The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 6
... applied to def , so that the point a may be on d , and the straight line ab upon de ; the point b shall coin- cide with the point e , because ab is equal to de ; and ab coinciding with de , ac shall coincide with df , because the angle ...
... applied to def , so that the point a may be on d , and the straight line ab upon de ; the point b shall coin- cide with the point e , because ab is equal to de ; and ab coinciding with de , ac shall coincide with df , because the angle ...
Σελίδα 9
... applied to def , so that the point b be on e , and the straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal to ef Therefore bc coinciding with ef ; ba and ac shall coincide with ed and df ...
... applied to def , so that the point b be on e , and the straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal to ef Therefore bc coinciding with ef ; ba and ac shall coincide with ed and df ...
Σελίδα 30
... applied to the straight line a b , is equal to the triangle c , and has the angle a bm equal to the angle d . Which was to be done . PROPOSITION XLV . - PROBLEM . To describe a parallelogram equal to a given rectilineal figure , and ...
... applied to the straight line a b , is equal to the triangle c , and has the angle a bm equal to the angle d . Which was to be done . PROPOSITION XLV . - PROBLEM . To describe a parallelogram equal to a given rectilineal figure , and ...
Σελίδα 31
... applying ( i . 44 ) to the given straight line a parallelogram equal to the first triangle a bd , and having an angle equal to the given angle . PROPOSITION XLVI . - PROBLEM . To describe a square upon a given straight line . LET ab be ...
... applying ( i . 44 ) to the given straight line a parallelogram equal to the first triangle a bd , and having an angle equal to the given angle . PROPOSITION XLVI . - PROBLEM . To describe a square upon a given straight line . LET ab be ...
Σελίδα 47
... applied to one another , so that their centres coincide , the circles must likewise coincide , since the straight lines from the centres are equal . II . A straight line is said to touch a circle when it meets the circle , and being ...
... applied to one another , so that their centres coincide , the circles must likewise coincide , since the straight lines from the centres are equal . II . A straight line is said to touch a circle when it meets the circle , and being ...
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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