The Elements of Euclid |
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Page 16
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw a the straight line AD equal to C ; and from the centre A , and at the dis- b 3. Post . tance AD , describe the circle DEF ...
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw a the straight line AD equal to C ; and from the centre A , and at the dis- b 3. Post . tance AD , describe the circle DEF ...
Page 19
... greater , and from it cut equal to AC , the less , and join DC ; there- fore , because in the triangles DBC , ACB ... greater than the angle BCD ; therefore the angle ADC is greater also than BCD ; AL C D 15.2 B much more then is the ...
... greater , and from it cut equal to AC , the less , and join DC ; there- fore , because in the triangles DBC , ACB ... greater than the angle BCD ; therefore the angle ADC is greater also than BCD ; AL C D 15.2 B much more then is the ...
Page 20
... greater than BCD ; much more than is the angle BDC greater then the angle BCD . Again , because CB is equal to DB , the angle BDC is equal to the angle BCD ; but BDC has been proved A . to be greater than the same BCD ; which is ...
... greater than BCD ; much more than is the angle BDC greater then the angle BCD . Again , because CB is equal to DB , the angle BDC is equal to the angle BCD ; but BDC has been proved A . to be greater than the same BCD ; which is ...
Page 26
... greater than either of the interior opposite angles CBA , BAC . Bisect AC in E , join BE and produce it to F , and ... greater than the angle LCF ; therefore the angle ACD is greater than BAE : in the same manner , if the site BC be ...
... greater than either of the interior opposite angles CBA , BAC . Bisect AC in E , join BE and produce it to F , and ... greater than the angle LCF ; therefore the angle ACD is greater than BAE : in the same manner , if the site BC be ...
Page 27
... greater than the angles ABC , ACB ; but ACD , ACB ~ are together equal to two right angles ; therefore the angles b ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is ...
... greater than the angles ABC , ACB ; but ACD , ACB ~ are together equal to two right angles ; therefore the angles b ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is ...
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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