Elements of Geometry and Trigonometry |
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Page 69
... multiplied by the same quantity M , we may infer that AxM = BxM + CXM ; in like manner , if we have , A = B + C , and D - E - C , and if the equal quantities are added together , then expunging the + C and -C , which destroy each other ...
... multiplied by the same quantity M , we may infer that AxM = BxM + CXM ; in like manner , if we have , A = B + C , and D - E - C , and if the equal quantities are added together , then expunging the + C and -C , which destroy each other ...
Page 72
... multiplied by their altitudes , Let ABCD , AEGF , be two rectangles ; then will the rect- angle , ABCD AEGF :: AB.AD ... Multiplying the corresponding terms of these proportions together , and observing that the term AEHD may be omit ...
... multiplied by their altitudes , Let ABCD , AEGF , be two rectangles ; then will the rect- angle , ABCD AEGF :: AB.AD ... Multiplying the corresponding terms of these proportions together , and observing that the term AEHD may be omit ...
Page 73
... multiplied by itself . The arithmetical squares of 1 , 2 , 3 , & c . are 1 , 4 , 9 , & c . So likewise , the geometrical square constructed on a double line is evidently four times greater than the square on a single one ; on a triple ...
... multiplied by itself . The arithmetical squares of 1 , 2 , 3 , & c . are 1 , 4 , 9 , & c . So likewise , the geometrical square constructed on a double line is evidently four times greater than the square on a single one ; on a triple ...
Page 75
... multiplied by the half sum of its parallél bases . Let ABCD be a trapezoid , EF its alti- D tude , AB and CD its parallel bases ; then will its area be equal to EFx ( AB + CD ) . H Through I , the middle point of the side BC , draw KL ...
... multiplied by the half sum of its parallél bases . Let ABCD be a trapezoid , EF its alti- D tude , AB and CD its parallel bases ; then will its area be equal to EFx ( AB + CD ) . H Through I , the middle point of the side BC , draw KL ...
Page 90
... like manner , ABC ABE :: AC : AE . Multiply together the corresponding terms of these proportions , omitting the common term ABE ; we have ABC ADE : AB.AC : AD.AE. Cor . Hence the two triangles would be equivalent , 90 GEOMETRY .
... like manner , ABC ABE :: AC : AE . Multiply together the corresponding terms of these proportions , omitting the common term ABE ; we have ABC ADE : AB.AC : AD.AE. Cor . Hence the two triangles would be equivalent , 90 GEOMETRY .
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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 cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides 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 solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex