Modern Methods in Elementary GeometryMacmillan, 1868 - 112 σελίδες |
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Σελίδα 79
... may be equal to a given square . The conditions ? 13. Bisect a given triangle by a straight line drawn through a point in one of its sides . BOOK IV . PROPORTIONAL LINES . SIMILAR FIGURES . THEOREM AREA OF FIGURES . 79.
... may be equal to a given square . The conditions ? 13. Bisect a given triangle by a straight line drawn through a point in one of its sides . BOOK IV . PROPORTIONAL LINES . SIMILAR FIGURES . THEOREM AREA OF FIGURES . 79.
Σελίδα 80
E. M. Reynolds. BOOK IV . PROPORTIONAL LINES . SIMILAR FIGURES . THEOREM I. PARALLEL straight lines which cut off equal parts from one of two straight lines cut off also equal parts from the other . Let AB , AC be straight lines meeting ...
E. M. Reynolds. BOOK IV . PROPORTIONAL LINES . SIMILAR FIGURES . THEOREM I. PARALLEL straight lines which cut off equal parts from one of two straight lines cut off also equal parts from the other . Let AB , AC be straight lines meeting ...
Σελίδα 81
... DF . L B M Again , if AB contain AD n times , so that AB = n.AD , then AC = n.AF , and BC = n , DF . AL m . AD Hence AB LM ՊՈՆ • Also 6 PROPORTIONAL LINES . SIMILAR FIGURES . 81 COR. 2. From the congruent triangles ADF, DEK...
... DF . L B M Again , if AB contain AD n times , so that AB = n.AD , then AC = n.AF , and BC = n , DF . AL m . AD Hence AB LM ՊՈՆ • Also 6 PROPORTIONAL LINES . SIMILAR FIGURES . 81 COR. 2. From the congruent triangles ADF, DEK...
Σελίδα 82
... AL AM LB MC ' then LM is parallel to BC . THEOREM III . AL AM = AB AC ' The sides about the angles of equiangular triangles are proportional . B ' А AA B C B Let ABC , A'B'C ' be equiangular triangles . Then 82 ELEMENTARY GEOMETRY .
... AL AM LB MC ' then LM is parallel to BC . THEOREM III . AL AM = AB AC ' The sides about the angles of equiangular triangles are proportional . B ' А AA B C B Let ABC , A'B'C ' be equiangular triangles . Then 82 ELEMENTARY GEOMETRY .
Σελίδα 83
... so that AB : A'B ' = AC : A'C ' , these triangles shall be equiangular . B C В A B ' Apply the triangle ABC to the triangle A'B'C ' , so that the point A may be on A ' , and 6-2 PROPORTIONAL LINES . SIMILAR FIGURES . 83.
... so that AB : A'B ' = AC : A'C ' , these triangles shall be equiangular . B C В A B ' Apply the triangle ABC to the triangle A'B'C ' , so that the point A may be on A ' , and 6-2 PROPORTIONAL LINES . SIMILAR FIGURES . 83.
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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