Elements of Geometry |
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Page 36
... formed by a tangent and a chord , has for its measure the half of the arc AMDC , compre- hended between its sides . Demonstration . At the point of contact A draw the diameter AD ; the angle BAD is a right angle ( 110 ) , and has for ...
... formed by a tangent and a chord , has for its measure the half of the arc AMDC , compre- hended between its sides . Demonstration . At the point of contact A draw the diameter AD ; the angle BAD is a right angle ( 110 ) , and has for ...
Page 40
... formed with the given adjacent sides and included angle . 148. Corollary . If the given angle be a right angle , the figure will be a rectangle ; and , if the adjacent sides are also equal , the figure will be a square . PROBLEM . 149 ...
... formed with the given adjacent sides and included angle . 148. Corollary . If the given angle be a right angle , the figure will be a rectangle ; and , if the adjacent sides are also equal , the figure will be a square . PROBLEM . 149 ...
Page 51
... formation of the square of a binomial , which is thus expressed , ( a + b ) 2 = a2 + 2ab + b2 . THEOREM . 182. If the line AC ( fig . 107 ) is the difference of two lines AB , Fig . 107 BC , the square described upon AC will contain the ...
... formation of the square of a binomial , which is thus expressed , ( a + b ) 2 = a2 + 2ab + b2 . THEOREM . 182. If the line AC ( fig . 107 ) is the difference of two lines AB , Fig . 107 BC , the square described upon AC will contain the ...
Page 53
... formed , which is the square of AC . It is manifest , that EFGH contains eight triangles , each of which is equal to ABE , and that ABCD contains four of them ; therefore the square EFGH is double of ABCD . Since AC : AB :: 2 : 1 , we ...
... formed , which is the square of AC . It is manifest , that EFGH contains eight triangles , each of which is equal to ABE , and that ABCD contains four of them ; therefore the square EFGH is double of ABCD . Since AC : AB :: 2 : 1 , we ...
Page 68
... formed by a tangent and a chord ( 131 ) has for its measure the half of the arc AD , and the angle C has the same measure ; con- sequently the angle OAD = C ; therefore the two triangles are similar , and OC : OA :: OA : OD , which ...
... formed by a tangent and a chord ( 131 ) has for its measure the half of the arc AD , and the angle C has the same measure ; con- sequently the angle OAD = C ; therefore the two triangles are similar , and OC : OA :: OA : OD , which ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence