## Elements of Geometry |

### From inside the book

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Page xiv

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**proportional**quantities form a new proportion . by By multiplying the proportion we shall have A2 : B2 : C2 : De Ꭿ : B :: C : Ꭰ , A3 : B3 :: C3 : D3 ; that is , the cubes of four**proportional**quantities form a new pro- portion . VI ... Page 33

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**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 angle ACD should be greater than ... Page 34

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**proportional**to the angles ; hence two sectors ACB , ACD , taken in the same circle , or in equal circles , ≈re to each other as the arcs AB , AD , the bases of these sectors . It will be perceived , therefore , that the arcs of a ... Page 45

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**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 47

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**proportional**( 111 ) ; 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 ...### Other editions - View all

### 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