The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 3
... square is that which has all its sides equal , and all its angles right angles . Square . Oblong . XXXI . An oblong is that which has all its angles right angles , but has not all its sides equal . XXXII . A rhombus is that which has ...
... square is that which has all its sides equal , and all its angles right angles . Square . Oblong . XXXI . An oblong is that which has all its angles right angles , but has not all its sides equal . XXXII . A rhombus is that which has ...
Σελίδα 31
... square upon a given straight line . LET ab be the given straight line ; it is required to describe a square upon a b . From the point a draw ( i . 11 ) a c at right angles to a b ; and make ( i . 3 ) a d equal to a b , and through the ...
... square upon a given straight line . LET ab be the given straight line ; it is required to describe a square upon a b . From the point a draw ( i . 11 ) a c at right angles to a b ; and make ( i . 3 ) a d equal to a b , and through the ...
Σελίδα 32
... square gb : and , in the same manner , by joining a e , bk , it is demonstrated , that the parallelogram cl is equal to the square hc ; therefore the whole square bdec is equal to the two squares gb , hc ; and the square bdec is ...
... square gb : and , in the same manner , by joining a e , bk , it is demonstrated , that the parallelogram cl is equal to the square hc ; therefore the whole square bdec is equal to the two squares gb , hc ; and the square bdec is ...
Σελίδα 33
... square in a parallelogram .. 12. Given a right - angled isosceles triangle to inscribe in it a square . 13. Given a finite straight line to describe a square of which that line Ishall be the diameter . 14. To construct a triangle that ...
... square in a parallelogram .. 12. Given a right - angled isosceles triangle to inscribe in it a square . 13. Given a finite straight line to describe a square of which that line Ishall be the diameter . 14. To construct a triangle that ...
Σελίδα 36
... square of a b a d C f therefore a straight Upon ab describe ( i . 46 ) the square a deb , and through c draw ( i . 31 ) cf , parallel to ad or be . Then a e is equal to the rectangles af , ce ; and ae is the square of a b ; and af is ...
... square of a b a d C f therefore a straight Upon ab describe ( i . 46 ) the square a deb , and through c draw ( i . 31 ) cf , parallel to ad or be . Then a e is equal to the rectangles af , ce ; and ae is the square of a b ; and af is ...
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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