## Elements of Geometry |

### From inside the book

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**faces**, the rectangle B will have for its absolute measure ; that is , it will be equal to superficial units . The more common and simple method is , to take the square as the unit of surface ; and that square has been preferred , whose ... Page 119

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**faces**would , by being produced , cut the solid angle ; if it were other- wise , the sum of the plane angles would no longer be limited , and might be of any magnitude whatever . THEOREM . 359. If two solid angles are respectively ... Page 125

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**faces**of a poly- edron is called a side or edge of the polyedron . 367. A regular polyedron is one , all whose**faces**are equal , regular polygons , and all whose solid angles are equal to each other . There are five polyedrons of this ... Page 126

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**faces**parallelograms , and is called a parallelopiped . A parallelopiped is rectangular when all its**faces**are rect- angles . 374. Among rectangular parallelopipeds is distinguished the cube or regular hexaedron comprehended under six ... Page 127

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**face**or base of a polyedron , we can imagine the vertices of the different solid angles of the polye- drons ...**faces**and in part below it ; it is wholly on one side of this plane . THEOREM . 384. Two polyedrons cannot have the ...### 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