## Elements of Geometry |

### From inside the book

Results 6-10 of 41

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**equivalent**to the squares AH , AI , therefore , 2 -2 AB : AC :: BD : DC , or , the squares of the two sides of a right angle are to each other , as the segments of the hypothenuse adjacent to these sides . THEOREM . 191. In a triangle ... Page 54

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**equivalent**( 170 ) . The triangles ADE , BDE , of which the common vertex is E , have the same altitude , and are to each other as their bases AD , DB ( 177 ) ; thus , ADE : BDE :: AD : DB . The triangles ADE , DEC , of which the common ... Page 62

... , we have , ABC : ADE :: AB × AC : AD × AE . 217. Corollary . The two triangles would be

... , we have , ABC : ADE :: AB × AC : AD × AE . 217. Corollary . The two triangles would be

**equivalent**, if the rectangle AB × AC were equal to the rectangle AD × AE , ΟΙ if AB : AD :: AE : AC , which is 62 Elements of Geometry . Page 72

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**equivalent**to the parallelogram ABCD . For , by construction , AB : XY :: XY : DE ; hence --2 XY = AB × DE ; -2 but AB × DE is the measure of the parallelogram , and XY is that of the square , therefore they are**equivalent**. 2. Let ABC ... Page 73

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**equivalent**to a given polygon . Solution . Let ABCDE ( fig . 146 ) be the given polygon . Fig . 146 . Draw the diagonal CE , which cuts off the triangle CDE ; through the point D draw DF parallel to CE to meet AE pro- Geom . 10 duced ...### 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