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Seite 114
... Wherefore if two triangles & c . — Q.E.D . PROPOSITION V. , THEOREM 2 . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced the angles on the other side of the base shall be ...
... Wherefore if two triangles & c . — Q.E.D . PROPOSITION V. , THEOREM 2 . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced the angles on the other side of the base shall be ...
Seite 115
... Wherefore if two angles , & c . - Q.E.D . Corollary .-- Hence every equiangular triangle is also equi- lateral . PROPOSITION VII . , THEOREM 4 . On the same base , and on the same side of it , there cannot be two triangles having their ...
... Wherefore if two angles , & c . - Q.E.D . Corollary .-- Hence every equiangular triangle is also equi- lateral . PROPOSITION VII . , THEOREM 4 . On the same base , and on the same side of it , there cannot be two triangles having their ...
Seite 116
... Wherefore on the same base , & c.— A B PROPOSITION VIII . , THEOREM 5 . Q.E.D. If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle which is ...
... Wherefore on the same base , & c.— A B PROPOSITION VIII . , THEOREM 5 . Q.E.D. If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle which is ...
Seite 117
... Wherefore if two triangles & c . - Q.E.D . PROPOSITION IX . , PROBLEM 4 . To bisect a given rectilineal angle . Let BAC be the given rectilineal angle : It is required to bisect it . Take any point D in AB . From AC cut off AE = AD ( I ...
... Wherefore if two triangles & c . - Q.E.D . PROPOSITION IX . , PROBLEM 4 . To bisect a given rectilineal angle . Let BAC be the given rectilineal angle : It is required to bisect it . Take any point D in AB . From AC cut off AE = AD ( I ...
Seite 118
... Wherefore the given straight line AB is bisected at the point D.-Q.E.F. PROPOSITION XI . , PROBLEM 6 . To draw a straight line at right angles to a given straight line from a given point in the same . Let AB be the given straight line ...
... Wherefore the given straight line AB is bisected at the point D.-Q.E.F. PROPOSITION XI . , PROBLEM 6 . To draw a straight line at right angles to a given straight line from a given point in the same . Let AB be the given straight line ...
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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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