The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 3
... these are called trape- ziums . XXXV . Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight DEFINITIONS . 3.
... these are called trape- ziums . XXXV . Parallel straight lines are such as are in the same plane , and which , being produced ever so far both ways , do not meet . POSTULATES . I. Let it be granted that a straight DEFINITIONS . 3.
Página 4
... produced to any length in a straight line . III . And that a circle may be described from any centre , at any dis- tance from that centre . AXIOMS . I. Things which are equal to the same thing are equal to one another . II . If equals ...
... produced to any length in a straight line . III . And that a circle may be described from any centre , at any dis- tance from that centre . AXIOMS . I. Things which are equal to the same thing are equal to one another . II . If equals ...
Página 5
... produce ( 2 post . ) the straight lines da , db , to e and f ; from the centre b , at the distance bc , describe ( 3 post . ) the circle cgh , and from the centre d , at the distance dg , describe the circle gkl . al shall be equal to ...
... produce ( 2 post . ) the straight lines da , db , to e and f ; from the centre b , at the distance bc , describe ( 3 post . ) the circle cgh , and from the centre d , at the distance dg , describe the circle gkl . al shall be equal to ...
Página 6
... produced , the angles upon the other side of the base shall also be equal . LET abc be an isosceles triangle , of which the side a b is equal to a c , and let the straight lines ab , a c be produced to d and e , the angle abc shall ...
... produced , the angles upon the other side of the base shall also be equal . LET abc be an isosceles triangle , of which the side a b is equal to a c , and let the straight lines ab , a c be produced to d and e , the angle abc shall ...
Página 8
... produce a c , ad to a f Join cd ; then , in the case in which the vertex of each of the triangles is without the other triangle , because ac is equal to a d , the angle a cd is equal ( i . 5 ) to the angle a dc : but the angle a cd is ...
... produce a c , ad to a f Join cd ; then , in the case in which the vertex of each of the triangles is without the other triangle , because ac is equal to a d , the angle a cd is equal ( i . 5 ) to the angle a dc : but the angle a cd 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