other; therefore the inscribed figure, m e o n, is a paralleic gram. It may be remarked also, that the parallelogram so formed will contain just one-half the area of the circumscribing quadrangle. These demonstrations, which relate mostly to the problems previously given, are introduced to satisfy the learner in regard to their mathematical accuracy. By studying and thoroughly understanding them, he will soonest arrive at a knowledge of their importance, and be likely the longer to retain them in memory. Should he have a relish for such exercises, and wish to continue them farther, he may consult Euclid's Elements, in which the whole subject of theoretical geometry is treated of in a manner sufficiently intelligible to be understood by the young mechanic. The house-carpenter, especially, needs information of this kind, and were he thoroughly acquainted with the principles of geometry, he would be much less liable to commit mistakes, and be better qualified to excel in the execu tion of his often difficult undertakings. SECTION JI.-ARCHITECTURE, HISTORY OF ARCHITECTURE. 168.-Architecture has been defined to be-"the art of build ing;" but, in its common acceptation, it is" the art of designing and constructing buildings, in accordance with such principles as constitute stability, utility and beauty." The literal signification of the Greek word archi-tecton, from which the word architect is derived, is chief-carpenter; but the architect has always been known as the chief designer rather than the chief builder. Of the three classes into which architecture has been divided-viz., Civil, Military, and Naval, the first is that which refers to the construction of edifices known as dwellings, churches and other public buildings, bridges, &c., for the accommodation of civilized man--and is the subject of the remarks which follow. Cain, 169. This is one of the most ancient of the arts: the scriptures inform us of its existence at a very early period. the son of Adam,-"builded a city, and called the name of the city after the name of his son, Enoch"--but of the peculiar style or manner of building we are not informed. It is presumed that it was not remarkable for beauty, but that utility and perhaps stability were its characteristics. Soon after the deluge--that me morable event, which removed from existence all traces of the works of man-the Tower of Babel was commenced. This was a work of such magnitude that the gathering of the materials, according to some writers, occupied three years; the period from its commencement until the work was abandoned, was twentytwo years; and the bricks were like blocks of stone, being twenty feet long, fifteen broad and seven thick. Learned men have given it as their opinion, that the tower in the temple of Belus at Baby lon was the same as that which in the scriptures is called the Tower of Babel. The tower of the temple of Belns was square at its base, each side measuring one turlong, and consequently half a mile in circumference. Its form was that of a pyramid and its height was 660 feet. It had a winding passage on the outside from the base to the summit, which was wide enough for two carriages. 170.--Historical accounts of ancient cities, of which there are now but few remains such as Babylon, Palmyra and Ninevah of the Assyrians; Sidon, Tyre, Aradus and Serepta of the Phonicians; and Jerusalem, with its splendid temple, of the Israelites -show that architecture among them had made great advances, Ancient monuments of the art are found also among other nations! the subterraneous temples of the Hindoos upon the islands, Elephanta and Salsetta; the ruins of Persepolis in Persia; pyramids, obelisks, temples, palaces and sepulchres in Egypt-all prove that the architects of those early times were possessed of skill and judgment highly cultivated. The principal characteristics of their works, are gigantic dimensions, immoveable solidity, and, in some instances, harmonious splendour. The extraordinary size of some is illustrated in the pyramids of Egypt. The largest of these stands not far from the city of Cairo: its base, which is square, covers about 11 acres, and its height is nearly 500 feet The stones of which it is built are immense-the smallest being full thirty feet long. 171.--Among the Greeks, architecture was cultivated as a fine art, and rapidly advanced towards perfection. Dignity and grace were added to stability and magnificence. In the Doric order, their first style of building, this is fully exemplified. Phidias, Ictinus and Callicrates, are spoken of as masters in the art at this period: the encouragement and support of Pericles stimulated them to a noble emulation. The beautiful temple of Minerva, erected upon the acropolis of Athens, the Propyleum, the Odeum and others, were lasting monuments of their success. The Ionic and Corinthian orders were added to the Doric, and many magnificent edifices arose. These exemplified, in their chaste proportions, the elegant refinement of Grecian taste. Improvement in Grecian architecture continued to advance, until perfection seems to have been attained. The specimens which have been partially preserved, exhibit a combination of elegant proportion, dignified simplicity and majestic grandeur. Architecture among the Greeks was at the height of its glory at the period immediately preceding the Peloponnesian war; after which the art declined. An excess of enrichment succeeded its former simple grandeur; yet a strict regularity was maintained amid the profusion of ornaAfter the death of Alexander, 323 B. C., a love of gaudy splendour increased: the consequent decline of the art was visible, and the Greeks afterwards paid but little attention to the science. ment. 172. While the Greeks were masters in architecture, which they applied mostly to their temples and other public buildings, the Romans gave their attention to the science in the construction of the many aqueducts and sewers with which Rome abounded; building no such splendid edifices as adorned Athens, Corinth and Ephesus, until about 200 years B. C., when their intercourse with the Greeks became more extended. Grecian architecture was introduced into Rome by Sylla; by whom, as also by Marius and Cæsar, many large edifices were erected in various cities of Italy. But under Cæsar Augustus, at about the beginning of the christian era, the art arose to the greatest perfection it ever at tained in Italy. Under his patronage, Grecian artists were encouraged, and many emigrated to Rome. It was at about this time that Solomon's temple at Jerusalem was rebuilt by Heroda Roman. This was 46 years in the erection, and was most pro bably of the Grecian style of building-perhaps of the Corinthian order. Some of the stones of which it was built were 46 feet long, 21 feet high and 14 thick; and others were of the astonishing length of 82 feet. The porch rose to a great height; the whole being built of white marble exquisitely polished. This is the building concerning which it was remarked--" Master, see what manner of stones, and what buildings are here." For the construction of private habitations also, finished artists were employed by the Romans: their dwellings being often built with the finest marble, and their villas splendidly adorned. After Augustuis, his successors continued to beautify the city, until the reign of Constantine; who, having removed the imperial residence to Constantinople, neglected to add to the splendour of Rome; and the art, in consequence, soon fell from its high excellence. Thus we find that Rome was indebted to Greece for what she possessed of architecture-not only for the knowledge of its principles, but also for many of the best buildings themselves; these having been originally erected in Greece, and stolen by the unprincipled conquerors-taken down and removed to Rome. Greece was thus robbed of her best monuments of architecture. Touched by the Romans, Grecian architecture lost much of its elegance and dignity. The Romans, though justly celebrated for their scientific knowledge as displayed in the construction of their various edifices, were not capable of appreciating the simple grandeur, the refined elegance of the Grecian style; but sought to improve upon it by the addition of luxurious enrichment, and thus deprived it of true elegance. In the days of Nero, whose palace of gold is so celebrated, buildings were lavishly adorned. Adrian did much to encourage the art; but not satisfied with the simplicity of the Grecian style, the artists of his time aimed at |