAM (c. 1455-1507)

Krafft and A. J. Lexell, and pursued his researches until he had constructed the new tables, which appeared in his Theoria motuum lunae (1772). Instead of confining himself, as before, to the fruitless integration of three See also:

DIFFERENTIAL

differential equations of the second degree, which are furnished by mathematical principles, he reduced them to the three co-ordinates which determine the place of the moon; and he divided into classes all the inequalities of ' that See also:

PLANET (Gr. ssXavirrns, a wanderer)

planet, as far as they depend either on the See also:

ELONGATION

elongation of ' the See also:

sun and moon, or upon the eccentricity, or the See also:

PARALLAX (Gr. aapa?X6, alternately)

parallax, or the inclination of the lunar See also:

ORBIT (from Lat. orbita, a track, orbis, a wheel)

orbit. The inherent difficulties of this task were immensely enhanced by the fact that Euler was virtually See also:

BLIND, MATHILDE (1841—1896)

blind, and had to carry all the elaborate computations it involved in his memory. A further difficulty arose fromthe burning of his See also:

house and the destruction of the greater See also:

PART

part of his See also:

PROPERTY

property in 1771. His See also:

MANUSCRIPTS

manuscripts were fortunately preserved.

His. own life, was only saved by the courage of a native of Basel, See also:

Peter Grimmon, who carried him out of the burning• house: Some time after this an operation restored Euler's sight; but a too harsh use of the recovered See also:

FACULTY (through the French, from the Lat. facultas, ability to do anything, from facilis, easy, facere, to do; another form of the word in Lat. facilitas, facility, ease, keeps the original meaning)

faculty, along with some carelessness on the part of the surgeons, brought about a relapse. With the assistance of his sons, and of Krafft and Lexell, however, he continued his labours, neither the loss of his sight nor the infirmities of an advanced See also:

AGE (Fr. age, through late Lat. aetaticum, from aetas)

age being sufficient to check his activity. Having engaged to furnish the Academy of St Petersburg with as many memoirs as would be sufficient to See also:

COMPLETE

complete its Acta for twenty years after his See also:

DEATH

death, he in seven years transmitted to the academy above seventy memoirs,. and left above two See also:

HUNDRED

hundred more, which were revised and completed by another See also:

hand. Euler's knowledge was more general than might have been expected in one who had pursued with such unremitting ardour mathematics and, astronomy as his favourite studies. He had made very considerable progress in medical, botanical and chemical See also:

SCIENCE (Lat. scientia, from scire; to learn, know)

science, and he was an excellent classical See also:

SCHOLAR, SCHOLARSHIP

scholar, and extensively ,read in general literature. He was much indebted to an uncommon memory, which seemed to retain every See also:

IDEA (Gr. Ibia, connected with i&eiv, to see; cf. Lat. species from specere, to look at)

idea that was conveyed to it, either from See also:

READING

reading or meditation. He could repeat the Aeneid of See also:

Virgil from the beginning to the end without hesitation, and indicate the first and last See also:

LINE

line of every See also:

page of the edition which he used. Euler's constitution was uncommonly vigorous, and his general See also:

HEALTH

health was always See also:

GOOD, JOHN MASON (1764-1827)

good. He was enabled to continue his labours to the very See also:

close of his life. His last subject of investigation was the motion of balloons, and the last subject on which he conversed was the newly discovered planet See also:

Herschel (See also:

Uranus). He died of See also:

APOPLEXY (Gr. arov n i.a, from aroaMvvew, to strike down, to stun)

apoplexy on the 18th of See also:

SEPTEMBER (Lat. septem, seven)

September 1783, whilst he was amusing himself at See also:

TEA (Chinese cha, Amoy dialect t€)

tea with one of his grandchildren. Euler's genius was great and his See also:

INDUSTRY (Lat. industria, from indu-, a form of the pre, position in, and either stare, to stand, or struere, to pile up)

industry still greater.

