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ABCD altitude angles equal axis base and altitude bisect center of similitude chord circumference cone construct cylinder diagonal diameter dicular diedral angles draw equal angles equal bases equal distances equal th equiangular figure find a point find the area frustum geometric locus given angle given circle given line given point given triangle Hence inscribed intersection isosceles triangle Let ABC line drawn locus which resolves measured meet OREM parallel planes parallelogram parallelopipedon pendicular perpen perpendicular plane angles plane XZ pole polygon polyhedral angle polyhedrons prism Prob Prop proportional Prove pyramid radical axis radii radius ratio rectangle regular polygon regular polyhedrons resolves this problem rhombus right line Scholium segment semicircle side AC similar sphere spherical polygons spherical triangle straight line surface symmetric tangent tetrahedrons THEOREM three sides triangle ABC trihedral angles vertex
Side 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.
Side 50 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.
Side 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.