The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 30
Euclides. produced ; let them meet in k , and through k draw kl . parallel to ea or fh , and produce ha , gb to the ... meets the parallels km , fg , the alternate angles mhg , hgf are equal ( i . 29 ) : add to each of these the angle hgl ...
Euclides. produced ; let them meet in k , and through k draw kl . parallel to ea or fh , and produce ha , gb to the ... meets the parallels km , fg , the alternate angles mhg , hgf are equal ( i . 29 ) : add to each of these the angle hgl ...
Σελίδα 37
... meets them ; the angles d ' kbc , gcb are therefore equal to two right angles ; and kbc is a right angle ; wherefore gcb is a right angle : and therefore also the angles ( i . 34 ) cgk , gkb , opposite to these , are right angles , and ...
... meets them ; the angles d ' kbc , gcb are therefore equal to two right angles ; and kbc is a right angle ; wherefore gcb is a right angle : and therefore also the angles ( i . 34 ) cgk , gkb , opposite to these , are right angles , and ...
Σελίδα 41
... meet ( 12 ax . ) if produced far a enough therefore eb , fd shall meet if produced towards b , d : let them meet in g , and join a g : then , : • b g . : because ac is equal to ce , the angle BOOK II . PROP . X. 41 .
... meet ( 12 ax . ) if produced far a enough therefore eb , fd shall meet if produced towards b , d : let them meet in g , and join a g : then , : • b g . : because ac is equal to ce , the angle BOOK II . PROP . X. 41 .
Σελίδα 47
... meets the circle , and being produced does not cut it . III . Circles are said to touch one another , which meet but do not cut one another . Definitions II . and III . IV . Straight lines are said to be equally distant from the centre ...
... meets the circle , and being produced does not cut it . III . Circles are said to touch one another , which meet but do not cut one another . Definitions II . and III . IV . Straight lines are said to be equally distant from the centre ...
Σελίδα 58
... meets the circumference . And because da is equal to dc , the angle dac is equal ( i . 5 ) to the angle acd ; but ... meet the circumference in h ; and because a gd is a right angle , and dag less ( i . 17 ) than a right angle , da is ...
... meets the circumference . And because da is equal to dc , the angle dac is equal ( i . 5 ) to the angle acd ; but ... meet the circumference in h ; and because a gd is a right angle , and dag less ( i . 17 ) than a right angle , da is ...
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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