The Elements of Euclid |
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Page 26
... 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 , join BE and produce it ... angle ACB ; therefore the angles 26 THE ELEMENTS.
... 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 , join BE and produce it ... angle ACB ; therefore the angles 26 THE ELEMENTS.
Page 27
Euclid Robert Simson. + these add the angle ACB ; therefore the angles ACD , ACB Book I. are greater than the angles ABC , ACB ; but ACD , ACB ~ are together equal to two right angles ; therefore the angles b 13. 1 . ABC , BCA are less ...
Euclid Robert Simson. + these add the angle ACB ; therefore the angles ACD , ACB Book I. are greater than the angles ABC , ACB ; but ACD , ACB ~ are together equal to two right angles ; therefore the angles b 13. 1 . ABC , BCA are less ...
Page 28
... angle , & c . Q. E. D. See No a 3. 1 . b 5. 1 . c 19. 1 . See Note . PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . Let ABC be a triangle ' ; any two sides of it together are greater than the ...
... angle , & c . Q. E. D. See No a 3. 1 . b 5. 1 . c 19. 1 . See Note . PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . Let ABC be a triangle ' ; any two sides of it together are greater than the ...
Page 33
... angle GBC is equal to the angle DEF ; therefore the base GC is equal to the base DF , and the triangle GBC to a 4 1 ... ABC is equal to the angle DEF ; the base therefore AC is equal to the base DF , and the third angle BAC to the third ...
... angle GBC is equal to the angle DEF ; therefore the base GC is equal to the base DF , and the triangle GBC to a 4 1 ... ABC is equal to the angle DEF ; the base therefore AC is equal to the base DF , and the third angle BAC to the third ...
Page 37
... ABC be a triangle , and let one of its sides BC be produ- ced to D ; the exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; and the three interior angles of the triangle , viz . ABC , BCA , CAB , are ...
... ABC be a triangle , and let one of its sides BC be produ- ced to D ; the exterior angle ACD is equal to the two interior and opposite angles CAB , ABC ; and the three interior angles of the triangle , viz . ABC , BCA , CAB , are ...
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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