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ABCD altitude angles equal axis base called chord circle circumference common cone consequently construct contained Corol corresponding cylinder describe determined diagonal diameter difference divided draw drawn edges equal equal distances equilateral extremities faces fall feet figure follows formed four given line given point greater half height Hence inscribed intersection join length less line drawn manner mean measured meet middle multiply opposite parallel parallelogram pass perpendicular plane XZ pole polygon polyhedral angle polyhedrons prism Prob problem Prop proportional Prove pyramid quantities radii radius ratio rectangle reference regular resolves respectively right angles rule segment sides similar solid Solution sphere spherical triangle square straight line suppose surface symmetric taken tangent THEOREM third triangle triangle ABC vertex vertices whole
Pàgina 33 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle.
Pàgina 50 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Pàgina 50 - Four quantities are said to be proportional when the ratio of the first to the second is the same as the ratio of the third to the fourth.
Pàgina 60 - Carol. 4. Parallelograms, or triangles, having an angle in each equal, are in proportion to each other as the rectangles of the sides which are about these equal angles. THEOREM LXXXII. IF a line be drawn in a triangle parallel to one of its sides, it will cut the other two sides proportionally.
Pàgina 23 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Pàgina 1 - A straight line is said to be perpendicular to a plane when it is perpendicular to every straight line which passes through its foot in that plane, and the plane is said to be perpendicular to the line.
Pàgina 51 - Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to the third, as the third to the fourth, as the fourth to the fifth, and so on, all in the same common ratio.
Pàgina 5 - ... 07958 in using the circumferences j then taking one-third of the product, to multiply by the length, for the content. Ex. 1. To find the number of solid feet in a piece of timber, whose bases are squares, each side of the greater end being 15 inches, and each side of the less end 6 inches ; also, the length or perpendicular altitude 2-1 feet.