Elements of Geometry: With Practical Applications ... |
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Page 2
... produce a straight physical line , which will approach more nearly to the mathematical line as the size of the string is diminished . ( 5. ) All the lines which we form upon paper or upon the black- board , for the purpose of ...
... produce a straight physical line , which will approach more nearly to the mathematical line as the size of the string is diminished . ( 5. ) All the lines which we form upon paper or upon the black- board , for the purpose of ...
Page 7
... produced . They are obviously every where equally distant . ( 16. ) The ordinary frames of windows and doors , and nearly all architectural frame work , consist of systems of parallel lines at right angles with each other . All fabrics ...
... produced . They are obviously every where equally distant . ( 16. ) The ordinary frames of windows and doors , and nearly all architectural frame work , consist of systems of parallel lines at right angles with each other . All fabrics ...
Page 12
... produce a terminated straight line to any length . III . To describe the circumference of a circle , from any centre , with any radius , or , in other words , at any distance from that centre . PROPOSITIONS . PROPOSITION I. THEOREM ...
... produce a terminated straight line to any length . III . To describe the circumference of a circle , from any centre , with any radius , or , in other words , at any distance from that centre . PROPOSITIONS . PROPOSITION I. THEOREM ...
Page 16
... BGD . B Solution . Produce BD until DF is equal to BD : draw AF , cutting the mirror at G , and G will be the point required . For , comparing the triangle GFD with GBD , we have DF equal to 16 ELEMENTS OF GEOMETRY .
... BGD . B Solution . Produce BD until DF is equal to BD : draw AF , cutting the mirror at G , and G will be the point required . For , comparing the triangle GFD with GBD , we have DF equal to 16 ELEMENTS OF GEOMETRY .
Page 21
... produced , the exterior angle is greater than either of the two interior and 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 ...
... produced , the exterior angle is greater than either of the two interior and 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 ...
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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.