The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 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.
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ab is equal to ac , and let the straight lines ab , ac be produced to d and e , the angle abc shall be ...
... produced , the angles upon the other side of the base shall also be equal . LET abc be an isosceles triangle , of which the side ab is equal to ac , and let the straight lines ab , ac be produced to d and e , the angle abc shall be ...
Σελίδα 8
... produce ac , ad to e , f ; therefore , because ac is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the base cd are equal ( i . 5 ) to one another : but the angle ecd is greater than the angle bcd ...
... produce ac , ad to e , f ; therefore , because ac is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the base cd are equal ( i . 5 ) to one another : but the angle ecd is greater than the angle bcd ...
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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