Short And Comprehensive Course of Geometry And Trigonometry Designed for Gener

Cover Short And Comprehensive Course of Geometry And Trigonometry Designed for Gener
Short And Comprehensive Course of Geometry And Trigonometry Designed for Gener
Andrew H Baker
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Cor. 2. — The convex surface of a cylinder is equal to the product of the circumference of its base and altitude. For a prism having a regular polygon for its base becomes a cylinder, by increasing the number of sides indefinitely, and the perimeter of the polygon, forming its base, becomes the circumference of the base of the cylinder.
Cor. 3. Convex surface of a cylinder = 4rrR 2, Surface of the two bases = 2ttFP, Entire surface of the cylinder = 67rR 2 .
BOOK VII. 69 THEOREM III.
The volume
...of a rectangular parallelopipedon is equal to the product of its three dimensions.
The area of the rectangular base is the product of its two dimensions, and for every unit in altitude there will be as many solid units as there are square units in the base; hence, the volume is equal to the product of the three dimensions.
Cor. 1. — A rectangular parallelopipedon can be divided into two equal triangular prisms ; and the volume of each is equal to the area of the base multiplied by the altitude.


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