The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
... bc , or cba ; that which is contained by a b , db , is named the angle abd ... equal to one another , each of the angles is called a right angle ; and the ... equal to one another . XVI . And this point is called the centre of the circle ...
... bc , or cba ; that which is contained by a b , db , is named the angle abd ... equal to one another , each of the angles is called a right angle ; and the ... equal to one another . XVI . And this point is called the centre of the circle ...
Σελίδα 5
... bc is equal to ba but it has been proved that ca is equal to ab ; therefore ca , cb , are each of them equal to ab ; but things which are equal to the same are equal to one another ( 1 ax . ) ; therefore ca is equal to cb ; wherefore ca ...
... bc is equal to ba but it has been proved that ca is equal to ab ; therefore ca , cb , are each of them equal to ab ; but things which are equal to the same are equal to one another ( 1 ax . ) ; therefore ca is equal to cb ; wherefore ca ...
Σελίδα 6
... equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the one ... bc shall be equal to the base ef ; and the triangle abc to the triangle def ; and the other angles to which the ...
... equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the one ... bc shall be equal to the base ef ; and the triangle abc to the triangle def ; and the other angles to which the ...
Σελίδα 7
... equal ( i . 3 ) to a f , the less , and join fc , gb . f b a c مع Because af is equal to a g , and ab to a c , the ... bc is common to the two triangles bfc , cgb ; wherefore the tri- angles are equal ( i . 4 ) , and their remaining ...
... equal ( i . 3 ) to a f , the less , and join fc , gb . f b a c مع Because af is equal to a g , and ab to a c , the ... bc is common to the two triangles bfc , cgb ; wherefore the tri- angles are equal ( i . 4 ) , and their remaining ...
Σελίδα 9
... bc is equal to ef Therefore bc coinciding with ef ; ba and ac shall coincide with ed and df ; for , if the base bc coincides with the base ef , but the sides ba , ca do not coincide with the sides ed , fd , but have a different ...
... bc is equal to ef Therefore bc coinciding with ef ; ba and ac shall coincide with ed and df ; for , if the base bc coincides with the base ef , but the sides ba , ca do not coincide with the sides ed , fd , but have a different ...
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a b c abcd adjacent angles angle a cb angle abc angle bac angle edf angle equal base bc bc is equal bisected centre circle abc circumference bc describe diameter double draw equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio greater than f inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment semicircle shewn square of a c straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle