Elements of Geometry: With Practical Applications ...H.H. Howley and Company, 1847 - 308 páginas |
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Página 45
... equivalent . Let the two parallelograms ABCD , ABFG have the same base AB , and the same altitude ; then will they be equivalent , G DF A B G F D A Since they have the same altitude , their upper bases will be in the same line GC ...
... equivalent . Let the two parallelograms ABCD , ABFG have the same base AB , and the same altitude ; then will they be equivalent , G DF A B G F D A Since they have the same altitude , their upper bases will be in the same line GC ...
Página 46
... equivalent ; for they may be so , applied as to have their equal bases coincide , and then by this proposition they will be equivalent . PROPOSITION II . THEOREM . Two triangles having the same base and same altitude , are equivalent ...
... equivalent ; for they may be so , applied as to have their equal bases coincide , and then by this proposition they will be equivalent . PROPOSITION II . THEOREM . Two triangles having the same base and same altitude , are equivalent ...
Página 47
... equivalent . ( 36. ) Problem . To find a triangle that shall be equivalent to a given polygon . Let ABCDF be the given polygon . Draw the diagonal CF , cutting off the triangle CDF ; through the point D , draw DG parallel to CF , and ...
... equivalent . ( 36. ) Problem . To find a triangle that shall be equivalent to a given polygon . Let ABCDF be the given polygon . Draw the diagonal CF , cutting off the triangle CDF ; through the point D , draw DG parallel to CF , and ...
Página 48
... equivalent ( B. II , Prop . 1 ) ; and since ABD is half the parallelogram ABCD , it follows that ABF is also half the same parallelogram . Cor . A triangle is half the parallelogram having the same base , and being situated between the ...
... equivalent ( B. II , Prop . 1 ) ; and since ABD is half the parallelogram ABCD , it follows that ABF is also half the same parallelogram . Cor . A triangle is half the parallelogram having the same base , and being situated between the ...
Página 49
... equivalent to HF ; also since the figure KH is a paralle- logram , the triangle KBC is equal to the triangle BHC ( B. I , Prop . xxvII ) ; therefore the line BC divides the parallelogram AG into two equal parts , and the trapezoid ABCD ...
... equivalent to HF ; also since the figure KH is a paralle- logram , the triangle KBC is equal to the triangle BHC ( B. I , Prop . xxvII ) ; therefore the line BC divides the parallelogram AG into two equal parts , and the trapezoid ABCD ...
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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.