The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 31
... square upon a given straight line . LET ab be the given straight line ; it is required to describe a square upon a b . From the point a draw ( i . 11 ) ac at right angles to ab ; and make ( i . 3 ) ad equal to ab , and through the point ...
... square upon a given straight line . LET ab be the given straight line ; it is required to describe a square upon a b . From the point a draw ( i . 11 ) ac at right angles to ab ; and make ( i . 3 ) ad equal to ab , and through the point ...
Página 32
... square gbis double of the trian- gle fbc , because these also are upon the same base fb , and between the same ... ac : wherefore the square upon the side bc is equal to the squares upon the sides ba , ac . Therefore , in any right ...
... square gbis double of the trian- gle fbc , because these also are upon the same base fb , and between the same ... ac : wherefore the square upon the side bc is equal to the squares upon the sides ba , ac . Therefore , in any right ...
Página 36
... square adeb , and through e draw ( i . 31 ) cf , parallel to ad or be . Then ae is equal to the rectangles af , ce ; and ae is the square of ab ; and af is the rectangle con- tained by ba , ac ; for it is contained by da , a c , of ...
... square adeb , and through e draw ( i . 31 ) cf , parallel to ad or be . Then ae is equal to the rectangles af , ce ; and ae is the square of ab ; and af is the rectangle con- tained by ba , ac ; for it is contained by da , a c , of ...
Página 37
... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of ab is equal to the squares of ac ...
... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of ab is equal to the squares of ac ...
Página 38
... square of cd , is equal to the square of cb . Upon cb describe ( i . 46 ) ... ac is equal to cb ; therefore also al is equal to df . To each of these add ... square of cd ; therefore the gnomon cmg , together with 1g , is equal to ...
... square of cd , is equal to the square of cb . Upon cb describe ( i . 46 ) ... ac is equal to cb ; therefore also al is equal to df . To each of these add ... square of cd ; therefore the gnomon cmg , together with 1g , is equal to ...
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Términos y frases comunes
ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle