Elements of Geometry |
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Results 1-5 of 49
Page xi
... 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 ...
... 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
... 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 proportion ...
... 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 proportion ...
Page 2
... contain is Fig . 6. called a rectilineal figure , or polygon ( fig . 6 ) , and the lines taken together make the perimeter of the polygon . Fig . 7 . 14. The polygon of three sides is the most simple of these figures , and is called a ...
... contain is Fig . 6. called a rectilineal figure , or polygon ( fig . 6 ) , and the lines taken together make the perimeter of the polygon . Fig . 7 . 14. The polygon of three sides is the most simple of these figures , and is called a ...
Page 8
... 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 CAG = D , take AG = DE ...
... 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 CAG = D , take AG = DE ...
Page 30
... contained seven times in the angle ACB , and four times in the angle DCE . The partial angles AC m , m Cn , n Cp , & c . , DC x , x Cy , & c . , being equal to each other , the partial arcs Am , mn , np , & c . , D x , x y , & c ...
... contained seven times in the angle ACB , and four times in the angle DCE . The partial angles AC m , m Cn , n Cp , & c . , DC x , x Cy , & c . , being equal to each other , the partial arcs Am , mn , np , & c . , D x , x y , & c ...
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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