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Page 11
... opposite sides parallel , called parallelograms , and irregular figures , called trapeziums ( tables ) . The line joining the opposite angles of any quadrilateral is called a diameter , or diagonal . Parallelograms are of four kinds ...
... opposite sides parallel , called parallelograms , and irregular figures , called trapeziums ( tables ) . The line joining the opposite angles of any quadrilateral is called a diameter , or diagonal . Parallelograms are of four kinds ...
Page 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 ...
Page 24
... sides coincide , the parts included by them , i.e. the areas and remainings , coincide and are equal ( ax . 8 ) ... opposite the base , at which the other two sides of a triangle meet , is called the ' vertex , ' and the angle at ...
... sides coincide , the parts included by them , i.e. the areas and remainings , coincide and are equal ( ax . 8 ) ... opposite the base , at which the other two sides of a triangle meet , is called the ' vertex , ' and the angle at ...
Page 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 ...
Page 29
... 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 = △ ABC ( I. 4 ) . This is absurd ( ax . 9 ) . .. AB is not unequal to AC ...
... 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 = △ ABC ( I. 4 ) . This is absurd ( ax . 9 ) . .. AB is not unequal to AC ...
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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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