7*40
THEORY AND PRACTICE OF ENGINEERING.
Book II.
with its inner face : if the other be applied to the edge ofthe drawing board, the former, with the blade, can be turnedon the screw as a centre to any angle; the screw beingthen tightened, parallels forming that angle with the sideof the board can be drawn ; and, if applied to an adjoiningside, the blade will be at a right angle to its first position ;these bevel squares are exceedingly useful to architecturaldraughtsmen and engineers.
An Obtuse Angle is greater than a right angle, and con-tains more than a quarter of a circle or 90 degrees; theangle III K exceeds the angle LIK, or that of the quarterof a circle described from I as a centre.
The magnitude of an angle does not depend on the linesby which it is formed, but, as has been observed, upon theirdistance from each other; the obtuse is therefore greater thanthe acute, in consequence of the lines which constitute itbeing farther apart, or diverging more than those of theacute: the legs of a pair of compasses may be made toexhibit this; when separated but little, we have an acuteangle, and opened more and more we obtain the obtuse,the rule joint upon which the limbs move being consideredthe point cf the angle.
When a point of the compasses is applied to N, anda circumference described, the arc contained between, thelines which diverge from the centre, as M and P, serve tomeasure the angle.
An Acute Angle is less than a right angle, as M N O, be-cause also it is less than a quarter circle or 90 degrees.
A Right-angled Triangle has two sides at 90 degreesfrom each other, and the line which unites them is calledthe hypothenuse, as K L.
An Obtuse-angled Triangle is that which has its anglegreater than a right one.
An Acute-angled Triangle is that which has its angle lessthan a right angle: consequently an equilateral triangleis acute; in general every triangle has two acute angles.
The triangle NOP is obtuse angled; A B C an equi-lateral triangle : 11QS an isosceles triangle ; FE D a rightangle ; and LMKa scalene triangle.
Rectilinear Figures arc those which are contained orbounded by right lines, as TKLM.
In the square the right lines which form the sides fallupon parallel lines, and make the alternate angles equal, andthe lines being perpendicular to one of the two which arcparallel, it necessarily follows it must be so to the other.In a quadrilateral figure the surface is comprised withinfour equal right lines, which are called its sides, with all itsangles right ones.
Curvilinear Figures are such as are bounded by curvedlines, as NOP.
A plane figure contained by one line, called the circum-ference, is such that all straight lines drawn from thecentre to it are equal to one another. The straight lineand the circle are the only figures admitted into plane orelementary geometry, all questions in mathematics dependingon the intersections of straight lines with straight lines,straight lines with circles, or of circles with circles. Allfigures are formed bv the intersections of planes with solids,and are termed problems, for the understanding of whichit is necessary to have them bounded by straight lines andcircles. The circle is a very important figure in trigonometryor the measurement of angles, and the ratio that the cir-cumference bears to the diameter is a calculation that longexercised the heads of the learned: in the two concentriccircles of the figure, their relative circumferences are in pro-portion to their diameters, as N O and P.
u
Fig. 646.
Fig. 647,
Fig. 649.
Fig. 660.
Fig. 651.L
K T
Fig. 652.
0
J
\