The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 20
... manner it may be demonstrated , that they do not meet towards a , c , but those straight lines which meet neither way , though produced ever so far , are parallel ( 35 def . ) to one another . ab there- fore is parallel to cd ...
... manner it may be demonstrated , that they do not meet towards a , c , but those straight lines which meet neither way , though produced ever so far , are parallel ( 35 def . ) to one another . ab there- fore is parallel to cd ...
Σελίδα 27
... manner , it can be demonstrated , that no b d other line but ad is parallel to bc ; ad is therefore parallel to it . Wherefore equal triangles , & c . Q. E. D. PROPOSITION XL . — THEOREM . Equal triangles upon equal bases , in the same ...
... manner , it can be demonstrated , that no b d other line but ad is parallel to bc ; ad is therefore parallel to it . Wherefore equal triangles , & c . Q. E. D. PROPOSITION XL . — THEOREM . Equal triangles upon equal bases , in the same ...
Σελίδα 32
... 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 described upon the straight line bc ...
... 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 described upon the straight line bc ...
Σελίδα 35
... , because dk , that is ( i . 34 ) bg is equal to a ; and in like manner the rectangle eh is contained by a , e c . Therefore the rectangle contained fl by a , bc , is equal to the several BOOK II . PROP . I. 35 Definitions Propositions.
... , because dk , that is ( i . 34 ) bg is equal to a ; and in like manner the rectangle eh is contained by a , e c . Therefore the rectangle contained fl by a , bc , is equal to the several BOOK II . PROP . I. 35 Definitions Propositions.
Σελίδα 49
... manner it can be shewn , that no other point but fis the centre ; that is , f is the centre of the circle ab c . Which was to be found . COR . From this it is manifest , that if in a circle a straight line bisect another at right angles ...
... manner it can be shewn , that no other point but fis the centre ; that is , f is the centre of the circle ab c . Which was to be found . COR . From this it is manifest , that if in a circle a straight line bisect another at right angles ...
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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