## Elements of Geometry and Trigonometry |

### From inside the book

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Page 54

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**bases**of those sectors . It is hence evident that the arcs of the circle , which serve as a measure of the different angles , are proportional to the different sectors , in the same circle , or in equal circles . PROPOSITION XVIII ... Page 68

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**base**. Thus , AD is the altitude of the triangle BAC B 6. The altitude of a parallelogram is the perpendicular which measures the distance between two opposite sides taken as**bases**, Thus , EF is the altitude of the parallelo- A gram DB ... Page 69

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**bases**and equal altitudes , are equivalent . D CF EDF CE A B A B Let AB be the common**base**of the two parallelograms ABCD , ABEF : and since they are sup- posed to have the same altitude , their upper**bases**. DC , FE , will be both ... Page 70

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**base**and altitude , are equivalent . Cor . Every parallelogram is equivalent to the rectangle which has the same**base**and the same altitude . · PROPOSITION II . THEOREM . Every triangle is half the parallelogram which has the same**base**... Page 71

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**bases**AB , AE . E Suppose , first , that the**bases**are A commensurable , and are to each other , for example , as the ...**base**and altitude . The rectangle ABCD will contain seven partial rectangles , while AEFD will contain four : hence ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism produced proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex