Elements of Geometry: With Practical Applications ...H.H. Howley and Company, 1847 - 308 páginas |
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Página 12
... double of the same or equal things , are equal . VII . Things which are halves of the same thing , are equal . VIII . Every whole is equal to all its parts taken to- gether , and greater than any of them . IX . Things which coincide ...
... double of the same or equal things , are equal . VII . Things which are halves of the same thing , are equal . VIII . Every whole is equal to all its parts taken to- gether , and greater than any of them . IX . Things which coincide ...
Página 33
... double square . A straight line being drawn in a direction perpendicular to that in which the parallels are required to be drawn , the cross - piece of the T - square is laid upon this line , and the piece at right angles to it gives ...
... double square . A straight line being drawn in a direction perpendicular to that in which the parallels are required to be drawn , the cross - piece of the T - square is laid upon this line , and the piece at right angles to it gives ...
Página 55
... double the tri- angle ACD , on the same base AD , and between the same parallels AD , CM ; and since the doubles of ... double the square itself . Cor . 4. The sum of the squares of the sides of a rec- tangle is equal to the sum of the ...
... double the tri- angle ACD , on the same base AD , and between the same parallels AD , CM ; and since the doubles of ... double the square itself . Cor . 4. The sum of the squares of the sides of a rec- tangle is equal to the sum of the ...
Página 57
... double the triangle ACB ( B. II , Prop . m ) : hence the squares AF and BH are together also equal to the whole space ADKGB diminished by three times the triangle ACB , and con- sequently these two squares are equivalent to the square ...
... double the triangle ACB ( B. II , Prop . m ) : hence the squares AF and BH are together also equal to the whole space ADKGB diminished by three times the triangle ACB , and con- sequently these two squares are equivalent to the square ...
Página 65
... double of the square of a line drawn from the vertex to the middle of the base , together with double the square of the half base , is equal to the sum of the squares of the other two sides . Let ABC be a triangle , and CD the line ...
... double of the square of a line drawn from the vertex to the middle of the base , together with double the square of the half base , is equal to the sum of the squares of the other two sides . Let ABC be a triangle , and CD the line ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 224 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Página 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.
Página 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.
Página 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.
Página 226 - We conclude then, that the solidity of a cylinder is equal to the product of its base by its altitude.
Página 22 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Página 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.