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Side 11
... angles . ' OF FOUR - SIDED FIGURES . Four - sided figures are of two classes , those having their opposite sides parallel , called parallelograms , and irregular figures , called trapeziums ( tables ) . The line joining the opposite angles ...
... angles . ' OF FOUR - SIDED FIGURES . Four - sided figures are of two classes , those having their opposite sides parallel , called parallelograms , and irregular figures , called trapeziums ( tables ) . The line joining the opposite angles ...
Side 12
... opposite sides equal to one another , but all its sides are not equal nor its angles right angles . ' 34. All other four - sided figures besides these are called trapeziums . ' OF PARALLELS . 35. ' Parallel straight lines are such as ...
... opposite sides equal to one another , but all its sides are not equal nor its angles right angles . ' 34. All other four - sided figures besides these are called trapeziums . ' OF PARALLELS . 35. ' Parallel straight lines are such as ...
Side 28
... opposite angles are equal . Proposition VI . given - Two angles equal ; show that the two opposite sides are equal . Euclid here , as in many other converse propositions , adopts the indirect method of proof . This , which is not so ...
... opposite angles are equal . Proposition VI . given - Two angles equal ; show that the two opposite sides are equal . Euclid here , as in many other converse propositions , adopts the indirect method of proof . This , which is not so ...
Side 29
... angles at the base of a triangle being given equal , to show that the sides opposite to them are equal . A Cons . - Assuming AB to be greater than AC , make DB equal to it ( I. 3 ) , join DC . Proof ( Indirect ) .- Show that △ DBC ...
... angles at the base of a triangle being given equal , to show that the sides opposite to them are equal . A Cons . - Assuming AB to be greater than AC , make DB equal to it ( I. 3 ) , join DC . Proof ( Indirect ) .- Show that △ DBC ...
Side 33
... angles are opposite to equal sides . Hence an isosceles triangle has two equal angles , and , conversely , a triangle with two equal angles is isosceles ; an equilateral triangle is equiangular , and an equiangular triangle is ...
... angles are opposite to equal sides . Hence an isosceles triangle has two equal angles , and , conversely , a triangle with two equal angles is isosceles ; an equilateral triangle is equiangular , and an equiangular triangle is ...
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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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