The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 8
... equal to one another , and like- wise their sides cb , db , that are terminated in b . a Join cd ; then , in the case in which the vertex of each of the triangles is without the other triangle , because acis equal to ad , the angle acd is ...
... equal to one another , and like- wise their sides cb , db , that are terminated in b . a Join cd ; then , in the case in which the vertex of each of the triangles is without the other triangle , because acis equal to ad , the angle acd is ...
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 ...
... 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 ...
Página 10
... angle ac b by the straight linecd . abis cut into two equal parts in the point d . Because ac is equal to cb , and cd common to the two triangles acd , bcd ; the two sides a c , cd are equal to bc , cd , each to each ; and the angle ...
... angle ac b by the straight linecd . abis cut into two equal parts in the point d . Because ac is equal to cb , and cd common to the two triangles acd , bcd ; the two sides a c , cd are equal to bc , cd , each to each ; and the angle ...
Página 11
... equal to the two gh , hc , each to each ; and the base cfis equal ( 15 def . ) to the base cg ; therefore the angle chf is equal ( i . 8 ) to the angle chg ; and they are adjacent angles ; but when ( 10 def . ) a straight line ...
... equal to the two gh , hc , each to each ; and the base cfis equal ( 15 def . ) to the base cg ; therefore the angle chf is equal ( i . 8 ) to the angle chg ; and they are adjacent angles ; but when ( 10 def . ) a straight line ...
Página 12
Euclides. to each of these equals ; therefore the angles cbe , ebd are equal ( 2 ax . ) to the three angles cba , abe , ebd . Again , because the angle dba is equal to the two angles dbe , eba , add to these equals the angle abc , therefore ...
Euclides. to each of these equals ; therefore the angles cbe , ebd are equal ( 2 ax . ) to the three angles cba , abe , ebd . Again , because the angle dba is equal to the two angles dbe , eba , add to these equals the angle abc , therefore ...
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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