## Elements of Geometry |

### From inside the book

Results 1-5 of 54

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**contained**once more than it was in the first consequent ; the new ratio then will be equal to the primitive ratio increased by unity . If the same operation be performed upon the two ratios of a proportion , there will evidently result ... Page xiv

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**contained**in A multiplied by the number of linear units con- tained in B ; and we can easily conceive this product to be equal to that which results from the multiplication of the lines B and C. The magnitudes A and B , in the ... Page 2

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**contain**is called a rectilineal figure , or polygon ( fig . 6 ) , and the lines taken together make the perimeter of the polygon . 14. The polygon of three sides is the most simple of these figures , and is called a triangle ; that of ... Page 8

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**contained**by the former , is greater than the angle EDF ,**contained**by the latter ; the third side BC of the first triangle will be greater than the third side EF of the second . Demonstration . Make the angle CAGD , take AG = DE , and ... Page 32

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**contained**seven times in the angle ACB , and four times in the angle DCE . The partial angles ACm , m Cn , n Cp , & c . , DC x , x Cy , & c . , being equal to each other , the partial arcs A m , m n , np , & c . , D x , x y , & c ...### 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