Class lessons on Euclid1882 |
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Seite 46
... exterior angle ACD shall be greater than either of the interior and opposite angles CBA , BAC . The construction made use of by Euclid for the proof of this theorem is exceedingly ingenious . We may imagine that it was arrived at in ...
... exterior angle ACD shall be greater than either of the interior and opposite angles CBA , BAC . The construction made use of by Euclid for the proof of this theorem is exceedingly ingenious . We may imagine that it was arrived at in ...
Seite 47
... exterior angle ACD is greater than either of the interior and opposite angles . SUMMARY OF PROPOSITION XVI . , THEOREM 9 . The exterior angle of any triangle is greater than either of the interior and opposite angles . I. To show that ...
... exterior angle ACD is greater than either of the interior and opposite angles . SUMMARY OF PROPOSITION XVI . , THEOREM 9 . The exterior angle of any triangle is greater than either of the interior and opposite angles . I. To show that ...
Seite 48
... exterior angle , together with the adjacent interior angle , are equal to two right angles ( I. 13 ) . Produce BC , the base of triangle ABC , to D , then angles ACD , ACB are to- gether equal to two right angles . Now we know that ...
... exterior angle , together with the adjacent interior angle , are equal to two right angles ( I. 13 ) . Produce BC , the base of triangle ABC , to D , then angles ACD , ACB are to- gether equal to two right angles . Now we know that ...
Seite 49
... exterior angle of the triangle DBC , and is therefore greater than the interior and opposite angle ACB . Then angle ADB is less than angle ABC and greater than angle ACB , ' much more then must angle ABC be greater than angle ACB . ' E ...
... exterior angle of the triangle DBC , and is therefore greater than the interior and opposite angle ACB . Then angle ADB is less than angle ABC and greater than angle ACB , ' much more then must angle ABC be greater than angle ACB . ' E ...
Seite 53
... exterior angle of a triangle , of which the other is an interior and opposite angle ( I. 16 ) . The latter condition will be the most likely to help us here . amining the figure you will see Ex- B angle BDC is greater than △ BEC ( I ...
... exterior angle of a triangle , of which the other is an interior and opposite angle ( I. 16 ) . The latter condition will be the most likely to help us here . amining the figure you will see Ex- B angle BDC is greater than △ BEC ( I ...
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&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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