Elements of Geometry and Trigonometry |
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Page 36
... mean . PROPOSITION II . THEOREM . If the product of two quantities be equal to the product of two other quantities , two of them will be the extremes and the other two the means of a proportion . Let MxQ = Nx P ; then will M : N :: P ...
... mean . PROPOSITION II . THEOREM . If the product of two quantities be equal to the product of two other quantities , two of them will be the extremes and the other two the means of a proportion . Let MxQ = Nx P ; then will M : N :: P ...
Page 89
... mean proportional between the segments BD , DC , of the hypothenuse . Scholium . Since BD : AB :: AB : BC , the product of the extremes will be equal to that of the means , or AB2 = BD.BC . For the same reason we have AC2 = DC.BC ...
... mean proportional between the segments BD , DC , of the hypothenuse . Scholium . Since BD : AB :: AB : BC , the product of the extremes will be equal to that of the means , or AB2 = BD.BC . For the same reason we have AC2 = DC.BC ...
Page 113
... means of the deca- gon , polygons of 20 , 40 , 80 , & c . sides ; by means of the pente- decagon , polygons of 30 , 60 , 120 , & c . sides . It is further evident , that any of the inscribed polygons will be less than the inscribed ...
... means of the deca- gon , polygons of 20 , 40 , 80 , & c . sides ; by means of the pente- decagon , polygons of 30 , 60 , 120 , & c . sides . It is further evident , that any of the inscribed polygons will be less than the inscribed ...
Contents
BOOK | 7 |
Problems relating to the First and Third Books 57 | 57 |
BOOK IV | 68 |
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex