The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 48
Similar segments of a circle are those in which the angles are equal , or which contain equal angles . Definition XI . PROPOSITION I. - PROBLEM . To find the centre of a given circle . LET a b c be the given circle ; it is required to ...
Similar segments of a circle are those in which the angles are equal , or which contain equal angles . Definition XI . PROPOSITION I. - PROBLEM . To find the centre of a given circle . LET a b c be the given circle ; it is required to ...
Σελίδα 62
Upon the same straight line and upon the same side of it , there cannot be two similar segments of circles not coinciding with one another . d IF it be possible , let the two similar segments of circles , viz . a cb , adb be upon the ...
Upon the same straight line and upon the same side of it , there cannot be two similar segments of circles not coinciding with one another . d IF it be possible , let the two similar segments of circles , viz . a cb , adb be upon the ...
Σελίδα 63
And because the segment a cb is similar to the segment adb , and that similar segments of circles contain ( iii . def . 11 ) equal angles ; the angle a cb is equal to the angle a db , the exterior to the interior , which is impossible ...
And because the segment a cb is similar to the segment adb , and that similar segments of circles contain ( iii . def . 11 ) equal angles ; the angle a cb is equal to the angle a db , the exterior to the interior , which is impossible ...
Σελίδα 64
But similar segments of circles upon equal straight lines are equal ( iii . 24 ) to one another ; therefore the segment bac is equal to the segment ed f . But the whole circle a b c is equal to the whole def ; therefore the remaining ...
But similar segments of circles upon equal straight lines are equal ( iii . 24 ) to one another ; therefore the segment bac is equal to the segment ed f . But the whole circle a b c is equal to the whole def ; therefore the remaining ...
Σελίδα 73
Given a segment of a circle and a straight line , to describe on the line another segment of a circle which shall be similar to the given segment . 9. Given a point , a straight line , and a point in the line , to describe a circle ...
Given a segment of a circle and a straight line , to describe on the line another segment of a circle which shall be similar to the given segment . 9. Given a point , a straight line , and a point in the line , to describe a circle ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
angle a b c angle bac applied 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 interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole