The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 7
... fore the base fc is equal ( i . 4 ) to the base gb , and the triangle afc to the triangle a gb ; and the remaining angles of the one are equal ( i . 4 ) to the remaining angles of the other , each to each , to which the equal sides are ...
... fore the base fc is equal ( i . 4 ) to the base gb , and the triangle afc to the triangle a gb ; and the remaining angles of the one are equal ( i . 4 ) to the remaining angles of the other , each to each , to which the equal sides are ...
Σελίδα 14
... fore any two angles , & c . Q. E. D. PROPOSITION XVIII . — THEOREM . The greater side of every triangle is opposite to the greater angle . d LET abc be a triangle , of which the side ac is greater than the side a b ; the angle abc is ...
... fore any two angles , & c . Q. E. D. PROPOSITION XVIII . — THEOREM . The greater side of every triangle is opposite to the greater angle . d LET abc be a triangle , of which the side ac is greater than the side a b ; the angle abc is ...
Σελίδα 15
... fore the sides ba , ac are greater than be , ec . Again , because the two sides ce , ed of the triangle ced are greater than cd , add db to each of these ; therefore the sides ce , eb are greater than cd , db ; but it has been shewn ...
... fore the sides ba , ac are greater than be , ec . Again , because the two sides ce , ed of the triangle ced are greater than cd , add db to each of these ; therefore the sides ce , eb are greater than cd , db ; but it has been shewn ...
Σελίδα 17
... fore the base bc is equal ( i . 4 ) to the base eg ; and be- cause dg is equal to df , the angle dfg is equal ( i . 5 ) to the angle dgf ; but the angle dgf is greater than the angle egf ; there- fore the angle dfg is greater than egf ...
... fore the base bc is equal ( i . 4 ) to the base eg ; and be- cause dg is equal to df , the angle dfg is equal ( i . 5 ) to the angle dgf ; but the angle dgf is greater than the angle egf ; there- fore the angle dfg is greater than egf ...
Σελίδα 18
... fore the angle bac is not equal to the angle edf ; neither is it less : because then the base bc would be less ( i . 24 ) than the base ef ; but it is not ; therefore the angle bac is not less than the angle edf ; f and it was shewn ...
... fore the angle bac is not equal to the angle edf ; neither is it less : because then the base bc would be less ( i . 24 ) than the base ef ; but it is not ; therefore the angle bac is not less than the angle edf ; f and it was shewn ...
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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