B

The Conversing Statue.

E

H

423. Place a concave mirror, (made of tin or gilt pasteboard, and about two feet in diameter,) in a perpendicular direction, as A B in the foregoing figure. At the distance of five or six feet, let there be a partition, in which there is an opening EF, equal to the size of the mirror; and in this opening let a thin linen cloth, be placed, on which a picture is painted. This painting being in water colours, the sound will easily pass through.

Behind the partition, at the distance of two or three feet, place another mirror G H of the same size as the former; and let both be exactly opposite to each other. At the focus C*, of the mirror A B, let the ear of the figure of a man seated on a pedestal, be placed. The lower jaw of the figure must be made to open by a wire, and shut with a spring; and there must be another wire connected with the eyes, so as to give them motion and expression. These wires are.» to pass through the figure, under the floor, and be brought up behind the partition.

Let a person, properly instructed, be placed behind the partition, on the contrary side to where the statue is placed; and then propose to any person present, to put questions to the statue, by putting his mouth to its ear, and whispering softly; assuring the person that it will answer instantly. Now give a signal to the confederate behind the partition, who, by placing his ear in the focus I, of the mirror G H,

*The focus of each mirror is about the distance of from fifteen to eighteen inches.

will hear distinctly what the other said; and moving the eyes and jaws of the statue by the wires, will return an answer directly, which will in like manner be heard distinctly by the first speaker.

The statue may be made of wood, or plaster of Paris, and should be drest, as in the figure, in a man's habit. The mirrors may be fixed in the walls of a room at a proper distance from each other, and, in order to hide them from the view, they may be covered by a cambric handkerchief, as this thin covering does not in the least impede the sound.

CHAPTER XIX.

ALGEBRA.

424. ALGEBRA (Arabic, of uncertain derivation, but probably from al and geber, which signifies the reduction of fractions to a whole number) is a peculiar kind of arithmetic, for the solution of questions by means of numeral or literal equations.

The earliest treatise on algebra, which has come down to the present time, is that of Diophantus, of Alexandria, in Egypt, who flourished in the middle of the fourth century after Christ, and wrote a work on this subject in the Greek language, consisting originally of thirteen books, though, unfortunately for the interests of science, only the first six are now extant.

Other works on the subject, of a more easy and elementary kind, must, however, have existed long before the time of Diophantus, since he no where treats of the leading rules, as a writer in the infancy of the art would have done. Whether we are indebted for this admirable invention to the genius of the Greeks, as has hitherto been thought, or to that of some other ancient nation, cannot at this distance

of time be easily ascertained; though from the information which for more than a century past has been gradually obtained through our intercourse with the East, there are strong reasons for believing that algebra, as well as our common system of arithmetic, originated among the Hindoos, or natives of India, who are known to possess some valuable works on the subject, containing rules and principles apparently not derived from any foreign source.

We are in possession of two celebrated works of Indian algebra, called the Beja Ganita and the Lilavati, the first of which treats wholly on algebra, and the latter on arithmetic, algebra, and mensuration, both written in the Sanscrit dialect and character, about the end of the twelfth, or beginning of the thirteenth century of the Christian era.

But, not to dwell upon this part of the subject, which, it must be confessed, is still attended with some obscurity, it is well known that, in whatever age or country algebra was first invented, both the name and the science was first made known to us, about the end of the eleventh century, by the Arabians, or Moors, who were settled in Spain. Algebra was introduced into Italy by Leonardus Bonacci, commonly called Leonard of Pisa, an Italian merchant, in the beginning of the thirteenth century: after this many manuscript treatises appeared in Italy; but the first printed works on this subject are those of Lucas Pacciolus, or Lucas de Burgos, in the years 1470, 1476, 1481, and 1494.

Hitherto the science had advanced no farther than quadratic equations; the passage indeed to the higher orders was a matter of considerable difficulty, for a general method for extracting their roots in species has not even yet been accomplished, nor in all probability will the value of the unknown quantity be ever generally expressed according to any given degree in algebraic formulæ, though those of

numerical equations of every order may now be accurately found by the principles generally exhibited.

Soon after the publication of Lucas de Burgos, Scipio Ferreus, a professor of mathematics at Bologna, in Italy, first discovered, about the year 1505, a rule for resolving one of the cases of cubic equations; and, about thirty years afterwards, one, of his disciples, of the name of Florido, to whom he had shown his method, having proposed several questions depending on this formula, to Nicholas Tartalea, by way of challenge, Tartalea not only discovered the rule for resolving them, but also those for some other cases.

Tartalea communicated his discovery to the celebrated Cardan, who published, in the year 1539, a very complete treatise on arithmetic and algebra, in nine books, in the Latin language, at Milan; and in a new edition of the same performance, printed in 1545, he gave a tenth book, containing the whole doctrine of equations, which had been chiefly revealed to him by Tartalea, under an oath of secrecy, about the time of the publication of the first nine books.

The resolution of certain cases of equations of the fourth order very soon followed that of equations of the third; a discovery for which we are indebted to Louis Ferrari, a young man of great talents, and one of the disciples of Cardan.

After the publication of Cardan's work, Tartalea also published a work on algebra; but it contained nothing remarkable, except his rules for the resolution of cubic equations.

About the same time that Cardan and Tartalea flourished in Italy, the science of algebra began to be cultivated in Germany; particularly by Stifel, who first employed the characters, +, -, v, for plus, minus, and root, as also the numerical indices, for powers as far as regards integral numbers. He

likewise used the literal notation, A, B, C, D, for different unknown quantities.

A few years after the appearance of these in Italy and Germany, Robert Recorde proved by his writings, published at Cambridge, 1557, that algebra was not altogether unknown in England at that time.

Raphael Bombelli, of Bologna, who published a treatise on this subject in 1572, not only improved · the notation, but the science itself.

A very ingenious treatise was published on arithmetic and algebra, in the Flemish dialect, in 1605, by Simon Steven, of Bruges, who greatly improved the notation of powers first given by Stifel for integral exponents and extended them also to frac tional exponents.

But it is chiefly to the celebrated Vieta, whose algebraic works were written about the year 1600, though not printed till after his death, which happened in 1603, that we are indebted for having first. generalized the algorithm of the science, and enriched it far beyond what his predecessors had done, by many new discoveries.

We have already mentioned that Stifel first introduced the capital letters for unknown quantities; but Vieta employed the same letters to denote all quantities, whether known or unknown: he was the first that introduced a general method for extracting their roots by a process similar to that of extracting the roots of pure powers; his method is commonly known by the name of the Numeral Exegesis.

Next after Vieta may be recorded Albert Girard, an ingenious mathematician of the Low Countries. Among the most distinguished analysts of this period, we may reckon our countryman, the celebrated Harriot, who, in his Artis Analyticæ Praxis, published by his friend Walter Warner, first introduced the use of the small letters, a, b, c, &c. of the alphabet, using the consonants for known, and the vowels