The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 30
... abcd be the given rectilineal figure , and e the given rectilineal angle . It is required to describe a parallelogram equal to abcd , and having an angle equal to e . Join db , and describe ( i . 42 ) the parallelogram fh equal to the ...
... abcd be the given rectilineal figure , and e the given rectilineal angle . It is required to describe a parallelogram equal to abcd , and having an angle equal to e . Join db , and describe ( i . 42 ) the parallelogram fh equal to the ...
Página 50
... abcd be a circle , and a c , bd two straight lines in it which cut one another in the point e , and do not both pass through the centre : ac , bd , do not bisect one another . f a e b C For , if it be possible , let ae be equal to ec ...
... abcd be a circle , and a c , bd two straight lines in it which cut one another in the point e , and do not both pass through the centre : ac , bd , do not bisect one another . f a e b C For , if it be possible , let ae be equal to ec ...
Página 52
... abcd be a circle , and ad its diameter , in which let any point f be taken which is not the centre . Let the centre bee ; of all the straight lines fb , fc , fg , & c . that can be drawn from f to the circumference , fa is the greatest ...
... abcd be a circle , and ad its diameter , in which let any point f be taken which is not the centre . Let the centre bee ; of all the straight lines fb , fc , fg , & c . that can be drawn from f to the circumference , fa is the greatest ...
Página 57
... abcd be a circle , of which the diameter is ad , and the centree ; and let bc be nearer to the centre than fg ; ad is greater than any straight line bc , which is not a diameter , and be greater than fg . From the centre e , draw eh ...
... abcd be a circle , of which the diameter is ad , and the centree ; and let bc be nearer to the centre than fg ; ad is greater than any straight line bc , which is not a diameter , and be greater than fg . From the centre e , draw eh ...
Página 61
... abcd be a circle , and bad , bed angles in the same segment baed : the angles bad , bed are equal to one another . Take f the centre of the circle abcd : and , first , let the segment baed be greater than a semicircle , and join bf , fd ...
... abcd be a circle , and bad , bed angles in the same segment baed : the angles bad , bed are equal to one another . Take f the centre of the circle abcd : and , first , let the segment baed be greater than a semicircle , and join bf , fd ...
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Términos y frases comunes
ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle