The Elements of Euclid |
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Page 48
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . # From the point A draw a AC at right angles to AB ; and make b AD equal to AB , and through the point D draw DE ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . # From the point A draw a AC at right angles to AB ; and make b AD equal to AB , and through the point D draw DE ...
Page 49
... AC , AG upon the opposite sides of AB , make with it at the point A the ... square GB is double of the triangle FBC , because these also are upon the ... square GB : and in the same manner , by joining AE , BK , it is demonstrated that ...
... AC , AG upon the opposite sides of AB , make with it at the point A the ... square GB is double of the triangle FBC , because these also are upon the ... square GB : and in the same manner , by joining AE , BK , it is demonstrated that ...
Page 50
... square described upon BC , one of the sides of the triangle ABC , be equal to the squares upon the other sides BA , AC , the angle BAC is a right angle . b . D From the point A draw AD at right angles to AC , and make AD equal to BA ...
... square described upon BC , one of the sides of the triangle ABC , be equal to the squares upon the other sides BA , AC , the angle BAC is a right angle . b . D From the point A draw AD at right angles to AC , and make AD equal to BA ...
Page 52
... square of the whole line . Let the straight line AB be divided into A any two parts in the point C ; the rect- angle contained by AB , BC , together with the rectangle AB , AC , shall be equal to the square of AB . * Upon AB describe a the ...
... square of the whole line . Let the straight line AB be divided into A any two parts in the point C ; the rect- angle contained by AB , BC , together with the rectangle AB , AC , shall be equal to the square of AB . * Upon AB describe a the ...
Page 53
Euclid Robert Simson. AC ; for it is contained by DA , AC , of which AD is ... square of AB . If there- fore a straight line , & c . Q. E. D. PROP . III ... square of the foresaid part . C Let the straight line AB be divided into two parts ...
Euclid Robert Simson. AC ; for it is contained by DA , AC , of which AD is ... square of AB . If there- fore a straight line , & c . Q. E. D. PROP . III ... square of the foresaid part . C Let the straight line AB be divided into two parts ...
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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