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Page 24
... pairs of angles . You will see that we can include , or shut in , any angle in a triangle , by drawing a straight line meeting the lines con- taining the angle , or the arms of the angle as they are called . With this preface I hope ...
... pairs of angles . You will see that we can include , or shut in , any angle in a triangle , by drawing a straight line meeting the lines con- taining the angle , or the arms of the angle as they are called . With this preface I hope ...
Page 25
... pair of constructed triangles FBC , GCB . ( 3 ) A pair of triangles AFC and AGB formed by adding the given triangle to each of the constructed ones . D F A B C G E You will see , too , that as the triangles overlap each other , some of ...
... pair of constructed triangles FBC , GCB . ( 3 ) A pair of triangles AFC and AGB formed by adding the given triangle to each of the constructed ones . D F A B C G E You will see , too , that as the triangles overlap each other , some of ...
Page 26
... pair of triangles . Let us then compare the larger triangles , and if they are equal we can retrace our steps and show that the smaller pair are . In triangles FAC , GAB , we have F B G side AB = side AC ( sides of the isosceles ...
... pair of triangles . Let us then compare the larger triangles , and if they are equal we can retrace our steps and show that the smaller pair are . In triangles FAC , GAB , we have F B G side AB = side AC ( sides of the isosceles ...
Page 27
... pair of equal triangles , or , to put it more clearly , Z ABG = 2 ABC + 2 CBG LACF = Z ACB + BCF . And we know that angles ABG and ACF are equal , since they are similar angles of the large pair of triangles . Also angles CBG and BCF ...
... pair of equal triangles , or , to put it more clearly , Z ABG = 2 ABC + 2 CBG LACF = Z ACB + BCF . And we know that angles ABG and ACF are equal , since they are similar angles of the large pair of triangles . Also angles CBG and BCF ...
Page 43
... pairs subtract the common angle ABC , and we have remaining angle ABE equal to angle ABD , the part to the whole , which is absurd . Hence it is evident that no other line but BD can be drawn in a straight line with CB . SUMMARY OF ...
... pairs subtract the common angle ABC , and we have remaining angle ABE equal to angle ABD , the part to the whole , which is absurd . Hence it is evident that no other line but BD can be drawn in a straight line with CB . SUMMARY OF ...
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Common terms and phrases
&c.-Q.E.D. PROPOSITION ABCD alternate angles angle ABC angle ACB angles are equal angles equal base BC bisected Cheaper Edition circle cons construction Demy 8vo diameter enunciation equal bases equal in area equal sides equal triangles equilateral triangle Euclid exterior Fcap Frontispiece given angle given line given point given straight line given triangle gnomon gram half the line Illustrations interior and opposite interior angles isosceles triangle Join line equal meet opposite angles opposite sides parallelogram perpendicular Poems problem produced proof Prop rectangle contained rhombus right angles right-angled triangle Second Edition sides equal Small crown 8vo square on AC square on half SUMMARY OF PROPOSITION THEOREM Third Edition Translated triangle ABC triangles are equal twice the rect twice the rectangle vertical angle vols Wherefore whole line
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