The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 56
... touches it on the inside or outside . For , if it be possible , let the circle ebf touch the circle abc 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 abc 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 ...
Página 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 ...
Página 60
... touches a circle , and from the point of contact a straight line be drawn at right angles to the touching line , the centre of the circle shall be in that line . LET the straight line de touch the circle abc inc ; and from clet ca be ...
... touches a circle , and from the point of contact a straight line be drawn at right angles to the touching line , the centre of the circle shall be in that line . LET the straight line de touch the circle abc inc ; and from clet ca be ...
Página 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 ...
Página 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 dab 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 dab is equal to the angle c , therefore also the angle ...
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Términos y frases comunes
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