Elements of Geometry and Trigonometry |
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Page 51
... proportional to the other three . When the second term is equal to the third , it is said to be a mean proportional between the extremes . In this case , there are but three different quantities in the proportion , and the last is said ...
... proportional to the other three . When the second term is equal to the third , it is said to be a mean proportional between the extremes . In this case , there are but three different quantities in the proportion , and the last is said ...
Page 52
... proportion , A : B C D ; whence , B = A ; clearing of fractions , we have , BC AD ; which was to be proved . Cor . If B is equal to C , there will be but three pro- portional quantities ; in this case , the square of the mean ... means of a ...
... proportion , A : B C D ; whence , B = A ; clearing of fractions , we have , BC AD ; which was to be proved . Cor . If B is equal to C , there will be but three pro- portional quantities ; in this case , the square of the mean ... means of a ...
Page 119
... mean propor- tional between the hypothenuse and the adjacent segment : 3o . The perpendicular will be a mean proportional between the two segments of the hypothenuse . 1o . Let ABC be a right - angled triangle , A the vertex of the ...
... mean propor- tional between the hypothenuse and the adjacent segment : 3o . The perpendicular will be a mean proportional between the two segments of the hypothenuse . 1o . Let ABC be a right - angled triangle , A the vertex of the ...
Page 120
... mean proportional between BD and DC . For , the triangles ADB and ADC being similar , their homologous sides are proportional ; hence , BD : AD :: AD : DC ; which was to be proved . Cor . 1. From the proportions , and , BC : AB :: AB ...
... mean proportional between BD and DC . For , the triangles ADB and ADC being similar , their homologous sides are proportional ; hence , BD : AD :: AD : DC ; which was to be proved . Cor . 1. From the proportions , and , BC : AB :: AB ...
Page 121
... mean proportional between the diameter and the adjacent segment ; and , the perpendicular will be a mean proportional between the segments of the diameter . PROPOSITION XXIV . THEOREM . Triangles which have an angle in each equal , are ...
... mean proportional between the diameter and the adjacent segment ; and , the perpendicular will be a mean proportional between the segments of the diameter . PROPOSITION XXIV . THEOREM . Triangles which have an angle in each equal , are ...
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Common terms and phrases
ABCD ACĀ² adjacent angles altitude angle ACB apothem Applying logarithms base and altitude bisect centre chord circle circumference circumscribed coincide cone consequently convex surface corresponding cosec cosine Cotang cylinder denote diagonals diameter distance divided draw drawn edges equally distant feet find the area Formula frustum given angle given line given point greater hence homologous hypothenuse included angle interior angles intersection less Let ABC log sin logarithm lower base mantissa mean proportional measured by half middle point number of sides opposite parallel parallelogram parallelopipedon perimeter perpendicular plane MN polyedral angle polyedron prism PROBLEM PROPOSITION proved pyramid quadrant radii radius rectangle regular polygons right angles right-angled triangle Scholium secant segment side BC similar sine slant height sphere spherical polygon spherical triangle square Tang tangent THEOREM triangle ABC triangular prisms triedral angle upper base vertex vertices whence