The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 9
... abc be applied to def , so that the point b be on e , and the straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal to ef Therefore bc coinciding with ef ; ba and ac shall coincide with ed ...
... abc be applied to def , so that the point b be on e , and the straight line be upon ef ; the point c shall also coin- cide with the point f , be- cause bc is equal to ef Therefore bc coinciding with ef ; ba and ac shall coincide with ed ...
Σελίδα 10
... abc , abd have the seg- ment ab common to both of them . From the point b draw be at right angles to ab ; and because abc is a straight line , the angle cbe is equal ( 10 def . ) to the angle e ba ; in the same manner , because abd is a ...
... abc , abd have the seg- ment ab common to both of them . From the point b draw be at right angles to ab ; and because abc is a straight line , the angle cbe is equal ( 10 def . ) to the angle e ba ; in the same manner , because abd is a ...
Σελίδα 12
... abc are equal to the three angles dbe , eba , abc but the angles cbe , ebd have been demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( 1 ax . ) to one another ; therefore the angles ...
... abc are equal to the three angles dbe , eba , abc but the angles cbe , ebd have been demonstrated to be equal to the same three angles ; and things that are equal to the same are equal ( 1 ax . ) to one another ; therefore the angles ...
Σελίδα 13
... abc be any triangle ; any two of its angles together are less than two right angles . Produce bc to d ; and because acd is the exterior angle of the triangle a bc , acd is greater ( i . 16 ) than the interior and opposite angle abc ; to ...
... abc be any triangle ; any two of its angles together are less than two right angles . Produce bc to d ; and because acd is the exterior angle of the triangle a bc , acd is greater ( i . 16 ) than the interior and opposite angle abc ; to ...
Σελίδα 14
... abc , are less than two right angles . There- fore any two angles , & c . Q. E. D. PROPOSITION XVIII . — THEOREM . The greater side of every triangle is opposite to the greater angle . d LET abc be a triangle , of which the side ac is ...
... abc , are less than two right angles . There- fore any two angles , & c . Q. E. D. PROPOSITION XVIII . — THEOREM . The greater side of every triangle is opposite to the greater angle . d LET abc be a triangle , of which the side ac is ...
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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