His works, if printed in their completeness, would occupy from 6o to 8o See also:

QUARTO

quarto volumes: He was See also:

SIMPLE

simple and upright in his See also:

CHARACTER (Gr. xapareri7p, from xap&crew, to scratch)

character,' and had a strong religious faith. He was twice married; his second wife being a See also:

HALF

half-See also:

SISTER

sister of his first, and he had a numerous. See also:

FAMILY

family, several of whom attained to distinction. His eloge was written for the FrenchAcademy by the See also:

MARQUIS

marquis de See also:

CONDORCET, MARIE JEAN ANTOINE NICOLAS CARITAT, MARQUIS DE (1743-1794)

Condorcet, and an account of his life, with a See also:

list of his works, was written by Von Fuss, the secretary to the Imperial Academy of St Petersburg.. The works which Euler published separately are: Dissertatio physica de See also:

SONG

song (Basel, 1727, in 4to) ;' Mechanica, sive motus scientia analytice;expasita (St Petersburg, 1736, in 2 vols. 4to) ; Ennleitung in See also:

die Arithmetik (ibid., 1738, in 2 vols. 8vo), in See also:

German and Russian; Tentamen novae theoriae musicae (ibid. 1739, in 4to); Methodus inveniendi limas curvas, maximi minimive proprictate gaudentes (See also:

LAUSANNE

Lausanne, 1744, in 4to) ; Theoria motuum planetarum et cometarum (Berlin, 1744, in 4to) ; Beantwortung, &c., or Answers to Different Questions respecting Comets (ibid., 1744, in 8vo) ; Neue Grundsatze, c., or New Principles of See also:

ARTILLERY (the O. Fr. artiller, to equip with engines of war, probably comes from Late Lat. articulum, dim. of ars, art, cf. " engine " from ingenium, or of artus, joint)

Artillery, translated from the See also:

ENGLISH

English of See also:

Benjamin See also:

ROBINS, BENJAMIN (1707–1751)

Robins, with notes and illustrations (ibid., 1745, in 8vo) ; Opuscula varii argumenti (ibid., 1746-1751, in 3 vols. 4(o) ; Novae et carrectae tabulae ad loco lunae computanda (ibid., 1746, in 4to); Tabulae astronomicae See also:

SOLIS, ANTONIO DE (1610-16S6)

solis et lunae _(ibid., 4to) ; Gedanken, &c., or Thoughts on the Elements of Bodies (ibid. 4to) ; Rettung der See also:

gall-See also:

LICHEN (lichen ruber)

lichen Offenbarung, &c., See also:

Defence of Divine See also:

REVELATION, BOOK OF

Revelation against See also:

FREE

Free-thinkers (ibid., 1747, in 4t0) ; Introductio it analysin infinitorum (Lausanne, 1748, in 2 vols. 4t0) ; Scientia navalis, seu tractatus de construendis ac dirigendis navi bus (St Petersburg, 1749, in 2 vols. 4to) ; Theoria motus lunae (Berlin, 1753, in 4to) ; Dissertatio de principio mininiae actionis, ' una cum examine objectionum cl. prof. Koenigii (ibid., 1753, in 8vo) ; Institutianes calculi diflerentialis, cum ejus usu in analysiIntnitorum ac doctrina serierum (ibid., 1755, in 410) ; Constructio lentium objectivarum, &c.

(St Petersburg, 1762, in 4to); Theoria motus corporum solidoruni seu rigidorum (See also:

ROSTOCK

Rostock, 1765, in 4to); Institutiones,calculi integralis (St Petersburg, 1768-1770, in 3 vols. 4to) ; Lett', es a une Princesse d'Allernagne sur quelques sujets de physique it de philosophic (St Petersburg, 1768-1772, in 3 vols. 8vo) ; Anleitung zur Algebra, or Introduction to Algebra (ibid., 1770, in 8vo); Dioptrica (ibid., 1767-1771, in 3 vols. 4t0); Theoria motuum See also:

LUNGE, GEORG (1839- )

lunge nova method() pertr.arctata (ibid., 1772, in 4to) ; Novae tabulae lunares (ibid., in 8vo); l he'orie complete de la construction et de la manteuvre See also:

des vaisseaux (ibid., .1773, in 8vo) ; Eclaircissements svr etablissements en favour taut des veuves que des marts, without a date; Opuscula analytica (St Petersburg, 1783-1785, in 2 vols. 4t0). See Rudio, Leonhard Euler (Basel, 1884) ; M. Cantor, Geschichte der 1lfathematik.

End of Article: EULER, LEONHARD (1707-1783)

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