The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 3
... triangle is that which has three equal sides . XXV . An isosceles ... angle . XXVIII . An obtuse - angled triangle is that which has an obtuse ... opposite sides equal to one another , but all its sides are not equal , nor ...
... triangle is that which has three equal sides . XXV . An isosceles ... angle . XXVIII . An obtuse - angled triangle is that which has an obtuse ... opposite sides equal to one another , but all its sides are not equal , nor ...
Σελίδα 6
... triangle abc to the triangle def ; and the other angles to which the equal sides are opposite , shall be equal , each to each , viz . the angle abc to the angle For , if the triangle abc be applied to def , so that the point a may be on ...
... triangle abc to the triangle def ; and the other angles to which the equal sides are opposite , shall be equal , each to each , viz . the angle abc to the angle For , if the triangle abc be applied to def , so that the point a may be on ...
Σελίδα 7
... opposite ; viz . the angle acf to the angle abg , and the angle afc to the angle agb : and because the whole af is equal to the whole ag , of which the parts ab , ac , 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 agb : and because the whole af is equal to the whole ag , of which the parts ab , ac , 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 ... opposite sides of it , make the adjacent angles together equal to two right ... opposite sides of ab , make the adjacent angles abc , abd equal together ...
... angle dba is equal to the two angles dbe , eba , add to these equals the ... opposite sides of it , make the adjacent angles together equal to two right ... opposite sides of ab , make the adjacent angles abc , abd equal together ...
Σελίδα 13
... angles made by any number of lines meeting in one point , are together equal to four right angles . PROPOSITION XVI . - THEOREM . If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite ...
... angles made by any number of lines meeting in one point , are together equal to four right angles . PROPOSITION XVI . - THEOREM . If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite ...
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ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle