MEASURING OF St'lERFICIES, or quantities of two dimen• si)(ns, is variously delunninated according to its subjects: when lands are the subject, it is called geodesy, or Sixineying; in other cases, simply measuring. The instruments used arc the ten-foot rod, chain. compass, circumferentor, &e.
MEasunixo OF SOLIDS, or quantities of three dimensions. is called sit', eometry ; but where it relates to the capacities of vessels, lir the liquors they C(litairy particularly. gullyig, The instruments for this art are the ganging-rod, sliding. rule, &c.
From the definition of measuring, where the measure is expressed to be siniiiar or homogeneous to. i. e. of the same kind with, the thing measured, it is evident.that, in the first case, or in quantities of one dimension, the measure must be a line; in the second, a superfieies ; and in the third, a solid. For example, a line cannot measure a surface; the art of measuring no more than the of a known quantity to the unknown, till the two become equal. Now a surface has breadth, and a line has maw ; and if one lin( have no breadth. two or a hundred have none. A line therefore, can Dever be applied so to a surfice as to I)( equal to it, i. e. to measure it. And from the like reasoning
it is evident, a supelli•ies, y. hich has no depth, cannot become equal to, i.e. cannot measure, a solid which has.
\Vhile a line continues such, it may he measured by any part ()I' itself; but w hen the line [iegins to flow, and tr generate a new dimension. the measure must keep pace, :1111: flow too ; i. e. as the one commences superficies, the ()the: must do so too. Thus we come to have square measures, am: cubic. measures.
Ilence we see why the measure of a circle is an arc oi part of the circle, for a right line can only touch a circle it one point, but the periphery of a circle consists of infinit( points. The right 11110, Illerer“re, to measnre the circle must lie applied infinite times, which is impossible. Again the right line only touches the circle in a mathematical point, no parts nor dimensions, and has consequently no nuomitude; but a thing that has neither magnitude nor dimensions bears no proportion to another that has, and cannot therelbre measure it. we see the reason of the division of circles into IlIGO parts or arcs, called degrees.
Ste A RC. CIRCLE, alld ENSCRATION.