GEOMETRY, in its original sense, re lated simply to the measurement of the earth, and was invented by the Egypti ans, whose lands being annually inundat ed, required to be frequently measured out to the respective owners, so that each might repossess his property. It seems probable, that in the operations attendant on that act of justice, many discoveries were made relating to the properties of figures, which gradually led on to an extension of the science, and to the cultivation the arts of navigation and astronomy, which, indeed, first flou rished in that quarter. We are rather in the dark as to many improvements made in the infancy of geometry, and its at tendant speculations ; many tracts of sup posed value having been entirely lost, though some faint traces and fragments of their subjects, if not oftheir contents, have from time to time been discovered. The Grecians appear to have been enthu siasts in their reception of the new sci ence; accordingly we find that Males, Pythagoras, Archimedes, Euclid, &c. ex erted themselves to instruct their coun trymen, and thus to prepare the way for the philosophy of Ptolemy, Copernicus, and others of the ancient school ; and of Des Cartes, Leibnitz, and the immortal Newton, in our more enlightened times.
At present, geometry is justly considered to be the basis of many liberal sciences, and to be an indispensable part of the education of those who purpose exer cising even the more mechanical arts to advantage.
We shall submit to our readers a gene ral view of this most useful and fascinat ing attainment, and, by a gradual display of its rudiments, open the field to further advancement, which may be easily insur ed, by consulting those authors who have become eminent for the display of what ever relates to the superior branches of geometry. In the first instance, we shall submit the following definitions, as laid down by Euclid in his Elements, recom mending them to the serious attention of the student; they being absolutely ne cessary towards his competent apprecia tion and understanding of the succeeding propositions.