Elements of Geometry and Trigonometry |
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Page 55
... inscribed in the same segment are equal ; because they are all measured by the half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is mea- sured by half the semicircumference ...
... inscribed in the same segment are equal ; because they are all measured by the half of the same arc BOC . B Cor . 2. Every angle BAD , inscribed in a semicircle is a right angle ; because it is mea- sured by half the semicircumference ...
Page 114
... inscribed . N P H T G K B S M F R E L Since T is the middle point of the arc BTA , and N the mid- dle point of the equal arc BNC , it follows , that BT = BN ; or that the vertex B of the inscribed polygon , is at the middle point of the ...
... inscribed . N P H T G K B S M F R E L Since T is the middle point of the arc BTA , and N the mid- dle point of the equal arc BNC , it follows , that BT = BN ; or that the vertex B of the inscribed polygon , is at the middle point of the ...
Page 118
... inscribed polygon without it , it follows that the perimeters of the polygons will unite on the circumference of the circle , and become equal to it . Cor . 3. When the number of sides of the inscribed polygon is indefinitely increased ...
... inscribed polygon without it , it follows that the perimeters of the polygons will unite on the circumference of the circle , and become equal to it . Cor . 3. When the number of sides of the inscribed polygon is indefinitely increased ...
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