The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 21
... meet ( 12 ax . ) together if continually produced ; therefore the straight lines ab , cd , if produced far enough , shall meet ; but they never meet , since they are parallel by the hypothesis ; therefore the angle a gh is not unequal ...
... meet ( 12 ax . ) together if continually produced ; therefore the straight lines ab , cd , if produced far enough , shall meet ; but they never meet , since they are parallel by the hypothesis ; therefore the angle a gh is not unequal ...
Σελίδα 22
... meets the two straight lines bc , ef , makes the alternate angles e a d , adc equal to one another , ef is parallel ( i . 27 ) to bc . Therefore the straight line e af is drawn through the given point a parallel to the given straight ...
... meets the two straight lines bc , ef , makes the alternate angles e a d , adc equal to one another , ef is parallel ( i . 27 ) to bc . Therefore the straight line e af is drawn through the given point a parallel to the given straight ...
Σελίδα 23
... meets them , the alternate angles abc , bcd are equal ( i . 29 ) ; and because ab is equal to cd , and bc common to the two triangles a bc , dcb , the two sides a b , bc , are equal to the two dc , cb : and the angle abc is equal to the ...
... meets them , the alternate angles abc , bcd are equal ( i . 29 ) ; and because ab is equal to cd , and bc common to the two triangles a bc , dcb , the two sides a b , bc , are equal to the two dc , cb : and the angle abc is equal to the ...
Σελίδα 24
... meets them , the alternate angles c b abc , bcd are equal ( i . 29 ) to one another ; and because a c is parallel to bd , and bc meets them , the alternate angles a cb , cbd , are equal ( i . 29 ) to one another ; wherefore the two ...
... meets them , the alternate angles c b abc , bcd are equal ( i . 29 ) to one another ; and because a c is parallel to bd , and bc meets them , the alternate angles a cb , cbd , are equal ( i . 29 ) to one another ; wherefore the two ...
Σελίδα 29
... meet if produced ; let them meet in k , and through BOOK I. PROPS . XLIII . , XLIV . 29 29.
... meet if produced ; let them meet in k , and through BOOK I. PROPS . XLIII . , XLIV . 29 29.
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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