Modern Methods in Elementary Geometry |
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Page 5
E. M. Reynolds. THEOREM III . Any straight line AB is less than the two straight lines AC , CB which have the same extremities A and B. For AB is the shortest line that A B can be drawn from A to B. THEOREM IV . Two straight lines AC ...
E. M. Reynolds. THEOREM III . Any straight line AB is less than the two straight lines AC , CB which have the same extremities A and B. For AB is the shortest line that A B can be drawn from A to B. THEOREM IV . Two straight lines AC ...
Page 6
... line ACDEB is less than another broken line AFGB by which it is enclosed . THEOREM V. The perpendicular is the shortest line that can be drawn B- FE D from a point A to a straight line BC ; and of the others AE which is nearer to the ...
... line ACDEB is less than another broken line AFGB by which it is enclosed . THEOREM V. The perpendicular is the shortest line that can be drawn B- FE D from a point A to a straight line BC ; and of the others AE which is nearer to the ...
Page 10
... lines are drawn each parallel to CD , which is absurd . COR . 1. The other angles at G are equal to the corre- sponding angles at H. COR . 2. The alternate angles AGH , GHD are equal . COR . 3. The two interior angles BGH , GHD are toge ...
... lines are drawn each parallel to CD , which is absurd . COR . 1. The other angles at G are equal to the corre- sponding angles at H. COR . 2. The alternate angles AGH , GHD are equal . COR . 3. The two interior angles BGH , GHD are toge ...
Page 11
E. M. Reynolds. THEOREM IX . Straight lines AB , CD parallel to the same line KL are parallel to one another . E Draw EFHG cutting AB , KL , and CD , in F , H , and G. F A B H Then = EFB FHL . K L G And = FHL HGD . C-- D Therefore EFB ...
E. M. Reynolds. THEOREM IX . Straight lines AB , CD parallel to the same line KL are parallel to one another . E Draw EFHG cutting AB , KL , and CD , in F , H , and G. F A B H Then = EFB FHL . K L G And = FHL HGD . C-- D Therefore EFB ...
Page 12
... drawn from A to BC . Then since AB = AC , these lines B are equally remote from the perpen- dicular . A Therefore and BD = DC , C = B. I. 6. Cor . 1 . = COR . 1. Also BAD CAD . Hence in an isosceles tri angle the perpendicular bisects ...
... drawn from A to BC . Then since AB = AC , these lines B are equally remote from the perpen- dicular . A Therefore and BD = DC , C = B. I. 6. Cor . 1 . = COR . 1. Also BAD CAD . Hence in an isosceles tri angle the perpendicular bisects ...
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Common terms and phrases
Algebra alternate angle altitude ARITHMETIC base BC² BEGINNERS bisect BROOKE FOSS WESTCOTT Cambridge centre chord Christ's College circle touching circumference Clifton College cloth coincide congruent CONIC SECTIONS construct contains convex angle Crown 8vo describe a circle diagonals diameter dicular distance divide Edward Thring ELEMENTARY TREATISE equal angles equally distant equiangular equilateral triangle Examination Papers Exercises exterior angle Fcap Fellow of St GEOMETRY given circle given line given point given square given straight line greater Greek Text Head Master Hence inscribe intersect John's College Join JOSEPH WOLSTENHOLME Jugurtha late Fellow Latin Let ABCD line drawn locus Mathematical Lecturer measure meet middle point MIXED MATHEMATICS numerous parallel to BC parallelogram perpen perpendicular polygon problems quadrilateral figure radius rectangle right angles Second Edition Shew similar triangles student tangent THEOREM VII Third Edition trapezium triangle ABC vertex
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