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Through any point k on the axis Op, draw lines parallel to AB. With distance kO as a radius and f as a center, draw an arc intersecting the line through k, thus locating a point on the parabola. Repeat for Oj, Oi, etc. com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. 41 A parabolic envelope. cones, etc. through the use of mathematical equations or formulas. Included here are the most frequently used and important mensuration formulas for the common geometric figures, both plane and solid.
Any use is subject to the Terms of Use as given at the website. 28 Circumference and radii proportionality. 29 Dividing a line equally. ■ To divide any straight line into any number of equal spaces (Fig. 29). To divide line AB into five equal spaces, draw line AC at any convenient angle such as angle BAC. With a divider or compass, mark off five equal spaces along line AC. Now connect point 5 on line AC with the endpoint of line AB. Draw line CB, and parallel transfer the other points along line AC to intersect line AB, thus dividing it into five equal spaces.
18 Quadrilateral (four-sided figure). 19 Tangent at a point on a circle. com) Copyright © 2004 The McGraw-Hill Companies. All rights reserved. Any use is subject to the Terms of Use as given at the website. Walsh CH02 8/30/05 9:11 PM Page 38 Mathematics for Machinists and Metalworkers 38 ■ Chapter Two Two circles’ common point of tangency is intersected by a line drawn between their centers (see Fig. 20). Side a ϭ a′; angle A ϭ angle A′ (see Fig. 21). Angle A ϭ 1⁄2 angle B (see Fig. 22). Angle A ϭ angle B ϭ angle C.