Elements of Geometry |
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Page xiv
... proportional quantities form a new proportion . By multiplying the proportion by we shall have A2 : B2 :: C2 D3 A B :: C : D , A3 : B 3 3 :: C3 : D3 , that is , the cubes of four proportional quantities form a new pro- portion . VI ...
... proportional quantities form a new proportion . By multiplying the proportion by we shall have A2 : B2 :: C2 D3 A B :: C : D , A3 : B 3 3 :: C3 : D3 , that is , the cubes of four proportional quantities form a new pro- portion . VI ...
Page 31
... proportional ( 111 ) † , namely , angle ACD : angle ACI :: arc AO : arc AI . But the arc AO is greater than the arc AI ; it is necessary then , in order that this proportion may take place , that the an- gle ACD should be greater than ...
... proportional ( 111 ) † , namely , angle ACD : angle ACI :: arc AO : arc AI . But the arc AO is greater than the arc AI ; it is necessary then , in order that this proportion may take place , that the an- gle ACD should be greater than ...
Page 32
... proportional to the angles ; hence two sectors ACB , ACD , taken in the same circle or in equal circles , are to each other , as the arcs AB , AD , the bases of these sectors . It will be perceived therefore , that the arcs of a circle ...
... proportional to the angles ; hence two sectors ACB , ACD , taken in the same circle or in equal circles , are to each other , as the arcs AB , AD , the bases of these sectors . It will be perceived therefore , that the arcs of a circle ...
Page 43
... proportional . By homologous sides are to be understood those , which have the same position in the two figures , or which are adjacent to equal angles . The angles , which are equal in the two figures , are called homologous angles ...
... proportional . By homologous sides are to be understood those , which have the same position in the two figures , or which are adjacent to equal angles . The angles , which are equal in the two figures , are called homologous angles ...
Page 45
... proportional ( m ) ; that is AIKD : AEFD :: AI : AO . Now AO is greater than AI ; it is necessary then , in order that this proportion may take place , that the rectangle AEFD should be greater than AIKD ; but it is less ; therefore the ...
... proportional ( m ) ; that is AIKD : AEFD :: AI : AO . Now AO is greater than AI ; it is necessary then , in order that this proportion may take place , that the rectangle AEFD should be greater than AIKD ; but it is less ; therefore the ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence