The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 6
... angle acb to dfe . LET abc , def be two triangles , which have the two sides ab , ac equal to the two sides de , df , each to each , viz . ab to de , and acto df ; and the angle bac equal to the angle edf , the base be shall be equal to ...
... angle acb to dfe . LET abc , def be two triangles , which have the two sides ab , ac equal to the two sides de , df , each to each , viz . ab to de , and acto df ; and the angle bac equal to the angle edf , the base be shall be equal to ...
Página 9
... angle bacis a equal to the angle edf . dg Ce f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line bc upon ef ; the point c shall also coin- cide with the point f , be- b cause bc is equal ...
... angle bacis a equal to the angle edf . dg Ce f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line bc upon ef ; the point c shall also coin- cide with the point f , be- b cause bc is equal ...
Página 17
... angle dce is equal ( i . 8 ) to the angle fag . Therefore , at the given point a in the given straight line ab , the ... edf ; the base bc is also greater than the base ef . Of the two sides de , df , let de be the side which is not greater ...
... angle dce is equal ( i . 8 ) to the angle fag . Therefore , at the given point a in the given straight line ab , the ... edf ; the base bc is also greater than the base ef . Of the two sides de , df , let de be the side which is not greater ...
Página 18
... angle edf . For , if it be not greater , it must either be equal to it , or less ; but the angle bac is not equal to the angle edf ; because then the base bc would a b d C e be equal ( i . 4 ) to ef ; but it is not ; there- fore the ...
... angle edf . For , if it be not greater , it must either be equal to it , or less ; but the angle bac is not equal to the angle edf ; because then the base bc would a b d C e be equal ( i . 4 ) to ef ; but it is not ; there- fore the ...
Página 19
... angle abc is equal to the angle def ; the base therefore ac is equal ( i . 4 ) to the base df , and the third angle bac to the third angle edf . Next , let the sides which are opposite to equal angles in each triangle be equal to one ...
... angle abc is equal to the angle def ; the base therefore ac is equal ( i . 4 ) to the base df , and the third angle bac to the third angle edf . Next , let the sides which are opposite to equal angles in each triangle be equal to one ...
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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