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In presenting this Translation to the Public, it will be only requisite to remark, that the principal cause of its appearance is owing to the want of such a publication, in order to combine the study of Euclid with Algebra; and the text of this great Prelate being the best adapted for such, has induced the Editor to adopt it. It would doubtless be of much advantage even in Classical learning, to commence these studies at an early age; as the mode of reasoning, and the application of the mental faculties required in learning Euclid and Algebra, expand the mind and give a freedom to thought, which clears the intellect for every other branch of learning. Geometry has been now taught for more than 2000 years, and considered, at all times, the foundation of Science, but its source is uncertain. The history of the rise of Geometry, supported by Diodorus, Strabo, and others, informs us that the Egyptians invented Surveying, for the purpose of preserving in memory the boundaries of their property, yearly destroyed by the overflowing of the Nile. The Jews appear to have been void of any knowledge of Geometry. Some writers tell us, that Pythagoras visited India; this, together with other reasons, induce many to form an opinion, that Geometry came from that country. Pythagoras, who was born about 568 years before the Christian era, was one of the earliest that formed Schools of Geometry; he also discovered the 47th Proposition of the First Book, and is said to have sacrificed 100 cattle for joy. Anaxagoras, born at Clazomene in Ionia, about 500 years before Christ, was an advancer of Science. He taught Philosophy at Athens, Socrates and Pericles, amongst others, were his pupils ; but being banished from that city, he retired to the school of his late master at Lampsacus, in which he taught until his death. The magistrates of the town demanded of him how they should honour him after his death, to this he replied that he wished only to be honoured, by the schools of Lampsacus yearly observing the day of his death as a holiday for the boys. The inh ants erected a tomb to his memory, with the epitaph,

Ενθαδε πλεισoν αληθειας επι τερμα περισας
Ουρανιου κοσμου, κειται Αναξαγορας.

Plato, who lived 348 years before Christ, was a great advancer of Science. He visited Egypt, and on his return opened a school at Athens, in a grove called the Academy, placing the following inscription over the entrance:

Ουδιες αγεωμετρητος, εισιτω. There is nothing known of Euclid's birth ; however, he had a school at Alexandria, in the time of the first Ptolemy, from which School, amongst others, eminated Archimedes, who was born in Syracuse about 280 years before Christ. Euclid reduced the fundamental principles of Geometry, which had been delivered by Geometricians before him, and added more of his own. Being asked by Ptolemy for an easy mode of acquiring Geometry, he replied that “ there was no royal road.” He well merited the Elements retaining his name, although it is evident that he was not the author of all under that title; yet even the compilation of such a work would be sufficient to deserve the praise he has received from all enlightened nations. Apollonius was cotemporary with Archimedes. The first Latin translation, from the Arabic, appears to have been in the reign of Henry I. by a monk of Bath, named ATHELARD.

From about the 10th century, the Astronomy, Philosophy, and Physic taught in Europe, were principally drawn from Arabian Schools that were established in Italy and Spain, or from Arabian Sages. Charlemagne who was crowned Emperor of Rome, A.D., 800, and died A.D., 814, laboured much to cultivate Science. In the 11th century, the school of Salernum, the chief-town of the Picentini, in Italy, was thought more of than any other, for the study of Physic; yet the medical precepts were drawn from the Saracen schools or the Arabian writers.

In this century, the seven liberal arts were as follow, GRAMMAR, RHETORIC, LOGIC, ARITHMETIC, Music, GEOMETRY, and ASTRONOMY ; the first three were called Trivium, and the Schools in which they were taught Triviales; the four last were called Quadrivium; they were also named the four Mathematical arts.

The First Book of Euclid gives the definitions, axioms, and postulates, requisite for establishing the propositions ; it treats of right lines, triangles, &c.

The 48 Pr ositions here set before us, should be wellgrounded in the memory of every student, before advancing a step beyond them, at the same time becoming acquainted with the Algebra, as set forth in this little volume.

The Second Book lays before us, the equality between squares and rightangled figures or squares constructed on the parts of any divided line, &c.

The Third Book treats of the properties of the circle.

With paying attention, and not stepping forward too quickly, until all going before is established in the mind, students will advance with pleasure and stability, finding that getting an idea of the utility of Algebra, at the same time, will save them much labour, at a future period of their education.

The word Algebra, is certainly derived from the Arabic. In that language the art is called, Al-gjabr W'al-makabala, which is literally, the art of Resolution and Equation ; therefore, it is probable, that we had the word from the Arabic name of the Art, and not from the philosopher Geber. It appears that the Arabians received it from the Persians and Indians ; but the Persians seem to refer the art to the Greeks ; however, its source is still disputed.

Dr. Isaac Barrow, Tutor to Sir I. Newton, was one of those who first introduced Algebraical symbols into Geometry. The sign v , which is derived from the letter r, being the initial of radix, or root, was first used to signify the square root, by M. Stifel; the signs + and also introduced by him, in the 16th century. The sign = was first used to denote equality, by R. Recorde, in a Treatise named The Whetstone of Witte, published in 1557; and the x was first used by Oughtrede, in 1631. This Mathematician is said to have died for joy, A.D., 1660, caused by the restoration of King Charles.

It would be indeed advantageous to youth to have this branch taught, combined with Arithmetic and Geometry; therefore, it is the earnest hope of the Editor of this Work, that he may yet see every school adopt such a plan of instruction; so that the higher classes, as well as the entrance course of our Universities, may bear the motto of Plato's school at Athens, before quoted; namely—“ Let no one ignorant of Geometry enter here.”


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