108 



ALGAUOTTI ALGEBRA. 



to give his genius a wrong direction, since the excel- 

 lencie- of these pictures lire directly oppo-e.l ID ilio-e 

 of sculpture. In 1625, he went to Venice, and 

 thence to Rome. The duke of Mantua liuil recom- 

 mcn.led hun to cardinal Ludovisi, nephew of pope 

 Gregory XV., who was intent on renewing Uie 

 magnificence of the garden- .,f SallusL Her. A. 

 was employed in restoring mutilated antiques (e. g. a 

 Men-iiiy), and in prejwring original works. Here 

 he became acquainted with his countryman Domeni- 

 chino. The statue of St Magdalen, for the church 

 of St Silvestre, on the Quirinal, was his first great 

 work. Cardinals and princes now availed them- 

 selves of his talents, ana the French court wished 

 him to come to Paris ; but the prince Pam&li suc- 

 ceeded in retaining him in Rome, where he din I. 

 June 10, l(ju I, fifty-two years old, and was buried in 

 the church St Giovanni di Bolognesi. His Flight 

 of Attila, a basso relievo in marble with figures of the 

 site of life, over the altar of St Leo, in St Peter's 

 church, is his most renowned work. But, with all 

 the excellencies of this work, an inclination to give 

 to sculpture the effect of painting is observable. 

 This was owing to the influence of the school of 

 Caracci on him. His God of sleep, of nero antico, in 

 the villa Borghese, lias often been taken for an an- 

 tique. The basso-relievo of the Flig/it of Attila lias 

 often been engraved. It may be seen in Cicogna- 

 ra's Storia della Scoltura. 



ALGAROTTI, Francesco, count ; born at Venice, 

 1712 ; an Italian writer, who united the study of the 

 sciences with a cultivated taste forthe fine arts. He 

 studied at Rome, Venice, and Bologna. He was a 

 distinguished connoisseur in the fine arts, and ex- 

 celled in mathematics, astronomy, and natural philo- 

 sophy. He had a predilection for this last science, 

 as well as for anatomy, and devoted himself to them. 

 He was acquainted with the Latin and Greek 

 tongues. And paid great attention to the Tuscan 

 style and language. He visited France, England, 

 Russia, Germany, Switzerland, and all the important 

 towns of Italy. The last ten years of his life he 

 spent in his own country. When twenty-one years 

 old, he wrote at Paris, the greater part of his Neu- 

 tonianismo per le Dame, 1737, after the model of 

 Fontenelle's Plurality of Worlds, and thereby laid 

 the foundation of his fame. Until 1739, A. lived 

 alternately in Paris, at Cirey, with the marchioness 

 du Chatelet, and in London. At that time he made 

 a journey to Petersburg with lord Baltimore. On 

 his return, he visited Frederic II., then crown-prince, 

 and residing at Rheinsburg. The prince was so 

 much pleased with him, that, after his ascension to 

 the throne, he invited him to live with him, and 

 raised him to the rank of count He was not less 

 esteemed by Augustus III., king of Poland, who 

 conferred on him the office of privy-councillor. A. 

 now lived alternately at Berlin and Dresden, but 

 particularly in the former place, after receiving from 

 Frederic, in 1747, the order of merit and the office 

 of chamberlain. In 1754, he returned to his own 

 country, where he resided first at Venice, afterwards 

 at Bologna, and, after 1762, at Pisa. Here he died 

 of a consumption, 1764, after suffering long from 

 hypochondria. He himself formed the design of the 

 monument which Frederic II. caused to be erected 

 over his grave, in the court of the campo santo, at 

 Pisa. He was called, in the inscription, with refer- 

 ence to his Congresso di Citera, and his Nevtonia- 

 titmo, a rival of Ovid, and a scholar of Newton. 

 A.'s knowledge was extensive and thorough in many 

 departments. In painting and architecture, he was 

 one of the best critics in Europe. Many artists were 

 formed under his direction. He drew and etched 

 with much skill. In his works, which embrace a 



great variety of subjects, he shows much wit and 

 aculeness. His poems, though not of a very high 

 onler, an- pleasing, and his letters are considered 

 among the fiiiot. in the Italian language. The latest 

 collection of his works appeared at Venice, from 

 1791 to 1794, 17 vok 



A i t.t-.r.uA is a general method of resolving mathe- 

 matical problems by means of equations, or it is a 

 method of performing the calculations of all sorts o! 

 quantities by means of general -ins or character-. 

 Some authors define algebra as tin- art of resolving 

 mathematical problems; but this i- the idea of 

 analysis, or the analytic art in general, rather than 

 of algebra, which is only one species of it. In the. 

 application of algebra to the resolution of problems, 

 we must first translate the problem out of common 

 into algebraic language, by expressing all the condi- 

 tions and quantities, Loth known ana unknown, by 

 their proper characters, arranged in an equation, or 

 several equations, if necessary, and treating the un- 

 known quantity as if it were a known one ; lliis fonns 

 the composition. Then the resolution or analytic 

 part is the disentangling the unknown quantity from 

 the several others with which it is connected, so as 

 to retain it alone on one side of the equation, while. 

 all the known quantities are collected on the other 

 side, thus obtaining the value of the unknown. This 

 process is called analysis or resolution ; and hence 

 algebra is a species of the analytic art, and is called 

 the modern analysis, in contradistinction to the an- 

 cient analysis, which chiefly regarded geometry and 

 its application. The mode of applying algebra to 

 the resolution of problems may be seen in the follow- 

 ing example : If we wish, from the given difference 

 ot two numbers, and the difference of their squares, 

 to find the numbers themselves, then the algebraist 

 represents, in his language, the first of these differ- 

 ences by a, the second by 6, the unknown niimlx-rs 

 to be found by x and y, and marks the relation be- 

 tween the things given and those sought by the ex- 

 pressions x y = a, and x* y* = b. Then .r* 

 y, he continues to say in his language, = (K + y) 



(x y)- thus is a- -J- y=-J and hence, by addition 



b 4- aa , b aa . . , 



and subtraction, x = -~- , and y = ^ , which 



is then the general expression of this proposition. 

 For particular cases, we have only to substitute the 

 respective numbers instead of a and b, in order to 

 have immediately the corresponding values of x and 

 y. The oldest known work on algebra, tliat we 

 possess, is by Diophantus of Alexandria. (The best 

 edition of the works of this geometrician, who is 

 commonly supposed to have lived in the fourth cen- 

 tury, is that of Toulouse, 1670, folio, with a com- 

 mentary by Bachet, and notes by Fennat.) Europe, 

 however, owes its first acquaintance with this science, 

 not to the Alexandrian writer, but (as is the case 

 with much of its knowledge) to the Arabians, as, in- 

 deed, the name itself shows. The Arabians brought 

 their algebra to Spain, whence it found its way to 

 Italy. The state of this science at that time may be 

 learned from the work of Lucas de Burgo sancti 

 sepulchri, Summa Arithmetics et Geometric, Propor- 

 tionumyue et Proportionalitatum, Venice, 1494. Tar- 

 taglia of Brescia, Gardanus of Milan, and Ferrari of 

 Bologna, are highly distinguished names among the 

 Italian algebraists of this early period. In Germany, 

 also, the study of algebra was prosecuted in the first 

 half of the sixteenth century, of winch the work of 

 Mich. Stifel, professor of mathematics at Jena, 

 Arithmetica Integra cum pr<ef. Melanchthonis, !su- 

 remb. 1544, 4to, gives the most decisive proof. In 

 England, Recorde, in France, Peletarius, were dis- 



