The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 6
... demonstrated . PROPOSITION V. - THEOREM . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . LET abc be an ...
... demonstrated . PROPOSITION V. - THEOREM . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall also be equal . LET abc be an ...
Σελίδα 7
... demonstrated , that the whole angle abg is equal to the whole a cf , the parts of which , the angles cbg , bcf are also equal ; the remaining augle abc is therefore equal to the remaining angle a cb , which are the angles at the base of ...
... demonstrated , that the whole angle abg is equal to the whole a cf , the parts of which , the angles cbg , bcf are also equal ; the remaining augle abc is therefore equal to the remaining angle a cb , which are the angles at the base of ...
Σελίδα 8
... demonstrated to be greater than it ; which is b vertices , as d ; be within the other triangle a cb ; e , f ; therefore , because a c is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the base cd are equal ...
... demonstrated to be greater than it ; which is b vertices , as d ; be within the other triangle a cb ; e , f ; therefore , because a c is equal to ad in the triangle acd , the angles ecd , fdc upon the other side of the base cd are equal ...
Σελίδα 10
... demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines 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 ...
... demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines 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 ...
Σελίδα 12
... 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 cbe , ebd are equal to the angles dba , abc ; but cbe , ebd are two right angles ...
... 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 cbe , ebd are equal to the angles dba , abc ; but cbe , ebd are two right angles ...
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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