The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 47
... circles be applied to one another , so that their centres coincide , the circles must likewise coincide , since the straight lines from the centres are equal . II . A straight line is said to touch a circle when it meets the circle ...
... circles be applied to one another , so that their centres coincide , the circles must likewise coincide , since the straight lines from the centres are equal . II . A straight line is said to touch a circle when it meets the circle ...
Σελίδα 51
... circle , & c . Q. E. D. : PROPOSITION V. THEOREM . If two circles cut one another , they shall not have the same ... touch one another internally , they shall not have the same centre . LET the two circles abc , cde , touch one another ...
... circle , & c . Q. E. D. : PROPOSITION V. THEOREM . If two circles cut one another , they shall not have the same ... touch one another internally , they shall not have the same centre . LET the two circles abc , cde , touch one another ...
Σελίδα 54
... circle . LET the point d be taken within the circle abc , from which to the cir- cumference there fall more than two equal straight lines , viz . da , db , dc , the point d is the centre of the ... circles touch 54 THE ELEMENTS OF EUCLID .
... circle . LET the point d be taken within the circle abc , from which to the cir- cumference there fall more than two equal straight lines , viz . da , db , dc , the point d is the centre of the ... circles touch 54 THE ELEMENTS OF EUCLID .
Σελίδα 55
Euclides. PROPOSITION XI . - THEOREM . If two circles touch each other internally , the straight line which joins their centres being produced shall pass through the point of contact ... circle cannot touch BOOK III . PROPS . XI . , XII . 55.
Euclides. PROPOSITION XI . - THEOREM . If two circles touch each other internally , the straight line which joins their centres being produced shall pass through the point of contact ... circle cannot touch BOOK III . PROPS . XI . , XII . 55.
Σελίδα 56
Euclides. PROPOSITION XIII . - THEOREM . 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 ebf touch the circle a bc in more points than ...
Euclides. PROPOSITION XIII . - THEOREM . 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 ebf touch the circle a bc in more points than ...
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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