The Elements of Euclid |
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Page 37
Euclid Robert Simson. EAF is drawn through the given point A parallel to the given Book I. straight line BC . Which was to be done . PROP . XXXII . THEOR . IF a side of any triangle be produced , the exterior angle is equal to the two ...
Euclid Robert Simson. EAF is drawn through the given point A parallel to the given Book I. straight line BC . Which was to be done . PROP . XXXII . THEOR . IF a side of any triangle be produced , the exterior angle is equal to the two ...
Page 44
... given rectilineal angle . Let ABC be the given triangle , and D the given rectilineal angle . It is required to describe a parallelogram that shall be equal to the given triangle ABC , and have one of its angles equal to D. A F G Bisect ...
... given rectilineal angle . Let ABC be the given triangle , and D the given rectilineal angle . It is required to describe a parallelogram that shall be equal to the given triangle ABC , and have one of its angles equal to D. A F G Bisect ...
Page 45
... given angle D. Which was to be done . PROP . XLIII . THEOR . THE complements of the parallelograms which are about ... given straight line to apply a parallelogram , which shall be equal to a given triangle , and have one - of its angles ...
... given angle D. Which was to be done . PROP . XLIII . THEOR . THE complements of the parallelograms which are about ... given straight line to apply a parallelogram , which shall be equal to a given triangle , and have one - of its angles ...
Page 46
... angle EBG equal to the C angle D , so that BE be D F E K M B b 31. 1 . € 29. 1 . c H A L in the same straight line ... given recti- lineal figure , and having an angle equal to a given rec- tilineal angle . Let ABCD be the given ...
... angle EBG equal to the C angle D , so that BE be D F E K M B b 31. 1 . € 29. 1 . c H A L in the same straight line ... given recti- lineal figure , and having an angle equal to a given rec- tilineal angle . Let ABCD be the given ...
Page 47
... angle Book 1 and because the angle E is equal to each of the angles FKH , GHM , the angle FKH is equal to GHM : add ... given rec- tilineal figure ABCD , having the angle FKM equal to the gi ven angle E. Which was to be done . e COR ...
... angle Book 1 and because the angle E is equal to each of the angles FKH , GHM , the angle FKH is equal to GHM : add ... given rec- tilineal figure ABCD , having the angle FKM equal to the gi ven angle E. Which was to be done . e COR ...
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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