Elements of Geometry: With Practical Applications ...H.H. Howley and Company, 1847 - 308 sider |
Inni boken
Resultat 1-5 av 78
Side 47
... similar reason , the triangle CAH may be substituted for the equivalent triangle CAB , and thus the pentagon ABCDF will be changed into an equivalent triangle HCG . It is obvious the same process may be applied to a polygon having any ...
... similar reason , the triangle CAH may be substituted for the equivalent triangle CAB , and thus the pentagon ABCDF will be changed into an equivalent triangle HCG . It is obvious the same process may be applied to a polygon having any ...
Side 57
... similar reason , the angle KML is equal to CBA , and the side LM is equal to the side AB ; hence the triangle LKM is equal to the triangle ACB ( B. I , Prop . iv ) . Now , since the three triangles ADL , LKM , MGB , are each equal to ...
... similar reason , the angle KML is equal to CBA , and the side LM is equal to the side AB ; hence the triangle LKM is equal to the triangle ACB ( B. I , Prop . iv ) . Now , since the three triangles ADL , LKM , MGB , are each equal to ...
Side 66
... similar way it may be shown that the sum of the squares of the two lines , drawn from any point in the circumference of the smaller circle , to the extremities of any diameter of the larger circle , is equal to the same constant ...
... similar way it may be shown that the sum of the squares of the two lines , drawn from any point in the circumference of the smaller circle , to the extremities of any diameter of the larger circle , is equal to the same constant ...
Side 68
... similar reason , CD2 + DA2 = 2 AF2 + 2 DF2 ; therefore AB2 + BC2 + CD2 + DA2 = 4 AF2 + 2 BF2 + 2 DF2 . But 4 AFAC2 , and 2 BF2 + 2 DF2 = 4 BG2 + 4 FG2 ; [ B. II , Prop . v , Cor . ] . [ B. II , Prop . xII ] , therefore AB + BC2 + CD2 + ...
... similar reason , CD2 + DA2 = 2 AF2 + 2 DF2 ; therefore AB2 + BC2 + CD2 + DA2 = 4 AF2 + 2 BF2 + 2 DF2 . But 4 AFAC2 , and 2 BF2 + 2 DF2 = 4 BG2 + 4 FG2 ; [ B. II , Prop . v , Cor . ] . [ B. II , Prop . xII ] , therefore AB + BC2 + CD2 + ...
Side 92
... Similar figures are those which have the angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional . 4. The perimeter , or contour of a figure , 92 ELEMENTS OF GEOMETRY .
... Similar figures are those which have the angles of the one equal to the angles of the other , each to each , and the sides about the equal angles proportional . 4. The perimeter , or contour of a figure , 92 ELEMENTS OF GEOMETRY .
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Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 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.
Side 224 - The radius of a sphere is a straight line, drawn from the centre to any point of the...
Side 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.
Side 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.
Side 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.
Side 226 - We conclude then, that the solidity of a cylinder is equal to the product of its base by its altitude.
Side 22 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Side 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.