Class lessons on Euclid1882 |
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Página 13
... interior angles on the same side of it , taken together , less than two right angles , these straight lines being con- tinually produced , shall at length meet upon that side on which are the angles which are together less than two ...
... interior angles on the same side of it , taken together , less than two right angles , these straight lines being con- tinually produced , shall at length meet upon that side on which are the angles which are together less than two ...
Página 46
... 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 this way : — X According to the rule given in Lecture VI ...
... 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 this way : — X According to the rule given in Lecture VI ...
Página 47
... angles are equal ( I. 15 ) . Then , joining FC , we have con- structed the triangles BAE , FEC equal = B D in all ... interior and opposite angles . SUMMARY OF PROPOSITION XVI . , THEOREM 9 . The exterior angle of any triangle is greater ...
... angles are equal ( I. 15 ) . Then , joining FC , we have con- structed the triangles BAE , FEC equal = B D in all ... interior and opposite angles . SUMMARY OF PROPOSITION XVI . , THEOREM 9 . The exterior angle of any triangle is greater ...
Página 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 angle ...
... 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 angle ...
Página 49
... angle opposite to it ( I. 18 ) . ( B ) The greater angle of every triangle has ... angles in the same triangle ? From the 5th and 6th propositions we learn ... interior and opposite angle ACB . Then angle ADB is less than angle ABC and ...
... angle opposite to it ( I. 18 ) . ( B ) The greater angle of every triangle has ... angles in the same triangle ? From the 5th and 6th propositions we learn ... interior and opposite angle ACB . Then angle ADB is less than angle ABC and ...
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Términos y frases comunes
&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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