The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 56
... touches it on the inside or outside . For , if it be possible , let the circle ebf touch the circle a bc in more points than one , and first on the inside , in the points b , d ; join bd , and draw ( i . 10 , 11 ) gh bisecting bd at ...
... touches it on the inside or outside . For , if it be possible , let the circle ebf touch the circle a bc in more points than one , and first on the inside , in the points b , d ; join bd , and draw ( i . 10 , 11 ) gh bisecting bd at ...
Σελίδα 59
... 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 two , it would fall within it ( iii . 2 ) . Also , it is evident that there can be but one straight ...
... 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 two , it would fall within it ( iii . 2 ) . Also , it is evident that there can be but one straight ...
Σελίδα 60
Euclides. PROPOSITION XVIII . - THEOREM . 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 ...
Euclides. PROPOSITION XVIII . - THEOREM . 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 ...
Σελίδα 68
Euclides. PROPOSITION XXXII . - THEOREM . 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 ...
Euclides. PROPOSITION XXXII . - THEOREM . 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 ...
Σελίδα 69
... touches the circle ; and because ab drawn from the point of contact a cuts the circle , the angle dab is equal to the angle in the alternate segment ahb ( iii . 32 ) but the angle da b is equal to the angle C , therefore also the angle ...
... touches the circle ; and because ab drawn from the point of contact a cuts the circle , the angle dab is equal to the angle in the alternate segment ahb ( iii . 32 ) but the angle da b is equal to the angle C , therefore also the angle ...
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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