The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 34.
Σελίδα 6
Which was to be 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 .
Which was to be 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 .
Σελίδα 7
... and the angle bcf to the angle cbg : and since it has been demonstrated , that the whole angle a bg is equal to the whole a cf , the parts of which , the angles cbg , bcf are also equal ; the remaining augle a b c is therefore equal ...
... and the angle bcf to the angle cbg : and since it has been demonstrated , that the whole angle a bg is equal to the whole a cf , the parts of which , the angles cbg , bcf are also equal ; the remaining augle a b c is therefore equal ...
Σελίδα 8
... therefore the angle adc is greater also than bcd ; much greater then is the angle bdc than the angle bed . Again , because c b is equal to db , the angle bdc is equal ( i . 5 ) to the angle bed ; but it has been demonstrated to be ...
... therefore the angle adc is greater also than bcd ; much greater then is the angle bdc than the angle bed . Again , because c b is equal to db , the angle bdc is equal ( i . 5 ) to the angle bed ; but it has been demonstrated to be ...
Σελίδα 10
By help of this problem , it may be demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines a b c , abd have the segment a b common to both of them .
By help of this problem , it may be demonstrated , that two straight lines cannot have a common segment . If it be possible , let the two straight lines a b c , abd have the segment a b common to both of them .
Σελίδα 12
... therefore the angles dba , a b c are equal to the three angles d be , e ba , a bc : 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 . ) ...
... therefore the angles dba , a b c are equal to the three angles d be , e ba , a bc : 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 . ) ...
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a b c angle a b c angle bac base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given straight line greater half ILLUSTRATED inscribe join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square square of a c straight line a b Take taken third touches the circle triangle triangle a b c wherefore whole