ISBN 10: 1236437853 / ISBN 13: 9781236437853
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Inhaltsangabe: This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 Excerpt: ... that is, the radius of the inscribed circle. Cor.--When the number of sides of the polygon is indefinitely increased, it becomes a circle, and the radius of the inscribed circle, which has been increasing as the number of sides increased, is now the radius of the circle, and the perimeter of the polygon is the circumference of the circle; hence, the area of a circle is equal to its circumference multiplied by one-half its radius. BOOK Y. THEOREM 1. When the distance between the centers of two circles is greater than the sum of their radii, they are external, and the straight line joining their centers will be the shortest distance between the center of either cifcle and the circumference of the other; and if this line be extended to the concave arcs of both circles, it will be greater than between any two other points in the circumference. Let C and C be the centers of two circles external to each other; CB is the shortest distance from C to any point in the circumference C; for, let the tangents DE and D-E-be drawn at B and A-, they will be perpendicular to CC; and as a perpendicular is the shortest distance from a point to a line, CB is the shortest distance from C to the tangent DE, and any other line from C to the circumference is oblique to the line DE, and must go beyond it before it can reach the circumference. 2. CA is longer than any other line drawn from C to the circumference C, as CF. Draw the chord BF; BF is less than AB a diameter; hence, THEOREM 11. When the distance between the centers is equal to the sum of the radii, they are tangents externally, and the straight line joining their centers passes through the point oftangency. They must touch on the line joining their centers, as CD + DC = CC; let D be this point, and through D draw AB per...

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Andrew H. Baker
Verlag: RareBooksClub
ISBN 10: 1236437853 ISBN 13: 9781236437853
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Buchbeschreibung RareBooksClub. Paperback. Buchzustand: New. This item is printed on demand. Paperback. 26 pages. Dimensions: 9.7in. x 7.4in. x 0.1in.This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1878 Excerpt: . . . that is, the radius of the inscribed circle. Cor. --When the number of sides of the polygon is indefinitely increased, it becomes a circle, and the radius of the inscribed circle, which has been increasing as the number of sides increased, is now the radius of the circle, and the perimeter of the polygon is the circumference of the circle; hence, the area of a circle is equal to its circumference multiplied by one-half its radius. BOOK Y. THEOREM 1. When the distance between the centers of two circles is greater than the sum of their radii, they are external, and the straight line joining their centers will be the shortest distance between the center of either cifcle and the circumference of the other; and if this line be extended to the concave arcs of both circles, it will be greater than between any two other points in the circumference. Let C and C be the centers of two circles external to each other; CB is the shortest distance from C to any point in the circumference C; for, let the tangents DE and D-E-be drawn at B and A-, they will be perpendicular to CC; and as a perpendicular is the shortest distance from a point to a line, CB is the shortest distance from C to the tangent DE, and any other line from C to the circumference is oblique to the line DE, and must go beyond it before it can reach the circumference. 2. CA is longer than any other line drawn from C to the circumference C, as CF. Draw the chord BF; BF is less than AB a diameter; hence, THEOREM 11. When the distance between the centers is equal to the sum of the radii, they are tangents externally, and the straight line joining their centers passes through the point oftangency. They must touch on the line joining their centers, as CD DC CC; let D be this point, and through D draw AB per. . . This item ships from La Vergne,TN. Paperback. Buchnummer des Verkäufers 9781236437853

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