The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 7
... fore the base fc is equal ( i . 4 ) to the base gb , and the triangle afc to the triangle agb ; 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 agb ; 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 ...
Página 14
... fore any two angles , & c . Q. E. D. PROPOSITION XVIII . - THEOREM . The greater side of every triangle is opposite to the greater angle . a LET abc be a triangle , of which the side ac is greater than the side ab ; 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 . a LET abc be a triangle , of which the side ac is greater than the side ab ; the angle abc is ...
Página 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 ...
Página 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 ; a d but the angle dgf is greater than the angle egf ; there- fore the angle dfg b is greater ...
... 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 ; a d but the angle dgf is greater than the angle egf ; there- fore the angle dfg b is greater ...
Página 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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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