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Page 16
... angles , & c . , made use of in a propo- sition are named from the letters of the alphabet taken con ... angle ABC or CBA . A rectilineal figure usually has a letter placed at each ... given finite 16 CLASS LESSONS ON EUCLID .
... angles , & c . , made use of in a propo- sition are named from the letters of the alphabet taken con ... angle ABC or CBA . A rectilineal figure usually has a letter placed at each ... given finite 16 CLASS LESSONS ON EUCLID .
Page 22
... angle included by these sides , severally equal to two sides , and the angle included by them of another , these ... given below . In the triangles which we are considering we are given- ( 1 ) Two sides in one equal to two sides in ...
... angle included by these sides , severally equal to two sides , and the angle included by them of another , these ... given below . In the triangles which we are considering we are given- ( 1 ) Two sides in one equal to two sides in ...
Page 23
... angle between them are given equal , we know that these equal parts will coincide . What results can we observe from ... Given : In two triangles two sides and the included angle equal . To be demonstrated : That the triangles are ...
... angle between them are given equal , we know that these equal parts will coincide . What results can we observe from ... Given : In two triangles two sides and the included angle equal . To be demonstrated : That the triangles are ...
Page 25
... angle ABC = angle ACB . Produce the equal sides to D and E we have to show ( 2 ) that angle DBC is = to angle ECB ... given triangle ABC . ( 2 ) A pair of constructed triangles FBC , GCB . ( 3 ) A pair of triangles AFC and AGB formed by ...
... angle ABC = angle ACB . Produce the equal sides to D and E we have to show ( 2 ) that angle DBC is = to angle ECB ... given triangle ABC . ( 2 ) A pair of constructed triangles FBC , GCB . ( 3 ) A pair of triangles AFC and AGB formed by ...
Page 28
... angle at A is common to Therefore the triangles are equal in all respects ( I. 4 ) , and the angle ABC = ACB = ACB . Proposition VI . is what is called the converse of the first part of Proposition V. , i.e. we are given what we were re ...
... angle at A is common to Therefore the triangles are equal in all respects ( I. 4 ) , and the angle ABC = ACB = ACB . Proposition VI . is what is called the converse of the first part of Proposition V. , i.e. we are given what we were re ...
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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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