Modern Methods in Elementary GeometryMacmillan, 1868 - 112 σελίδες |
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Σελίδα 34
... touch BC in one point , and the triangle will have a right angle . Thirdly . If the given side be greater than the perpendi- cular from A to BC , the arc will meet BC in two points , as C and D. We must now further distinguish two cases ...
... touch BC in one point , and the triangle will have a right angle . Thirdly . If the given side be greater than the perpendi- cular from A to BC , the arc will meet BC in two points , as C and D. We must now further distinguish two cases ...
Σελίδα 41
... touch it . THEOREM VI . The straight line AB drawn at right angles to the radius OA from its extremity A is a tangent to the circle at A. For the perpendicular OA is shorter than any other line OC that can be drawn from 0 to A. Hence ...
... touch it . THEOREM VI . The straight line AB drawn at right angles to the radius OA from its extremity A is a tangent to the circle at A. For the perpendicular OA is shorter than any other line OC that can be drawn from 0 to A. Hence ...
Σελίδα 42
... touch in more than one . 0 0 B For every point on the circumference of I is equally dis- tant from the centre I. But only two equal straight lines can be drawn from I to the circumference of 0 . [ II . 3. Cor . Therefore the ...
... touch in more than one . 0 0 B For every point on the circumference of I is equally dis- tant from the centre I. But only two equal straight lines can be drawn from I to the circumference of 0 . [ II . 3. Cor . Therefore the ...
Σελίδα 43
... touch each other they have a common tangent at the point of contact . B A 0- If one circle touch the other internally the tangent to the outer circle is obviously the tangent to the inner . If the circles touch externally let AB be the ...
... touch each other they have a common tangent at the point of contact . B A 0- If one circle touch the other internally the tangent to the outer circle is obviously the tangent to the inner . If the circles touch externally let AB be the ...
Σελίδα 44
... touch one another , the straight line joining their centres must pass through the point of contact . For the centre of either circle must lie on the normal at the point of contact . Arcs and Angles . THEOREM X. In equal circles or in ...
... touch one another , the straight line joining their centres must pass through the point of contact . For the centre of either circle must lie on the normal at the point of contact . Arcs and Angles . THEOREM X. In equal circles or in ...
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A'BC Algebra alternate angle altitude angle equal arc CD ARITHMETIC BC² bisect BROOKE FOSS WESTCOTT CA² Cambridge centre chord circle touching circumference cloth coincide congruent CONIC SECTIONS contain convex angle convex polygon Crown 8vo diagonals diameter dicular divide Edward Thring ELEMENTARY TREATISE equal angles equally distant equally remote equiangular equiangular and similar equilateral triangle Examples exterior angle Fcap Find the locus GEOMETRY given angle given circle given line given point given straight line greater Hence intersect isosceles John's College late Fellow Let ABCD line drawn MATHEMATICAL measure meet middle point opposite sides parallel to CD parallelogram perpen perpendicular polygon produced quadrilateral figure radius rectangle right angles right-angled triangle Schools Second Edition segments Shew shortest line similar triangles student tangent THEOREM THEOREM VII Third Edition trapezium triangle ABC vertex