Elements of Geometry |
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Page 35
... similar reason , the angle CAD has for its measure the half of ED ; therefore BAC + CAD , or BAD , has for its measure the half BE + ED , or the half of BD . Let us suppose , in the second place , that the centre C ( fig . 65 ) , Fig ...
... similar reason , the angle CAD has for its measure the half of ED ; therefore BAC + CAD , or BAD , has for its measure the half BE + ED , or the half of BD . Let us suppose , in the second place , that the centre C ( fig . 65 ) , Fig ...
Page 45
... similar , but similar figures may be very unequal . 163. In two different circles , similar arcs , similar sectors , similar segments , are such as correspond to equal angles at the centre . Thus , the angle A ( fig . 92 ) being equal ...
... similar , but similar figures may be very unequal . 163. In two different circles , similar arcs , similar sectors , similar segments , are such as correspond to equal angles at the centre . Thus , the angle A ( fig . 92 ) being equal ...
Page 47
... similar , it may be shown , that the fourth term of the proportion cannot be smaller than AE ; consequently it is equal to AE . Whatever , therefore , be the ratio of the bases , two rectangles ABCD , AEFD , of the same altitude , are ...
... similar , it may be shown , that the fourth term of the proportion cannot be smaller than AE ; consequently it is equal to AE . Whatever , therefore , be the ratio of the bases , two rectangles ABCD , AEFD , of the same altitude , are ...
Page 48
... similar manner , another rectangle by measuring its sides by the same linear unit ; we obtain thus a second product , and the ratio of these two products is equal to that of the rectangles , conformably to the proposition , which has ...
... similar manner , another rectangle by measuring its sides by the same linear unit ; we obtain thus a second product , and the ratio of these two products is equal to that of the rectangles , conformably to the proposition , which has ...
Page 58
... similar , when they have , at the same time , their angles equal , each to each , and the homologous sides proportional ( 162 ) ; therefore the equiangular triangles BAC , CDE , are two similar figures . 203. Corollary . In order to be ...
... similar , when they have , at the same time , their angles equal , each to each , and the homologous sides proportional ( 162 ) ; therefore the equiangular triangles BAC , CDE , are two similar figures . 203. Corollary . In order to be ...
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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