## Elements of Geometry |

### From inside the book

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**angles**, with- out having its sides**equal**( See art . above referred to ) ; The parallelogram ( fig . 13 ) , which has its opposite sides par- allel ; The rhombus or lozenge ( fig . 14 ) , which has its sides**equal**, without having its ... Page 3

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**equal**; an equiangular polygon is one which has all its**angles equal**. • 20. Two polygons are equilateral with respect to each other , when they have their sides**equal**, each to each , and placed in the same order ; that is , when , by ... Page 4

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**angles**are**equal**. Demonstration . Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and GH to EF , the**angles**ACD , EGH , will be**equal**. Take the four distances CA , CB , GE , GF ,**equal**to each other , the ... Page 5

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**angle**ACD is the sum of the**angles**ACE , ECD ; therefore ACD + BCD is the sum of the three**angles**ACE , ECD , BCD . The first of these is a right**angle**, and the two others are together**equal**to a right**angle**; therefore the sum of the two ... Page 6

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**equal**to two right**angles**, the two exterior sides AC , CB , are in the same straight line . Demonstration . For if CB is not the line AC produced , let CE be that line produced ; then , ACE being a straight line , the**angles**ACD , DCE ...### 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