The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 5
... shewn that bc is equal to bg ; wherefore al and bc are each of them equal to bg ; and things that are equal to the same are equal to one another ; therefore the straight line al is equal to bc . Wherefore from the given point a a ...
... shewn that bc is equal to bg ; wherefore al and bc are each of them equal to bg ; and things that are equal to the same are equal to one another ; therefore the straight line al is equal to bc . Wherefore from the given point a a ...
Σελίδα 14
... shewn that it is not equal to ab ; therefore a c is greater than a b . Wherefore the greater angle , & c . b C Q. E. D. PROPOSITION XX . THEOREM . Any two sides of a triangle are together greater than the third side . LET abc be a ...
... shewn that it is not equal to ab ; therefore a c is greater than a b . Wherefore the greater angle , & c . b C Q. E. D. PROPOSITION XX . THEOREM . Any two sides of a triangle are together greater than the third side . LET abc be a ...
Σελίδα 15
... shewn that ba , ac , are greater than be , ec , much greater then are ba , ac than bd , dc . b Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle bdc of the triangle ...
... shewn that ba , ac , are greater than be , ec , much greater then are ba , ac than bd , dc . b Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle bdc of the triangle ...
Σελίδα 18
... shewn that it is not equal to it ; therefore the angle bac is greater than the angle edf . Wherefore , if two triangles , & c . Q. E. D. PROPOSITION XXVI . - THEOREM . If two triangles have two angles of the one equal to two angles of ...
... shewn that it is not equal to it ; therefore the angle bac is greater than the angle edf . Wherefore , if two triangles , & c . Q. E. D. PROPOSITION XXVI . - THEOREM . If two triangles have two angles of the one equal to two angles of ...
Σελίδα 21
... shewn that the angle agk is equal to the angle ghf ; therefore also agk is equal to gkd ; and they are alternate angles ; therefore ab is parallel ( i . 27 ) to cd ; Wherefore , straight lines , & c . Q. E. D. k g b h f d PROPOSITION ...
... shewn that the angle agk is equal to the angle ghf ; therefore also agk is equal to gkd ; and they are alternate angles ; therefore ab is parallel ( i . 27 ) to cd ; Wherefore , straight lines , & c . Q. E. D. k g b h f d PROPOSITION ...
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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