Elements of Geometry: With Practical Applications ... |
From inside the book
Results 1-5 of 35
Page 16
... G ; then will the two triangles be identical , or equal in all respects . A A For , conceive the triangle ABC to be placed upon the triangle DFG , in such a manner that the point C may coincide with the point G , and the side CA with ...
... G ; then will the two triangles be identical , or equal in all respects . A A For , conceive the triangle ABC to be placed upon the triangle DFG , in such a manner that the point C may coincide with the point G , and the side CA with ...
Page 17
... point in this plane equally distant from the tops C & D. AG Solution . Join CD , and bisect it by the perpendicular FG ; then will the point G be the point sought . For , if we join GC , GD , we shall have the triangle GFC equal to GFD ...
... point in this plane equally distant from the tops C & D. AG Solution . Join CD , and bisect it by the perpendicular FG ; then will the point G be the point sought . For , if we join GC , GD , we shall have the triangle GFC equal to GFD ...
Page 19
... point G. Therefore the two triangles are identical ( Ax . IX ) , having the two sides AC and BC respectively equal to DG and FG , and the remaining angle C equal to the remaining angle G. PROPOSITION V. THEOREM . In an isosceles ...
... point G. Therefore the two triangles are identical ( Ax . IX ) , having the two sides AC and BC respectively equal to DG and FG , and the remaining angle C equal to the remaining angle G. PROPOSITION V. THEOREM . In an isosceles ...
Page 24
... point G ( Post . III ) . Join DG , FG ( Post . I ) , and the tri- angle DGF will be the triangle required , since the three sides are equal to the three lines A , B , C. A B C Scholium . It is obvious that the arcs described from D and ...
... point G ( Post . III ) . Join DG , FG ( Post . I ) , and the tri- angle DGF will be the triangle required , since the three sides are equal to the three lines A , B , C. A B C Scholium . It is obvious that the arcs described from D and ...
Page 26
... point D , in a given line DF , to make an angle equal to a given angle BAC . With any radius describe arcs from ... G. The line DG being drawn , will make the angle FDG equal to BAC . This is an application of Prop . IX , and the equality of ...
... point D , in a given line DF , to make an angle equal to a given angle BAC . With any radius describe arcs from ... G. The line DG being drawn , will make the angle FDG equal to BAC . This is an application of Prop . IX , and the equality of ...
Other editions - View all
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.