GEOMETRY, originally signified no more than the art of measuring the earth, or any distance or dimensions in it; but at present it denotes the science of magnitude in general; comprehending the doctrine and relations of whatever is susceptible of augmentation or diminution, considered in that light. Hence, to geometry may be referred the consideration not only of lines, surfaces, and solids; but also of time, velocity, number, weight, &c.
Plato thought the word geometry an improper name for this science, and accordingly substituted in its place the more extensive one of mensuration; and after him, others gave it the name of pantometry, as demonstrating not only the quantities of all manner of magnitudes, but also their qualities, ratios, positions, transformations, relations, &c. and Proclus calls it the knowlege of magnitudes and figures, and their limitations; also of their motions and affections of every kind.
Origin and progress of Geometry. This science had its rise in Asia, the invention, which at first consisted only in measuring the lands, that every person might have what belonged to him, was called geometry, or the art of measuring land; and it is probable, that the draughts and schemes which they were annually compelled to make, helped them to discover many excellent properties of these figures; which speculation has continued gradually to improve to this day.
From Asia it passed into Egypt, and thence into Greece, where it continued to receive improvement from Thales, Pythagoras, Archimedes, Euclid, &c. The elements of geometry, written by Euclid in 15 books, are a most convincing proof to what perfection this science was carried among the ancients. However, it must be acknowleged, that it fell short of modern geometry, the bounds of which, by the inventions of fluxions, and the discovery of the almost infinite order of curves are greatly enlarged.
Division of Geometry. This science is usually distinguished into elementary, and higher or sublime geometry. The first, or elementary geometry, treats of the properties of right lines, and of the circle, together with the figures and solids formed by them. The doctrine of lines comes first, then that of surfaces, and lastly that of solids. The higher geometry comprehends the doctrine of conic sections, and numerous other curves.
Speculative and practical Geometry. The former treats of the properties of lines and figures, as Euclid’s Elements, Apollonius’s Conic Sections, &c. and the latter shews how to apply these speculations to the use of mensuration, navigation, surveying, taking heights and distances, gauging, fortification, gunnery, &c.
Usefulness of Geometry. Its usefulness extends to almost every art and science. By the help of it, astronomers turn their observations to advantage: regulate the duration of times, seasons, years, cycles, and epochs; and measure the distance, motion, and magnitudes of the heavenly bodies. By it geographers determine the figure and magnitude of the whole earth; and delineate the extent and bearings of kingdoms, provinces, harbors, &c. It is from this science also that architects derive their just measure and construction of public edifices, as well as of private houses.
It is by the assistance of geometry that engineers conduct all their works, take the situation and plans of towns, the distances of places, and the measure of such things as are only accessible to the sight. It is not only an introduction to fortification, but highly necessary to mechanics. On geometry likewise depends the theory of gunnery, mining, music, optics, perspective, drawing, mechanics, hydraulics, pneumatics, &c.
We may distinguish the progress of geometry into three ages; the first of which was in its meridian glory at the time when Euclid’s Elements appeared; the second beginning with Archimedes, reaches to the time of Descartes; who by applying algebra to the elements of geometry, gave a new turn to this science, which has been carried to its utmost perfection by our learned countryman Sir Isaac Newton, and by the German philosopher Leibnitz.
GEORGE, or knight of St. George, has been the denomination of several military orders. See [Garter].