Elements of Geometry and Trigonometry, with Practical Applications

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. 1863 Excerpt: ... Cor. 1. Hence the sphere is to the circumscribed cylinder as 2 to 3; and their solidities are to each other as their surfaces. 606. Cor. 2. Since a cone is one third of a cylinder of the same base and altitude (Prop. V. Cor. 1), if a cone has the diameter of its base and its altitude each equal to the diameter of a given sphere, the solidities of the cone and sphere are to each other as 1 to 2; and the solidities of the cone, sphere, and circumscribing cylinder are to each other, respectively, as 1, 2, and 3. BOOK XI. APPLICATIONS OF GEOMETRY TO THE MENSURATION OF PLANE FIGURES. DEFINITIONS. 607. Mensuration Of Plane Figures is the process of determining the areas of plane surfaces. 608. The Area of a figure, or its quantity of surface, is determined by the number of times the given surface contains some other area, assumed as the unit of measure, 609. The Measuring Unit assumed for a given surface is called the superficial unit, and is usually a square, taking its name from the linear unit forming its side; as a square whose side is 1 inch, 1 foot, 1 yard, fcc. Some superficial units, however, have no corresponding linear unit; as the rood, acre, &c. Note.--For other linear measures, see National Arithmetic, Art 133, 134, 13Q. 611. Table Of Surface Measures. 144 Square Inches make 1 Square Foot. 1 Square Yard. 1 Square Rod or Pole. Also, 9 Square Feet 30£ Square Yards 40 Square Rods 4 Roods 640 Acres 1 Rood. 1 Acre. 1 Square Mile. 1 Square Rod. 1 Square Chain. 1 Acre. 625 Square Links 16 Square Rods 10 Square Chains 612. Since an acre is equal to 10 chains, or 100,000 links, square chains may be readily reduced to acres by pointing off one decimal place from the right, and squara links by pointing off five decimal places from the right. Problem I....