The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 55
... pass through the point of contact . a LET the two circles abc , ade touch each other internally in the point a , and ... pass through it . Therefore , if two circles , & c . Q. E. D. PROPOSITION XII . - THEOREM . If two circles touch ...
... pass through the point of contact . a LET the two circles abc , ade touch each other internally in the point a , and ... pass through it . Therefore , if two circles , & c . Q. E. D. PROPOSITION XII . - THEOREM . If two circles touch ...
Σελίδα 56
... passes through the point of contact ( iii . 11 ) ; but it does not pass through it , because the points b , d are without the straight line gh , which is absurd . Therefore one circle cannot touch another on the in- side in more points ...
... passes through the point of contact ( iii . 11 ) ; but it does not pass through it , because the points b , d are without the straight line gh , which is absurd . Therefore one circle cannot touch another on the in- side in more points ...
Σελίδα 57
... passing through the centre , cuts the straight line ab , which does not pass through the centre , at right angles , it also bisects it ( iii . 3 ) ; wherefore af is equal to fb , and ab double of af . For the same reason , cd is double ...
... passing through the centre , cuts the straight line ab , which does not pass through the centre , at right angles , it also bisects it ( iii . 3 ) ; wherefore af is equal to fb , and ab double of af . For the same reason , cd is double ...
Σελίδα 59
... passes between that straight line and the per- pendicular a e . And this is all that is to be understood , when , in the Greek text , and translations from it , the angle of the semicircle is said to be greater than any acute ...
... passes between that straight line and the per- pendicular a e . And this is all that is to be understood , when , in the Greek text , and translations from it , the angle of the semicircle is said to be greater than any acute ...
Σελίδα 63
... pass through the other points ; and the circle of which abc is a segment is described . And because the centre d is in a c , the segment abc is a semicircle . b A44 d d C But if the angles abd , bad are not equal to one another , at the ...
... pass through the other points ; and the circle of which abc is a segment is described . And because the centre d is in a c , the segment abc is a semicircle . b A44 d d C But if the angles abd , bad are not equal to one another , at the ...
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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