The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 37
... reason hf also is a square , and it is upon the side hg , which is equal to a c . Therefore hf , ck are the squares of ac , cb ; and because the complement ag is equal ( i . 43 ) to the complement ge , and that a g is the rectangle ...
... reason hf also is a square , and it is upon the side hg , which is equal to a c . Therefore hf , ck are the squares of ac , cb ; and because the complement ag is equal ( i . 43 ) to the complement ge , and that a g is the rectangle ...
Σελίδα 39
... as in the preceding . Because cb is equal to bd , and that cb is equal ( i . 34 ) to g k , and bd to kn ; therefore gk is equal to kn : for the same reason , pr is equal a c b d gk m P r to ro BOOK II . PROPS . VII . , VIII . 39.
... as in the preceding . Because cb is equal to bd , and that cb is equal ( i . 34 ) to g k , and bd to kn ; therefore gk is equal to kn : for the same reason , pr is equal a c b d gk m P r to ro BOOK II . PROPS . VII . , VIII . 39.
Σελίδα 41
... reason , each of the angles ceb , ebc is half a right angle ; and therefore the whole a eb is a right angle : and because the angle gef is half a right angle , and eg fa right angle , for it is equal ( i . 29 ) to the interior and ...
... reason , each of the angles ceb , ebc is half a right angle ; and therefore the whole a eb is a right angle : and because the angle gef is half a right angle , and eg fa right angle , for it is equal ( i . 29 ) to the interior and ...
Σελίδα 42
... reason , each of the angles ceb , ebc is half a right angle ; therefore aeb is a right angle and because ebc is half a right angle , dbg is also ( i . 15 ) half a right angle , for they are vertically opposite ; but bdg is a right angle ...
... reason , each of the angles ceb , ebc is half a right angle ; therefore aeb is a right angle and because ebc is half a right angle , dbg is also ( i . 15 ) half a right angle , for they are vertically opposite ; but bdg is a right angle ...
Σελίδα 52
... reason cf is greater than gf . Again , be- cause gf fe are greater ( i . 20 ) than eg , and eg is equal to ed , gf , fe are greater than ed ; take away the common part fe , and the remainder gf is greater than the remainder fd ...
... reason cf is greater than gf . Again , be- cause gf fe are greater ( i . 20 ) than eg , and eg is equal to ed , gf , fe are greater than ed ; take away the common part fe , and the remainder gf is greater than the remainder fd ...
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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