The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
Αναζήτηση στο βιβλίο
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 abc 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 abc be the given circle ; it is required to ...
Σελίδα 62
... similar segments of circles not coinciding with one another . d If it be possible , let the two similar segments of circles , viz . a cb , a db be upon the same side of the same straight line a b , not coinciding with one an- other ...
... similar segments of circles not coinciding with one another . d If it be possible , let the two similar segments of circles , viz . a cb , a db be upon the same side of the same straight line a b , not coinciding with one an- other ...
Σελίδα 63
... similar to the segment ad b , 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 im- possible ( i . 16 ) . Therefore there ...
... similar to the segment ad b , 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 im- possible ( i . 16 ) . Therefore there ...
Σελίδα 64
... similar ( iii . def . 11 ) to the segment edf ; and they are upon equal straight lines bc , ef . But similar segments of circles upon equal straight lines are equal ( iii . 24 ) to one another ; therefore the segment bac is equal to the ...
... similar ( iii . def . 11 ) to the segment edf ; and they are upon equal straight lines bc , ef . But similar segments of circles upon equal straight lines are equal ( iii . 24 ) to one another ; therefore the segment bac is equal to the ...
Σελίδα 73
... similar to the given segment . 9. Given a point , a straight line , and a point in the line , to describe a circle which shall pass through the first point , and touch the straight line in the other point . SECT . II . THEOREMS . 10 ...
... similar to the given segment . 9. Given a point , a straight line , and a point in the line , to describe a circle which shall pass through the first point , and touch the straight line in the other point . SECT . II . THEOREMS . 10 ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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