The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
... angle at a point , it may be expressed by a letter placed at that point ; as the angle at e . X. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right ...
... angle at a point , it may be expressed by a letter placed at that point ; as the angle at e . X. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right ...
Σελίδα 3
... equal sides . XXV . An isosceles triangle is that which has only two sides equal . Δ Δ Δ Equilateral . Isosceles ... angles . XXX . Of four - sided figures , a square is that which has all its sides equal , and all its angles right ...
... equal sides . XXV . An isosceles triangle is that which has only two sides equal . Δ Δ Δ Equilateral . Isosceles ... angles . XXX . Of four - sided figures , a square is that which has all its sides equal , and all its angles right ...
Σελίδα 4
... equal to the same thing are equal to one another . II . If equals be added to equals , the wholes are equal . III ... angles are equal to one another . XII . If a straight line meets two straight lines , so as to make the two interior ...
... equal to the same thing are equal to one another . II . If equals be added to equals , the wholes are equal . III ... angles are equal to one another . XII . If a straight line meets two straight lines , so as to make the two interior ...
Σελίδα 6
... equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one ...
... equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each ; and have likewise the angles contained by those sides equal to one ...
Σελίδα 7
... equal ( i . 3 ) to a f , the less , and join fc , gb . f b a c مع Because af is equal to a g , and ab to a c , the ... angles , & c . Q. E. D. b d COR . Hence every equiangular triangle is also equilateral . a PROPOSITION VII . — THEOREM ...
... equal ( i . 3 ) to a f , the less , and join fc , gb . f b a c مع Because af is equal to a g , and ab to a c , the ... angles , & c . Q. E. D. b d COR . Hence every equiangular triangle is also equilateral . a PROPOSITION VII . — THEOREM ...
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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