The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 19.
Σελίδα 56
One circle cannot touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle e bf touch the circle a b c in more points than one , and first on the inside , in the ...
One circle cannot touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle e bf touch the circle a b c in more points than one , and first on the inside , in the ...
Σελίδα 59
From this it is manifest , that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it , touches the circle ; and that it touches it only in one point , because if it did meet the circle in ...
From this it is manifest , that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it , touches the circle ; and that it touches it only in one point , because if it did meet the circle in ...
Σελίδα 60
THEOREM . a If a straight line touches a circle , the straight line drawn from the centre to the point of contact shall be perpendicular to the line touching the circle . LET the straight line de touch the circle a b c in the point c ...
THEOREM . a If a straight line touches a circle , the straight line drawn from the centre to the point of contact shall be perpendicular to the line touching the circle . LET the straight line de touch the circle a b c in the point c ...
Σελίδα 68
If a straight line touches a circle , and from the point of contact a straight line be drawn cutting the circle , the angles made by this line with the line touching the circle shall be equal to the angles which are in the alternate ...
If a straight line touches a circle , and from the point of contact a straight line be drawn cutting the circle , the angles made by this line with the line touching the circle shall be equal to the angles which are in the alternate ...
Σελίδα 69
17 ) the straight line e f touching the circle a bc in the point b , and at the point b , in the straight line bf , make ( i . 23 ) the angle fb c equal to the angle d : therefore , because the straight line ef touches the circle a b c ...
17 ) the straight line e f touching the circle a bc in the point b , and at the point b , in the straight line bf , make ( i . 23 ) the angle fb c equal to the angle d : therefore , because the straight line ef touches the circle a b c ...
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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