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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 inhabitants erected a tomb to his memory, with the epitaph

Ενθαδε πλείσον αληθείας επι τέρμα περησας

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 :

Ουδείς αγεωμέτρητος εισίτω.

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, emanated 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 contemporary 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 tenth 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 eleventh 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 that century, the seven liberal arts were as follows:-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 called 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 Forty-eight Propositions here set before us should be well grounded 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 publication.

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

The Third Book treats of the properties of the circle.

The Fourth Book treats of such regular figures as can be described by a circle; and also of the division of the circumference of a circle into equal parts.

The Fifth Book treats of proportion; and the Sixth Book applies it to Geometry, relating to figures which differ only in


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 more advanced 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. The portion of Algebra here attached to each book will be found to embrace and simplify all obstructions which usually retard the progress of students. WE trust that the Arithmetical and Algebraic proofs of Euclid's Second Book will be found of considerable advantage.


Dr. Isaac Barrow, Tutor to Sir I. Newton, was one of those who first introduced Algebraical symbols into Geometry. The sign 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 were also introduced by him, in the sixteenth 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 (as many have adopted) 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." Indeed we have received the assurance, from many quarters, that pupils have made more advancement when taught according to the system here laid down than in any other way.

The Compendium of Trigonometry, following the Sixth Book, has been designed, as much as possible, to introduce the Student to the more advanced investigations of that useful Science.

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