The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 6
... a c , and let the straight lines ab , a c be produced to d and e , the angle abc shall be equal to the angle a c b , and the angle cbd to the angle bce . In bd take any point f , and from ae 6 THE ELEMENTS OF EUCLID .
... a c , and let the straight lines ab , a c be produced to d and e , the angle abc shall be equal to the angle a c b , and the angle cbd to the angle bce . In bd take any point f , and from ae 6 THE ELEMENTS OF EUCLID .
Σελίδα 7
Euclides. In bd take any point f , and from ae the greater , cut off ag 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 two sides fa , a c are equal to the two ga , ab ...
Euclides. In bd take any point f , and from ae the greater , cut off ag 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 two sides fa , a c are equal to the two ga , ab ...
Σελίδα 9
... Take any point d in a b , and from ac cut ( i . 3 ) off ae equal to ad ; join de , and upon it describe ( i . 1 ) an equilateral triangle def ; then join af ; the straight line af bisects the angle bac Because ad is equal to a e , and ...
... Take any point d in a b , and from ac cut ( i . 3 ) off ae equal to ad ; join de , and upon it describe ( i . 1 ) an equilateral triangle def ; then join af ; the straight line af bisects the angle bac Because ad is equal to a e , and ...
Σελίδα 10
... Take any point d in a c , and make ( i . 3 ) ce equal to cd , and upon describe ( 1. 1 ) the equilateral triangle dfe , and join fc , the straight line fc drawn from the given point c is at right angles to the given straight line a b ...
... Take any point d in a c , and make ( i . 3 ) ce equal to cd , and upon describe ( 1. 1 ) the equilateral triangle dfe , and join fc , the straight line fc drawn from the given point c is at right angles to the given straight line a b ...
Σελίδα 11
... Take any point d upon the other side of a b , and from the centre c , at the distance cd , describe ( 3 post . ) the circle e gf meet- ing a bin f , g ; and bisect ( i . 10 ) fg in h , and join cf , ch , cg ; the straight line ch ...
... Take any point d upon the other side of a b , and from the centre c , at the distance cd , describe ( 3 post . ) the circle e gf meet- ing a bin f , g ; and bisect ( i . 10 ) fg in h , and join cf , ch , cg ; the straight line ch ...
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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