The Elements of Euclid |
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Page 17
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABC ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the equal sides are opposite , shall be equal each to each , viz . the angle ABC ...
Page 20
... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more than is ... BAC is e qual to the angle EDF . For , if the tri- D G angle ABC be ap- plied to DEF , so B СЕ F that the point B be ...
... angle ECD is greater than the angle BCD ; wherefore the angle FDC is likewise greater than BCD ; much more than is ... BAC is e qual to the angle EDF . For , if the tri- D G angle ABC be ap- plied to DEF , so B СЕ F that the point B be ...
Page 21
... angle BAC coincides with the angle EDF , and is equal to it . Therefore if two b 8. Ax . triangles , & c . Q. E. D. ر PROP . IX . PROB . TO bisect a given rectilineal angle , that is , to di- vide it into two equal angles . Let BAC be ...
... angle BAC coincides with the angle EDF , and is equal to it . Therefore if two b 8. Ax . triangles , & c . Q. E. D. ر PROP . IX . PROB . TO bisect a given rectilineal angle , that is , to di- vide it into two equal angles . Let BAC be ...
Page 26
... angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAC . Bisect AC in E ...
... angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of the interior opposite angles CBA , BAC . Bisect AC in E ...
Page 27
Euclid Robert Simson. + these add the angle ACB ; therefore the angles ACD , ACB Book I. are greater than the angles ... BAC , ACB , as also CAB , ABC , are less than two right angles , Therefore any two angles , & c . Q. E. D. PROP . XVIII , ...
Euclid Robert Simson. + these add the angle ACB ; therefore the angles ACD , ACB Book I. are greater than the angles ... BAC , ACB , as also CAB , ABC , are less than two right angles , Therefore any two angles , & c . Q. E. D. PROP . XVIII , ...
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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