they may have arisen from the observation of the naturally hollow sounds of concave bodies.

Q. Is not music in great repute?

A. It has ever been in the highest esteem in all ages and among all people; nor could authors express their opinion of it strongly enough, but by inculcating that it was used in heaven, and was one of the principal entertainments of the gods and the souls of the blessed.

Q. What are the effects of music?

A. It not only delightfully recreates the mind and gives it new vigour for business, but by it diseases are said to have been cured, seditions quelled, passions raised and calmed, and even madness occasioned.

MATHEMATICS.

Q. WHAT are mathematics ?

A. A science that contemplates whatever is capable of being numbered or measured.

Q. What is the etemology of the word?

A. It is derived from the Greek; and the original word [mathesis] signifies discipline or science; for this had the start of all other sciences, and the rest took their common name from it.

Q. How are mathematics divided ?

A. Into pure and mixed: the pure considers

quantity abstractedly, and without any relation to matter or bodies; the mixed is interwoven with physical considerations.

Q. Of what use is this science?

A. It opens and extends our ideas, strengthens and improves our understandings, fixes our attention, and, by teaching a habit of just reasoning, prepares us for all other kinds of study and every important employment of life.

Q. What are its principal branches?

A. Arithmetic, geometry, mcehanics, optics, astronomy, geography, chronology, and architecture.

ARITHMETIC.

Q. What is arithmetic ?

A. It is the science or knowledge of numbers, and has five principal rules for its operations, namely; numeration, addition, substraction, multiplication, and division.

Q. What does numeration teach?

A. To read or express the true value of any number of figures, written down, or named. Q. What does addition teach?

A. Addition teaches to collect several numbers or quantities into one sum; as 7 and 5 are 12, and 8 are 20.

Q. What does substraction teach P

A. It teaches to take a less number from a greater, and shows the remainder or difference. Q. What does multiplication teach?

A. It teaches to find a number, equal to any other taken, a proposed number of times, so that it is a compendous kind of addition.

Q. What is division?

A. It is the reverse of multiplication, and shews how often one number is contained in another.

Reduction, the rule of three, practice, interest, fellowship, the extraction of roots, &c. are no more than so many combinations of these five elementary rules.

Q. To whom is arithmetic necessary P

A. A knowledge of arithmetic is necessary to every one. It is the soul of commerce, and essentially necessary in every department of life.

OF COMMERCE.

Q. WHAT is commerce?

A. It is the exchanging of one thing for another, or the buying and selling of merchandise with a view of getting gain. It appears to be as ancient as the world; and at first consisted simply in exchanging things necessary for life. And

indeed this appears even now to be the state of commerce on the coast of Siberia, Russian and Norwegian Lapland, and among many of the Asiatic and African tribes, as well as those of America. Money was not, at that early period, known; nor is it now in use, as a medium of trade, among the people here mentioned.

Q. What nations have made themselves most famous in commerce.

A. The Phenicians, Egyptians, Carthaginians, Athenians, Rhodians, Romans, Gauls, Flemings ; and, in later times, the Venetians, Genoese, Dutch, and especially the British. The Americans, also are becoming a highly commercial people.

The Hanse Towns, once so famed for commerce, were a number of Europian cities joined together, in a league offensive and defensive against all enemies. Bremen, Lubec, Dantzic, Hamburgh, Amsterdam, Rotterdam, Antwerp, Bruges, Ostend, Dunkirk, Middleburg, Calais, Rouen, Bordeaux, St. Malo, Bayonne, Bilboa, Lisbon Seville, Cadiz, Carthagena, Barcelona, Marseilles, Leghorn, Naples, Messina, London, Rostac, Stralsund, Weimar, Konigsburg, Elbing, &c. were of the number.

GEOMETRY.

Q. What is geometry?

A. A science teaching the mensuration of quantity, extension, and magnitude; that is, of lines, surfaces, and solids.

The word is from the Greek, which signifies to measure the earth. It had its rise among the Egyptians, who were in a manner, compelled to invent it, to remedy the disorders occasioned by the annual inundations of the river Nile, which bore away the bounds and landmarks of their

estates.

Q. What is a line ?

A. A line is length only, having neither breadth nor thickness. It is supposed to be formed by the motion of a point; and is to be conceived as the limit of a surface, and not as a part of that surface, however small.

Q. What is a surface?

A. A surface, or superficies, is a magnitude extending in length and breadth, but without thickness or depth. It is produced by the motion of a line; and is chiefly considered as the external part of a solid.

Q. What is a solid ?

A. A magnitude endued with three dimensions, or extended in length, breadth, and depth. It is terminated or contained, under one or more