The Elements of Euclid |
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Page 27
... join BD ; and because ADB is the ex- terior angle of the triangle BDC , B c A Ꭰa 3. 1 . C it is greater than the interior and opposite angle DCB ; but b 16. 1 . ADB is equal to ABD , because the side AB is equal to the c 5. 1 . side ...
... join BD ; and because ADB is the ex- terior angle of the triangle BDC , B c A Ꭰa 3. 1 . C it is greater than the interior and opposite angle DCB ; but b 16. 1 . ADB is equal to ABD , because the side AB is equal to the c 5. 1 . side ...
Page 30
... join DE ; and make a D E F G the triangle AFG the sides of which shall $ 8.1 . See Note . be equal to the three B straight lines CD , DE , CE , so that CD be equal to AF , CE , to AG , and DE to FG ; and because DC , CE are equal to FA ...
... join DE ; and make a D E F G the triangle AFG the sides of which shall $ 8.1 . See Note . be equal to the three B straight lines CD , DE , CE , so that CD be equal to AF , CE , to AG , and DE to FG ; and because DC , CE are equal to FA ...
Page 31
... join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the angle BAC is equal A to the angle EDG ; therefore the base BC is equal to the base EG ; and because DG ...
... join EG , GF . Because AB is equal to DE , and AC to DG , the two sides BA , AC are equal to the two ED , DG , each to each , and the angle BAC is equal A to the angle EDG ; therefore the base BC is equal to the base EG ; and because DG ...
Page 38
... join the extremities of two equal and parallel straight lines , towards the same parts , are also themselves equal ... Join BC ; and because AB is parallel to CD , and BC meets them , C B D the alternate angles ABC , BCD are equala ; and ...
... join the extremities of two equal and parallel straight lines , towards the same parts , are also themselves equal ... Join BC ; and because AB is parallel to CD , and BC meets them , C B D the alternate angles ABC , BCD are equala ; and ...
Page 41
... Join BE , CH ; and be- B cause BC is equal to FG , and FG to EH , BC is equal to EH ; a 34. 1 . and they are parallels , and joined towards the same parts by the straight lines BE , CH ; but straight lines which join equal and parallel ...
... Join BE , CH ; and be- B cause BC is equal to FG , and FG to EH , BC is equal to EH ; a 34. 1 . and they are parallels , and joined towards the same parts by the straight lines BE , CH ; but straight lines which join equal and parallel ...
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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