Elements of Geometry: With Practical Applications ... |
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Page 38
... forming exterior angles , which we will denote by the capital letters A , B , C , etc. , while their corresponding interior angles are denoted by the small letters a , b , c , etc. Now any exterior angle , together with its adjacent ...
... forming exterior angles , which we will denote by the capital letters A , B , C , etc. , while their corresponding interior angles are denoted by the small letters a , b , c , etc. Now any exterior angle , together with its adjacent ...
Page 46
... forming the two parallelograms ABCF and ABGD , which are equivalent ( B. II , Prop . 1 ) . The triangle ABC is one half of the parallelogram ABCF , and the triangle ABD is one half of the parallelogram ABGD ( B. I , Prop . XXVII ) ...
... forming the two parallelograms ABCF and ABGD , which are equivalent ( B. II , Prop . 1 ) . The triangle ABC is one half of the parallelogram ABCF , and the triangle ABD is one half of the parallelogram ABGD ( B. I , Prop . XXVII ) ...
Page 58
... formed by the meeting of two sticks of timber was a right angle , they measured from the angular point on the one stick 6 feet , and on the other 8 feet ; then if the ten - foot pole would reach across from the one point to the other ...
... formed by the meeting of two sticks of timber was a right angle , they measured from the angular point on the one stick 6 feet , and on the other 8 feet ; then if the ten - foot pole would reach across from the one point to the other ...
Page 79
... formed by a tangent and chord is measured by half the arc of that chord . Let AB be a tangent , and CD A a chord drawn from the point of contact C ; then the angle BCD will be measured by half the arc CGD , and the angle ACD will be ...
... formed by a tangent and chord is measured by half the arc of that chord . Let AB be a tangent , and CD A a chord drawn from the point of contact C ; then the angle BCD will be measured by half the arc CGD , and the angle ACD will be ...
Page 82
... formed by a tangent to a circle , and a chord drawn from the point of contact , is equal to the angle in the alternate segment . If AB be a tangent , AC a chord , and D any angle in the alternate segment ADC ; then will the angle D be ...
... formed by a tangent to a circle , and a chord drawn from the point of contact , is equal to the angle in the alternate segment . If AB be a tangent , AC a chord , and D any angle in the alternate segment ADC ; then will the angle D be ...
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Common terms and phrases
a+b+c AC² altitude angle ACD angle BAC bisect centre chord circ circular sector circumference cone consequently convex surface cylinder diagonal diameter distance draw equal and parallel equiangular equilateral triangle equivalent exterior angle figure formed four right angles given line greater half the arc hypothenuse inscribed circle intersection isosceles join less Let ABC lines drawn magnitude measured by half meet multiplied number of sides opposite angles parallel planes parallelogram parallelopipedon pendicular perimeter perpendicular plane MN point G prism PROBLEM produced Prop PROPOSITION pyramid radii radius rectangle regular polygon respectively equal right angles right-angled triangle Sabc Schol Scholium semicircle semicircumference side AC similar similar triangles solid angle solid described sphere spherical triangle square straight line suppose tangent THEOREM three sides triangle ABC triangular prism vertex VIII
Popular passages
Page 37 - The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two.
Page 180 - THEOREM. If one of two parallel lines is perpendicular to a plane, the other will also be perpendicular to this plane. Let AP & ED be parallel lines, of which AP is perpendicular to the plane MN ; then will ED be also perpendicular to this plane.
Page 139 - PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle : it is required to inscribe a circle in the triangle ABC.
Page 224 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Page 43 - In a right-angled triangle, the side opposite the right angle is" called the Hypothenuse ; and the other two sides are cal4ed the Legs, and sometimes the Base and Perpendicular.
Page 184 - THEOREM. If two angles, not situated in the same plane, have their sides parallel and lying in the same direction, they will be equal, and the planes in which they are situated will be parallel.
Page 10 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Page 226 - We conclude then, that the solidity of a cylinder is equal to the product of its base by its altitude.
Page 22 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Page 12 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.