## Elements of Geometry |

### From inside the book

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**equivalent**whose surfaces are equal . Two figures may be**equivalent**, however dissimilar ; thus a circle may be**equivalent**to a square , a triangle to a rectangle , & c . The denomination of equal figures will be restricted to those ... Page 43

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**equivalent**. Demonstration . Let AB ( fig . 96 ) be the common base of the Fig . 963 two parallelograms ABCD , ABEF ; since they are supposed to have the same altitude , the sides DC , FE , opposite to the bases , will be situated in a ... Page 44

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**equivalent**. 167. Corollary . Every parallelogram ABCD ( fig . 97 ) is**equivalent**to a rectangle of the same base and altitude . THEOREM . 168. Every triangle ABC ( fig . 98 ) is half of a parallelogram ABCD of the same base and ... Page 48

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**equivalent**to the parallelogram ADKL , and has for its measure EF × AL . But AL = DK ; and , since the triangle IBL is equal to the triangle KCI , the side BLCK ; therefore AB + CD = AL + DK = 2AL ; thus AL is half the sum of the sides ... Page 51

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**equivalent**to the square AH , double of the triangle HBC . It may be demonstrated , in the same manner , that the rectangle CDEG is**equivalent**to the square AI ; but the two rectangles BDEF , CDEG , taken together , make the square BCGF ...### Other editions - View all

### 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