Elements of plane (solid) geometry (Higher geometry) and trigonometry (and mensuration), being the first (-fourth) part of a series on elementary and higher geometry, trigonometry, and mensuration
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ABCD altitude axis base becomes called centre chord circle circumference circumscribing common cone consequently construction contained convex surface corresponding curve cylinder described determine diameter difference distance divided draw drawn ellipse equal equation equivalent expressed faces feet figure follows formed four frustum given greater half height hence inches included inscribed length less magnitude manner mean measured meet multiplied opposite ordinates parabola parallel pass perpendicular plane polygon portion position prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radius ratio rectangle regular represent respectively revoloid right angles right line root RULE Scholium segment shown sides similar sine solidity space sphere spherical square straight line supposed surface taken tangent THEOREM third triangle ungula vertical whole
Page 34 - Prove that parallelograms on the same base and between the same parallels are equal in area.
Page 35 - The sum of any two sides of a triangle, is greater than the third side.
Page 60 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 56 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Page 36 - The volumes of similar solids are to each other as the cubes of their like dimensions.
Page 73 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 86 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let...
Page 209 - To find the solidity of a hyperbolic conoid, or otherwise called a hyperboloid. RULE. To the square of the radius of the base, add the square of the diameter...