The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 20
... fore is parallel to cd . Wherefore , if a straight line , & c . Q. E. D. PROPOSITION XXVIII . - THEOREM . If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same ...
... fore is parallel to cd . Wherefore , if a straight line , & c . Q. E. D. PROPOSITION XXVIII . - THEOREM . If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same ...
Σελίδα 21
... fore the angles a gh , bgh are greater than the angles bg h , ghd ; but the angles agh , bgh , are equal ( i . 13 ) to two right angles ; therefore the angles bgh , ghd , are less than two right angles ; but those straight lines which ...
... fore the angles a gh , bgh are greater than the angles bg h , ghd ; but the angles agh , bgh , are equal ( i . 13 ) to two right angles ; therefore the angles bgh , ghd , are less than two right angles ; but those straight lines which ...
Σελίδα 22
... fore the whole exterior angle acd is equal to the two interior and oppo- site angles ca b , abc ; to these equals add the angle a cb , and the angles a cd , a cb are equal to the three angles cba , bac , acb ; but the angles acd , a cb ...
... fore the whole exterior angle acd is equal to the two interior and oppo- site angles ca b , abc ; to these equals add the angle a cb , and the angles a cd , a cb are equal to the three angles cba , bac , acb ; but the angles acd , a cb ...
Σελίδα 24
... fore the triangle abc is equal ( i . 4 ) to the triangle b cd , and the diameter bc divides the parallelogram a cd b into two equal parts . Q. E. D. PROPOSITION XXXV . - THEOREM . Parallelograms upon the same base , and between the same ...
... fore the triangle abc is equal ( i . 4 ) to the triangle b cd , and the diameter bc divides the parallelogram a cd b into two equal parts . Q. E. D. PROPOSITION XXXV . - THEOREM . Parallelograms upon the same base , and between the same ...
Σελίδα 25
... fore the whole , or the remainder , ae is equal ( 2 or 3 ax . ) to the whole , or the remainder df ; ab also is equal to dc ; and the two ea , ab are a d e f a e d f b b therefore equal to the two fd , d c , each to each ; and the ...
... fore the whole , or the remainder , ae is equal ( 2 or 3 ax . ) to the whole , or the remainder df ; ab also is equal to dc ; and the two ea , ab are a d e f a e d f b b therefore equal to the two fd , d c , each to each ; and 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