The Elements of Euclid |
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Page 17
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does ...
... base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite ... base BC shall coincide with the base EF , because the point B coinciding with E , and C with F , if the base BC does ...
Page 18
... base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one s are equal to the remaining an in97 % gles of the other , each to each , -to which the equal sides are op- sposite ; viz ...
... base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the remaining angles of the one s are equal to the remaining an in97 % gles of the other , each to each , -to which the equal sides are op- sposite ; viz ...
Page 19
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB , the less to the great- er : which is absurd . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c ...
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB , the less to the great- er : which is absurd . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c ...
Page 20
... base CD are equal to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
... base CD are equal to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is ... base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one ...
Page 21
... base BC coin- cides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles ...
... base BC coin- cides with the base EF , but the sides BA , CA do not coincide with the sides ED , FD , but have a different situation , as EG , FG ; then , upon the same base EF , and upon the same side of it , there can be two triangles ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore