Class lessons on Euclid1882 |
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Page 34
... of the rule just given . It is required to bisect a given angle — that is , to divide it into two equal angles . Draw any angle BAC 34 CLASS LESSONS ON EUCLID . GEOMETRICAL ANALYSIS AND SYNTHESIS PROPOSI- TIONS 9-12-TABLE OF RESULTS-LOCI.
... of the rule just given . It is required to bisect a given angle — that is , to divide it into two equal angles . Draw any angle BAC 34 CLASS LESSONS ON EUCLID . GEOMETRICAL ANALYSIS AND SYNTHESIS PROPOSI- TIONS 9-12-TABLE OF RESULTS-LOCI.
Page 35
... bisected , by joining equal arms of the angle with the bisecting line , equal triangles are formed . Can we reverse this order and construct equal triangles whose vertical angles shall together make up the angle BAC ? To do this we must ...
... bisected , by joining equal arms of the angle with the bisecting line , equal triangles are formed . Can we reverse this order and construct equal triangles whose vertical angles shall together make up the angle BAC ? To do this we must ...
Page 36
... bisected . SUMMARY OF PROPOSITION IX . , PROBLEM 4 . To bisect a given rectilineal angle . Cons . - Cut off from the arms of the given angle equal D A E parts , AD , AE . Join DE . On it de- scribe the equilat . A DFE . Join AF . Proof ...
... bisected . SUMMARY OF PROPOSITION IX . , PROBLEM 4 . To bisect a given rectilineal angle . Cons . - Cut off from the arms of the given angle equal D A E parts , AD , AE . Join DE . On it de- scribe the equilat . A DFE . Join AF . Proof ...
Page 37
... Bisect its vertical angle ( I. 9 ) , producing the bisecting line to cut the base , i.e. the given line , which will then be itself bisected , as we have seen . SUMMARY OF PROPOSITION X. , PROBLEM 5 . To bisect a given finite straight ...
... Bisect its vertical angle ( I. 9 ) , producing the bisecting line to cut the base , i.e. the given line , which will then be itself bisected , as we have seen . SUMMARY OF PROPOSITION X. , PROBLEM 5 . To bisect a given finite straight ...
Page 38
... bisected at D , and the given point is not necessarily the point of bisection . Produce AB in one or both directions , and you will see that the construction still holds good . It remains for us to apply it to the problem we are engaged ...
... bisected at D , and the given point is not necessarily the point of bisection . Produce AB in one or both directions , and you will see that the construction still holds good . It remains for us to apply it to the problem we are engaged ...
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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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