MEMBER (from the French) any part of an edifice ; or any moulding in a collection.
hi ENSURATION (from the Latin mensura, measure ment) that branch of mathematics which is employed in ascertaining the extension, solidities, and capacities of bodies ; and in consequence of its very extensive to the various purposes of life, it may be considered as one of the most useful and important of all the mathematical sciences: in fact, mensuration, or geometry, which were anciently nearly synonymous terms, seem to have been the root whence all the other exact sciences, with the exception of arithmetic, have derived their origin.
As soon as men began to form themselves into society, and direct their attention towards the cultivation of the earth, it became as necessary to have some means of distinguishing one person's allotment from another, both as to position and quantity, as it did to enumerate the number of their flocks and herds ; and hence, in all probability, the former gave rise to the science of mensuration. as the latter did to that of arithmetic; and though we may easily imagine that each of them remained for ages in a rude uncultivated state, yet it is from this period that we must date their commencement ; and therelUre, to state the precise time when they were discovered, or by whom they were first introduced, would he to trace out the origin of society itself': on this head, therefore, we shall barely observe, that in all probability they first arose from the humblest efforts of unassisted genius, called forth by the great mother of invention, necessity ; and that they have since grown up by slow and imperceptible degrees, till they have at length acquired the dignity of the most perfect sciences; as the acorn which is first accidentally sown in a field, is in due course of time converted into the majestic oak But notwithstanding we cannot attribute the invention of the science of mensuration to any particular person or yet we may discover it in an 'Mita state, rising, as it were, into a scientific form, amongst the ancient Egyptians; and hence the honour of the discovery has frequently. been given
to this people, and to the circumstance of the overflowing of the Nile, which takes place about the middle of June, and ends in September. It is, however, to the Greeks that we must consider ourselves indebted for having first embodied the leading principles of this art into a regular system. Euclid's Elements of Geometry were probably first wholly directed to this subject; and many of those beautiful and elegant geometrical properties, which are so much and so justly admired, it is not unlikely, arose out of simple investi gations directed solely to the theory and practical application of mensuration. These collateral properties, when once dis covered, soon gave rise to others of a similar kind ; and thus geometry, NI hick was first instituted for a particular and limited purpose, became itself an independent and important science, which has perhaps done more towards harmonizing and expanding the human faculties, than all the other sciences united.
But notwithstanding the perfection which Euclid attained in geometry, the theory of mensuration was not in his time advanced beyond what related to right-lined figures; and this, so far as regards surfaces, might all be reduced to that of measuring a triangle; fer as all right-lined figures may be reduced to a number of trilaterals, it was only necessary to know how to measure these, in order to find the surface of any other figure whatever bounded only by right lines. The mensuration of solid bodies, however, was of a more varied and complex nature, and gave this celebrated geometrician a greater scope fJr the exercise of his superior talents, and, still confining himself to bodies bounded by the right-lined plane superfieies, he was able to perfiirm all that can be done even at this day. With regard to curvilinear figures, he attempted only the circle and the sphere, and it' he did not succeed in those, he filled only where there was no possibility of success ; but the ratio that such surfaces and solids have to each other he accurately determined.