Class lessons on Euclid1882 |
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Side 17
... construct a mathematical figure . Def . 24 tells us that an equilateral triangle is a figure having three equal sides . The given line will itself form one side of the triangle , and if we can draw two other lines equal to it in such a ...
... construct a mathematical figure . Def . 24 tells us that an equilateral triangle is a figure having three equal sides . The given line will itself form one side of the triangle , and if we can draw two other lines equal to it in such a ...
Side 25
... constructing the triangles we must do what we can to make them equal , so let us take point G , so that CG ( a side ... constructed triangles FBC , GCB . ( 3 ) A pair of triangles AFC and AGB formed by adding the given triangle to each ...
... constructing the triangles we must do what we can to make them equal , so let us take point G , so that CG ( a side ... constructed triangles FBC , GCB . ( 3 ) A pair of triangles AFC and AGB formed by adding the given triangle to each ...
Side 31
... construct two isosceles triangles , with a common base CD . What do we know further about these triangles ? Because they are isosceles the angles at their bases are equal , i.e. Angle ( 1 ) ACD = angle ( 2 ) ADC . " " ( 3 ) BCD = 99 ( 4 ) ...
... construct two isosceles triangles , with a common base CD . What do we know further about these triangles ? Because they are isosceles the angles at their bases are equal , i.e. Angle ( 1 ) ACD = angle ( 2 ) ADC . " " ( 3 ) BCD = 99 ( 4 ) ...
Side 35
... construct equal triangles whose vertical angles shall together make up the angle BAC ? To do this we must fulfil the conditions either of I. 4 or of I. 8. As we have no angles given equal , we must follow I. 8 and endeavour to construct ...
... construct equal triangles whose vertical angles shall together make up the angle BAC ? To do this we must fulfil the conditions either of I. 4 or of I. 8. As we have no angles given equal , we must follow I. 8 and endeavour to construct ...
Side 46
... constructed satisfy the conditions of I. 4 , and are therefore equal . Next , can we retrace our steps , and construct these equal triangles , without assuming angle ECX ? We can , as before , bisect AC in E , thus obtaining AE equal to ...
... constructed satisfy the conditions of I. 4 , and are therefore equal . Next , can we retrace our steps , and construct these equal triangles , without assuming angle ECX ? We can , as before , bisect AC in E , thus obtaining AE equal to ...
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Vanlige uttrykk og setninger
&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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