Elements of Geometry and Trigonometry |
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Page 89
... become perceptible . Examples of this are to be seen in all the demonstrations , in which the reductio ad absurdum is employed . In such demon- strations , where the object is to show that two quantities are equal , we proceed by ...
... become perceptible . Examples of this are to be seen in all the demonstrations , in which the reductio ad absurdum is employed . In such demon- strations , where the object is to show that two quantities are equal , we proceed by ...
Page 117
... become equal to each other , and equal also to the circle . For , if they are not ultimately equal , let D represent their smallest difference . Now , it has been proved in the proposition , that the diffe- rence between the ...
... become equal to each other , and equal also to the circle . For , if they are not ultimately equal , let D represent their smallest difference . Now , it has been proved in the proposition , that the diffe- rence between the ...
Page 118
... become equal , they will exactly coin- cide , and have a common perimeter . But as the sides of the circumscribed polygon cannot fall within the circle , nor the sides of the inscribed polygon without it , it follows that the perimeters ...
... become equal , they will exactly coin- cide , and have a common perimeter . But as the sides of the circumscribed polygon cannot fall within the circle , nor the sides of the inscribed polygon without it , it follows that the perimeters ...
Page 120
... become equal to the circumferences of the cir- cumscribed circles ( Prop . VIII . Cor . 2. ) , and we shall have circ . CA circ . OB :: CA : OB . Again , the areas of the inscribed polygons are to each other as CA2 to OB2 ( Prop . X ...
... become equal to the circumferences of the cir- cumscribed circles ( Prop . VIII . Cor . 2. ) , and we shall have circ . CA circ . OB :: CA : OB . Again , the areas of the inscribed polygons are to each other as CA2 to OB2 ( Prop . X ...
Page 121
... become equal to the circumfe- rence of the circle , the perpendicular OF will become equal to OA , and the area of the polygon to the area of the circle ( Prop . VIII . Cor . 1. & 3. ) . But the expression for the area will then become ...
... become equal to the circumfe- rence of the circle , the perpendicular OF will become equal to OA , and the area of the polygon to the area of the circle ( Prop . VIII . Cor . 1. & 3. ) . But the expression for the area will then become ...
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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 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