Use and Explanation of Characters. THE characters or figns used, for fake of brevity, in the following treatise, and thofe ufed by others, fignify the fame. that the phrases or words do which are here annexed to them. O cipher; 1 one; 2 two; 3 three; 4 four; 5 five; 6 fix; 7 feven; 8 eight; 9 nine; Signs, fignifications, is equal to, or make; + added to, or add ; explanations. as, 1 $ = 100 cents, i.e. 1 S is e qual to 100 cents. as, 5+5=10, i.e. 5 added to 5 is equal to 10. or- - subtracted from,or take; as, 3 -5= 2, i.e. 3 fubtracted from 52. from 5-3=2. Xorx multiplied by, or times; as, 3 x 2, or 2 x 3=6, ie. 3 times 2 or 3 multiplied by 2= 6. as, 623, i.e. 6 divided by 2 divided by: 3. 2 4,5 or 6:2, 2)6(3.2÷4. =,5. geometrical proportion; as, 2:4:3: 6, i.e. as 2 is to 4 fo is 3 to 6. ..::.. arithmetical proportion; as, 2..4:3..5, ie. 2 is to 4 as 3 to 5 arithmetically. 42 or 42 Square (of 4) required; as, 4 (4x4) 16. 274. 82-8 x 8. 23 or 23 cube (of 2) required; as, 23-(2x2x2)8.64. m 3 11 3 x 3 x 3 er 27. 2th or 2" any power (of2)required; as, 22 x 2, 22 x 2 x 2, or 2 24 —2 x 2 x 2 x 2, &c. 2 24, 1/4, 1/4 or square root of 4)required; as, 4-2. √9 3 3. 164. 225-5. 3 as, 8=2. 82. 38, V8 or cube root (of 8) required; as, 8 274 =3. 8,8 or 8m any root (of 8) required; as, '8, or 8, or 48,&c. B The number with the fign or figure prefixed is accounted the expreffion of the root or power required, and is equivalent thereto. The character prefixed to the number is called the radical fign and the figure the index. A root is the first term and ratio of a geometrical progreffion, its products are powers or terms. 5 Tvinculum, or connexion of the numbers over which it is drawn; as 5-21=4, i.e. the difference between 5 and 2 added to 1 =4. 5 - + 2 =2, i.e. the fum of 2 and 1 fubtracted from 5-2. 82 x 4-16, 82x4=1. y equality. A anfwer,or refult. +" addition. -g fubtracting. --- remainder. Xd multiplied. Xr multiplier. e divide. ÷n divifion. qt quotient. When the above figns are to reprefent the plural number, s is commonly added ; as, As for answers, xrs, &c, Geometrical Definitions. Contents, is the quantity of matter, substance, weight, or what is comprised within fides, lines or points. Sides are the edges or lines of a furface, or faces of a folid. Mean area, length, breadth, &c. is the area, length, &c. reduced to a medium, or such as the figure will bear from end to end or from fide to fide, without enlarging or depreciating its fize. A point is a small mark or end, without dimenfions; as · Dimenfions are the limits of the contents,& called lines; el A line is the distance between two points, and has length only; a right line is the shortest distance between two points, as, Parallel lines are right lines equally distant from each other in all places; A curved or arched line is a line bending between two points; fo if continued will enclose a circular plane; O A plane or jurface of any kind has two dimensions, length which is its greatest mean extenfion, and breadth its leaft; its contents is called area; a plain is a flat or level figure ; and a surface is the outfide of any thing. A figure is the fhape or image of any thing, and is confidered either as a furface or folid. A folid or body has three dimensions, length, breadth and thickness, its contents is called folidity; a A circle is a round figure, whofe circumference or periphery, which is the curve line or bounda ry, is confidered as being divided into 360 degrees or equal parts, each of these into 60 minutes, &c. 60 degrees is the distance from the centre or middle to the periphery, and is called the radius or femidiameter; as a c, double this is the diameter; as, a ab. An arch or arc is any part of the circumference of a circle; as, ali, or a a d. A chord is a right line drawn from one end of an arch to the ai. other; as, a k A fine is half the chord of an arch; as, gb is the fine of the arch gb. A verfed fine is that part of the radius which is contained between the fine and circumference; as, bh. A tangent is a right line raifed perpendicularly on one end of the diameter, and is terminated by a line drawn from the centre through the other end of the arch, which is called, A fecant; as bk is the tangent and ck the fecant of the arch bg. The complement of an arch is what it wants of 90 degrees or of a circle; as, dg is the complement of the arch bg. The Jupplement of an arch is what the arch wants of 180 degrees or of a circle; as adg is the fupplement of the arch gb. The fine, tangent or fecant of the complement of an arch is called the co-fine co-tangent or co-fecant of the arch; as, fg is the co-fine, de the co-tangent and ce the co-fecant of the arch gb or they are the fine, tangent and fecant of the arch dg. The fine, tangent or fecant of an arch is alfo the fine, tangent or fecant of an angle containing the fame number of degrees, |