The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 6
... base b c shall coincide with the base ef , because the point b coinciding with e , and c with f , if the base b c does not coincide with the base e f , two straight lines would enclose a space , which is impossible ( 10 ax . ) . Therefore ...
... base b c shall coincide with the base ef , because the point b coinciding with e , and c with f , if the base b c does not coincide with the base e f , two straight lines would enclose a space , which is impossible ( 10 ax . ) . Therefore ...
Σελίδα 7
... base bc is common to the two triangles bfc , cgb ; wherefore the tri- angles are equal ( i . 4 ) , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle fbc is equal to the angle g cb ...
... base bc is common to the two triangles bfc , cgb ; wherefore the tri- angles are equal ( i . 4 ) , and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle fbc is equal to the angle g cb ...
Σελίδα 9
... bc is equal to ef Therefore bc coinciding with ef ; ba and ac shall coincide with ed and df ; for , if the base bc coincides with the base ef , but the sides ba , ca do not coincide with the sides ed , fd , but have a different ...
... bc is equal to ef Therefore bc coinciding with ef ; ba and ac shall coincide with ed and df ; for , if the base bc coincides with the base ef , but the sides ba , ca do not coincide with the sides ed , fd , but have a different ...
Σελίδα 10
... bc , cd , each to each ; and the angle acd is equal to the angle bed ; therefore the base a d is equal to the base ( i . 4 ) d b , and the b straight line a b is divided into two equal parts in the point d . Which was to be done ...
... bc , cd , each to each ; and the angle acd is equal to the angle bed ; therefore the base a d is equal to the base ( i . 4 ) d b , and the b straight line a b is divided into two equal parts in the point d . Which was to be done ...
Σελίδα 13
... b c be produced to d , the exterior angle a cd is greater than either of the interior opposite angles cba , bac ... base ab is equal ( i . 4 ) to the base c f , and the triangle aeb to the triangle cef , and the re- maining angles to the ...
... b c be produced to d , the exterior angle a cd is greater than either of the interior opposite angles cba , bac ... base ab is equal ( i . 4 ) to the base c f , and the triangle aeb to the triangle cef , and the re- maining angles to the ...
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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