The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 3
... angle . XXVIII . An obtuse - angled triangle is that which has an obtuse angle . Right - angled .. Obtuse - angled ... opposite sides equal to one another , but all its sides are not equal , nor its angles right angles . XXXIV . All ...
... angle . XXVIII . An obtuse - angled triangle is that which has an obtuse angle . Right - angled .. Obtuse - angled ... opposite sides equal to one another , but all its sides are not equal , nor its angles right angles . XXXIV . All ...
Σελίδα 6
... opposite shall be equal , each to each . Which was to be demonstrated . PROPOSITION V. - THEOREM . The angles at the ... angle cbd to the angle bce . In bd take any point f , and from ae 6 THE ELEMENTS OF EUCLID .
... opposite shall be equal , each to each . Which was to be demonstrated . PROPOSITION V. - THEOREM . The angles at the ... angle cbd to the angle bce . In bd take any point f , and from ae 6 THE ELEMENTS OF EUCLID .
Σελίδα 7
... opposite ; viz . the angle acf to the angle abg , and the angle afc to the angle a gb : and because the whole af is equal to the whole a g , of which the parts a b , a c , are equal ; the remainder bf shall be equal ( 3 ax . ) to the ...
... opposite ; viz . the angle acf to the angle abg , and the angle afc to the angle a gb : and because the whole af is equal to the whole a g , of which the parts a b , a c , are equal ; the remainder bf shall be equal ( 3 ax . ) to the ...
Σελίδα 12
... angle dba is equal to the two angles dbe , eba , add to these equals the angle a bc , therefore the angles dba , abc ... opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall ...
... angle dba is equal to the two angles dbe , eba , add to these equals the angle a bc , therefore the angles dba , abc ... opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall ...
Σελίδα 13
... angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle bae is equal to the angle ecf ; but the angle ecd is greater than the angle e cf ; therefore the angle a cd is greater than ...
... angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle bae is equal to the angle ecf ; but the angle ecd is greater than the angle e cf ; therefore the angle a cd is greater than ...
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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