The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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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 ... than the other : let ab be the greater ; and from it cut ( i . 3 ) off db equal to a c , the less , and join dc ...
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 ... than the other : let ab be the greater ; and from it cut ( i . 3 ) off db equal to a c , the less , and join dc ...
Σελίδα 8
... greater than the angle bcd ; therefore the angle adc is greater also than then is the angle bdc than the angle bcd ... f ; therefore , because a c is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the base ...
... greater than the angle bcd ; therefore the angle adc is greater also than then is the angle bdc than the angle bcd ... f ; therefore , because a c is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the base ...
Σελίδα 13
... greater than either of the interior opposite angles . LET a b c be a triangle , and let its side b c be produced to ... f , and make e f equal to be ; join also fc , and produce ac to g . Because a e is equal to ec , and be to ef ; a e ...
... greater than either of the interior opposite angles . LET a b c be a triangle , and let its side b c be produced to ... f , and make e f equal to be ; join also fc , and produce ac to g . Because a e is equal to ec , and be to ef ; a e ...
Σελίδα 18
... greater than the base ef ; the angle bac is likewise greater than the angle ed f . For , if it be not greater , it must either be equal to it , or less ; but the angle bac is not equal to the angle e df ; because then the base bc would ...
... greater than the base ef ; the angle bac is likewise greater than the angle ed f . For , if it be not greater , it must either be equal to it , or less ; but the angle bac is not equal to the angle e df ; because then the base bc would ...
Σελίδα 49
... greater to the less , which is impossible : therefore g is not the centre of the circle a bc . In the same manner it can be shewn , that no other point but fis the centre ; that is , f ... than the angle dae ; but dae is equal to the angle ...
... greater to the less , which is impossible : therefore g is not the centre of the circle a bc . In the same manner it can be shewn , that no other point but fis the centre ; that is , f ... than the angle dae ; but dae is equal to the angle ...
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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