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Side 24 - A Circle is a plane figure bounded by a curve line, called the Circumference, which is every where equidistant from a certain point within, called its Centre. The circumference itself is often called a circle, and also the Periphery.
Side 33 - To describe the circumference of a circle through three given points, A, B, C. From the middle point B draw chords BA, BC, to the two other points, and bisect these chords perpendicularly by lines meeting in O, which will be the centre. Then from the centre O, at the distance of any one of the points, as ( ) A, describe a circle, and it will pass through the two other points B, C, as required.
Side 29 - From the given point A, to let fall a perpendicular on a. given line BC. From the given point A as a centre, with any convenient radius, describe an arc, cutting the given line at the two points D and E ; and from the two centres D, E, with any radius, describe two arcs, intersecting at F ; then draw AGF, which will be perpendicular to BC as required.
Side 38 - AB be the given line to be divided in extreme and mean ratio, that is, so as that the whole line may be to the greater part, as the greater part is to the less part. Draw BC perpendicular to AB, and equal to half AB. Join AC ; and with...
Side 38 - To Inscribe an Isosceles Triangle in a Given Circle, that shall have each of the Angles at the Base Double the Angle at the Vertex. DRAW any diameter AB of the given circle ; and divide the radius CB, in the point D, in extreme and mean ratio, by the last problem. From the point B apply the chords BE, BF, each equal to the greater part CD. Then join AE, AF, EF ; and AEF will be the triangle required.
Side 23 - A plane, or plane surface, is that to which a right line will every way coincide; but if not, it is curved. 21. Plane figures are bounded either by right lines or curves. 22. Plane figures, bounded by right lines, have names according to the number of their sides, or angles, for they have as many sides as angles — the least number is three.
Side 29 - OTHERWISE. When the given point C is near the end of the line. From any point D, assumed above the line, as a centre, through the given point C describe a circle, cutting the given line at E ; and through E and the centre D, draw the diameter EDF; then join CF, which will be the perpendicular required.
Side 34 - B to describe a Segment of a Circle, to Contain a Given Angle c. AT the ends of the given line make angles DAB, DBA, each equal to the given angle c. Then draw AE, BE, perpendicular to AD, BD ; and with the centre...
Side 25 - The Measure of an angle, is an arc of any circle contained between the two lines which form that angle, the angular point being the centre ; and it is estimated by the number of degrees contained in that arc.