The Elements of Euclid |
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Page 17
... 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 to the B angle DEF , and ...
... 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 to the B angle DEF , and ...
Page 18
... angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . a 3. 1 . 1 . In BD take any point F , and from AE the greater , cut off AG equal to AF , the less , and join ... ABC be a triangle having the angle THE ELEMENTS.
... angle ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . a 3. 1 . 1 . In BD take any point F , and from AE the greater , cut off AG equal to AF , the less , and join ... ABC be a triangle having the angle THE ELEMENTS.
Page 19
Euclid Robert Simson. • " Let ABC be a triangle having the angle ABC equal to the Book L angle ACB ; the side AB is also equal to the side AC . D A off DB a 3.1 . For if AB be not equal to AC , one of them is greater than the other : let ...
Euclid Robert Simson. • " Let ABC be a triangle having the angle ABC equal to the Book L angle ACB ; the side AB is also equal to the side AC . D A off DB a 3.1 . For if AB be not equal to AC , one of them is greater than the other : let ...
Page 24
... angle CBA be equal to ABD , each of them is a A E A D B D B 2 a def . 10. right angle ; but , if not , from the ... ABC ; there- fore the angles DBA , ABC are equal to the three angles DBE , EBA , ABC ; but the angles CBE , EBD have been ...
... angle CBA be equal to ABD , each of them is a A E A D B D B 2 a def . 10. right angle ; but , if not , from the ... ABC ; there- fore the angles DBA , ABC are equal to the three angles DBE , EBA , ABC ; but the angles CBE , EBD have been ...
Page 25
... angles CBA , ABD : take away the common angle ABC , the remaining angle ABE is equal to the remaining angle b S. Ax ABD , the less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And , in ...
... angles CBA , ABD : take away the common angle ABC , the remaining angle ABE is equal to the remaining angle b S. Ax ABD , the less to the greater , which is impossible ; therefore BE is not in the same straight line with BC . And , in ...
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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