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ABCD altitude angle ABC angle BCD angles equal bisect center of similitude chord circumference cone consequently construct cylinder diagonal diameter dicular draw equal angles equal bases equal distances equal th equiangular equilateral triangle figure find a point frustum geometric locus given angle given circle given line given point given triangle gles half the arc Hence indeterminate problems inscribed intersection isosceles triangle Let ABC line drawn line joining locus which resolves meet opposite angles opposite sides parallel planes parallelogram pendicular perpen perpendicular plane XZ 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 angles right line right-angled triangle Scholium segment semicircle side AC similar Solution sphere spherical triangle straight line surface symmetric tangent tetrahedrons three sides triangle ABC vertex
Page 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.
Page 50 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 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.
Page 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.
Page 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.
Page 117 - 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.
Page 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.
Page 213 - ... 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.