The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 6 - 10 από τα 47.
Σελίδα 20
In like 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 . a b therefore is parallel to cd .
In like 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 . a b therefore is parallel to cd .
Σελίδα 27
In the same manner , b it can be demonstrated , that no other line but ad is parallel to bc ; ad is therefore parallel to it . Wherefore equal triangles , & c . Q. E. D. g PROPOSITION XL . - THEOREM . Equal triangles upon equal bases ...
In the same manner , b it can be demonstrated , that no other line but ad is parallel to bc ; ad is therefore parallel to it . Wherefore equal triangles , & c . Q. E. D. g PROPOSITION XL . - THEOREM . Equal triangles upon equal bases ...
Σελίδα 32
to one another : therefore the parallelogram d 1 bl is equal to the 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 ...
to one another : therefore the parallelogram d 1 bl is equal to the 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 ...
Σελίδα 35
34 ) , bg is equal to a ; and in like manner the rectangle eh is contained by a , e c . Therefore the rectangle contained by a , bc , is equal to the several BOOK II . 35 PROP . I. Definitions Propositions.
34 ) , bg is equal to a ; and in like manner the rectangle eh is contained by a , e c . Therefore the rectangle contained by a , bc , is equal to the several BOOK II . 35 PROP . I. Definitions Propositions.
Σελίδα 49
In the same manner it can be shewn , that no other point but f is the centre ; that is , f is the centre of the circle a b c . Which was to be found . Cor . From this it is manifest , that if in a circle a straight line bisect another ...
In the same manner it can be shewn , that no other point but f is the centre ; that is , f is the centre of the circle a b c . Which was to be found . Cor . From this it is manifest , that if in a circle a straight line bisect another ...
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a b c angle a b c angle bac 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 join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square square of a c straight line a b Take taken third touches the circle triangle triangle a b c wherefore whole