The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 5
... the centre of the circle def , aeis equal C a e b f to ad ; but the straight line c is likewise equal to ad ; whence ae and care each of them equal to ad ; therefore the straight line a e is equal ( 1 ax . ) BOOK I. PROPS . II . , III . 5.
... the centre of the circle def , aeis equal C a e b f to ad ; but the straight line c is likewise equal to ad ; whence ae and care each of them equal to ad ; therefore the straight line a e is equal ( 1 ax . ) BOOK I. PROPS . II . , III . 5.
Página 6
... likewise the angles contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz ...
... likewise the angles contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz ...
Página 8
... likewise those which are terminated in the other extremity . c d IF it be possible , let there be two triangles acb , ad b , upon the same base a b , and upon the same side of it , which have their sides ca , da terminated in the ...
... likewise those which are terminated in the other extremity . c d IF it be possible , let there be two triangles acb , ad b , upon the same base a b , and upon the same side of it , which have their sides ca , da terminated in the ...
Página 9
... likewise their sides terminated in the other extremity ; but this is impossible ( i . 7 ) ; therefore , if the base bc coincides with the base ef , the sides ba , ac , cannot but coincide with the sides ed , df ; wherefore likewise ...
... likewise their sides terminated in the other extremity ; but this is impossible ( i . 7 ) ; therefore , if the base bc coincides with the base ef , the sides ba , ac , cannot but coincide with the sides ed , df ; wherefore likewise ...
Página 12
... likewise together equal to two right angles ; therefore the angles cba , abe are equal to the angles cba , abd : take away the common angle cba , the remaining angle abe is equal ( 3 ax . ) to the remaining angle abd , the less to the ...
... likewise together equal to two right angles ; therefore the angles cba , abe are equal to the angles cba , abd : take away the common angle cba , the remaining angle abe is equal ( 3 ax . ) to the remaining angle abd , the less to the ...
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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