Elements of Geometry: With Practical Applications ... |
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Page 9
... angles of a parallelogram are right angles , the figure is called a rectangle . XIX . When the four sides of a rectangle are equal , the figure is called a square . XX . When the four sides of a parallelogram are equal , and the angles ...
... angles of a parallelogram are right angles , the figure is called a rectangle . XIX . When the four sides of a rectangle are equal , the figure is called a square . XX . When the four sides of a parallelogram are equal , and the angles ...
Page 15
... opposite angles are equal . Let the two lines AB , CD inter- sect at the point F ; then will the angle AFC be equal to BFD , and the angle AFD equal to BFC . A D B For , since the line CF meets the line AB , the two angles AFC , BFC ...
... opposite angles are equal . Let the two lines AB , CD inter- sect at the point F ; then will the angle AFC be equal to BFD , and the angle AFD equal to BFC . A D B For , since the line CF meets the line AB , the two angles AFC , BFC ...
Page 20
... angles at the base are equal ; or , if a triangle have two sides equal , the angles opposite those sides will be equal . If the triangle ABC have the side AC equal to the side BC , then will the angle B be equal to the angle A. A D B ...
... angles at the base are equal ; or , if a triangle have two sides equal , the angles opposite those sides will be equal . If the triangle ABC have the side AC equal to the side BC , then will the angle B be equal to the angle A. A D B ...
Page 21
... opposite angles . Let ABC be a triangle , having the side AB produced to D ; then will the exterior angle CBD be greater than either of the interior and opposite angles BAC or BCA . 4 . B H For , conceive the side BC to be bisected in ...
... opposite angles . Let ABC be a triangle , having the side AB produced to D ; then will the exterior angle CBD be greater than either of the interior and opposite angles BAC or BCA . 4 . B H For , conceive the side BC to be bisected in ...
Page 22
... angles equal , the sides opposite to them are also equal , and the triangle will be isosceles . In the triangle ABC , let the angle CAB be equal to the angle CBA ; then will the side CB be equal to CA. D C : A For , if these sides are ...
... angles equal , the sides opposite to them are also equal , and the triangle will be isosceles . In the triangle ABC , let the angle CAB be equal to the angle CBA ; then will the side CB be equal to CA. D C : A For , if these sides are ...
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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.