## Elements of Geometry and Trigonometry |

### From inside the book

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**equal**areas , when they contain the same measuring unit an**equal**number of ...**multiplied**by the same quantity M , we may infer that Ax M = BxM + CXM ; in ...**base**of the two parallelograms ABCD , ABEF : and since they are sup- posed ... Page 72

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**multiplied**by their altitudes . Let ABCD , AEGF , be two rectangles ; then will the rect- angle , ABCD AEGF :: AB.AD ...**base**by the altitude may be assumed as the measure of a rectangle , provided we under- stand by this**product**, the ... Page 73

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**product**is thus obtained , and the ratio of the two pro- ducts is the same as ...**base**of which contains twelve units , and the altitude seven , this second ...**multiplied**by itself . The arithmetical squares of 1 , 2 , 3 , & c . are 1 ... Page 75

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**equal**to its altitude**multiplied**by the half sum of its parallel**bases**. D E K A F L B Let ABCD be a trapezoid , EF its a'ti- tude , AB and CD its parallel**bases**; then will its area be**equal**to EFx ( AB + CD ) . H Through I , the ... Page 144

... equal to the perimeter of its

... equal to the perimeter of its

**base multiplied**by its altitude . Let ABCDE - K be a right prism : then will its convex surface be equal to ( AB + BC + CD + DE + EA ) × AF . F K. H For , the convex surface is equal to the sum of all the ...### 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 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 proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC 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