The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 46
... lines drawn from the points of bisection to the opposite angles , four times the sum of the squares of these lines shall be equal to three times the sum of the squares of the three sides of the triangle . а BOOK III . DEFINITIONS .
... lines drawn from the points of bisection to the opposite angles , four times the sum of the squares of these lines shall be equal to three times the sum of the squares of the three sides of the triangle . а BOOK III . DEFINITIONS .
Σελίδα 47
DEFINITIONS . I. EQUAL circles are those of which the diameters are equal , or from the centres of which the straight lines to the circumferences are equal . This is not a definition , but a theorem , the truth of which is evident ...
DEFINITIONS . I. EQUAL circles are those of which the diameters are equal , or from the centres of which the straight lines to the circumferences are equal . This is not a definition , but a theorem , the truth of which is evident ...
Σελίδα 48
Definitions VIII . and IX . X. The sector of a circle is the figure contained by two straight lines drawn from the centre , and the circumference between them . Definition X. XI . Similar segments of a circle are those in which the ...
Definitions VIII . and IX . X. The sector of a circle is the figure contained by two straight lines drawn from the centre , and the circumference between them . Definition X. XI . Similar segments of a circle are those in which the ...
Σελίδα 74
17. If two circles cut each other , the straight line wbich joins their centres will bisect the straight line which joins the points of intersection . BOOK IV . DEFINITIONS . I. A RECTILINEAL figure is 74 THE ELEMENTS OF EUCLID .
17. If two circles cut each other , the straight line wbich joins their centres will bisect the straight line which joins the points of intersection . BOOK IV . DEFINITIONS . I. A RECTILINEAL figure is 74 THE ELEMENTS OF EUCLID .
Σελίδα 75
DEFINITIONS . I. A RECTILINEAL figure is said to be inscribed in another rectilineal figure , when all the angles of the inscribed figure are upon the sides of the figure in which it is inscribed , each upon each . II .
DEFINITIONS . I. A RECTILINEAL figure is said to be inscribed in another rectilineal figure , when all the angles of the inscribed figure are upon the sides of the figure in which it is inscribed , each upon each . II .
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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