A. TREATIS E O F MENSURATION. PART I. Of lineal and angular Menfuration, or the Menfuration of Lines and Angles. A If SECTION I Geometrical Definitions and Problems. Line is a length conceived with- A out breadth, and is denoted c every part of a line be directed towards the fame place, it is called a right line, as AB; and if the parts continually vary their directions, it is a curve line, as CD. An angle is the mutual inclination of two lines which meet. A If If they be right lines, it is called a rectilineal or a plane angle, as A. If they be curves, it is a curvilineal angle, as B. If the angle be made by a right line and a curve, it is a mixt angle, as C. The point where the two lines, or legs of the angle, meet, is called the angular point, as D. B To exprefs an angle, it is fufficient to name the letter denoting the angular point, if no other angle have the fame angular point, as the angle D; but if there be more than one angle formed at the same point, it is common to exprefs the intended angle by the two letters which are at the ends of its legs with the letter denoting the angular point between them, as the angle GFE, or GFH. A right angle is that which is made by two lines meeting fo, that either of them being produced, the two angles made by it on cach fide of the other are equal to one another, as the angle GFH, or angle GFE. An acute angle is that which is lefs than a right angle, as MKL; and an obtufe angle is that which is greater than a right angle, as MKI.—These two are, alfo, called oblique angles. L K Perpen Perpendicular lines are those which make a right angle, as GF and EFH. The distance between any point and a line is a line drawn from that point perpendicularly to the linc. Parallel lines are thofe of which e- N very point of the one is at the fame diftance from the other, as NO, P P 2. N A fuperficies, or furface is an extention of two dimenfions, viz. length and breadth. A plane, or plane fuperficies, is that with which a right line may, every way, coincide. A plane fuperficies receives feveral denominations according to the number and pofitions of the lines by which it is terminated, as follows. A triangle is a fpace included by three lines, and of confequence hath three angles; for every rectilineal plane figure hath as many angles as fides. A right-angled triangle is that which has one right angle, as A. A. An oblique-angled triangle, is that which hath oblique angles only, as B, or C. An acute-angled triangle is that which hath acute angles only, as B. An obtufe-angled triangle is that which hath an obtufe angle, as C. An equilateral, or equal-fided, triangle, is that whose three fides are all equal to each other, as D. B An An ifofceles triangle is that which hath only two fides equal to each other, as E. A quadrangle, or quadrilateral, is a plane figure of four fides. A parallelogram is a quadrangle whofe oppofite fides are parallel. A rectangle is a right-angled parallelogram, as A. A fquare is a right-angled equilateral parallelogram, as C; or it is an equilateral rectangle. A rhombus is an oblique-angled equilateral parallelogram, as D. A rhomboides is an oblique-angled parallelogram, as B. B A C A A trapezium is a quadrangle both whose pairs of oppofite fides are not parallel. A trapezoid is a trapezium having two fides parallel and the other two inclined. A line drawn between the two oppofite angles of a quadrilateral, is called a diagonal, as GII. Plane figures of more than four fides are, in general, termed polygons, and receive their particular denominations from the number of their fides; so a pentagon is a polygon confifting of five fides, a hexagon of fix, a heptagon of feven, an octagon of eight, a nonagon of nine, a decagon of ten, an undecagon of eleven, and a duodecagon of twelve. If the angles, and of confequence the fides of a polygon, be all equal to each other, it is called a regular polygon: if not, it is irregular. D An equilateral triangle is alfo a regular figure of three fides, and a fquare is one of four; the former being alfo called a trigon, and the latter a tetragon. A circle is a plane figure bounded by a curve (ADBEĂ) called the circumference, every point of which is at the fame diftance from a cer- A tain point (C) within, called the center. The circumference itself is very often called the circle. B . B The |
