The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
Euclides. these two is somewhere upon one of those straight lines , and the other upon the other line . Thus the angle which is contained by the straight lines ab , cb , is named the angle a bc , or cba ; that which is contained by a b ...
Euclides. these two is somewhere upon one of those straight lines , and the other upon the other line . Thus the angle which is contained by the straight lines ab , cb , is named the angle a bc , or cba ; that which is contained by a b ...
Σελίδα 5
... bc are equal to one another ; and the tri- angle abc is therefore equilateral , and it is described upon the given straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal ...
... bc are equal to one another ; and the tri- angle abc is therefore equilateral , and it is described upon the given straight line a b . Which was to be done . PROPOSITION II . - PROBLEM . From a given point to draw a straight line equal ...
Σελίδα 6
... straight lines , a part ae has been cut off equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM ... bc shall be equal to the base ef ; and the triangle abc to the triangle def ; and the other angles to which the equal ...
... straight lines , a part ae has been cut off equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM ... bc shall be equal to the base ef ; and the triangle abc to the triangle def ; and the other angles to which the equal ...
Σελίδα 9
... bc equal to the base ef . The angle bac is equal to the angle ed f a b d g се f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line be upon ef ; the point c shall also coin- cide with the ...
... bc equal to the base ef . The angle bac is equal to the angle ed f a b d g се f For , if the triangle abc be applied to def , so that the point b be on e , and the straight line be upon ef ; the point c shall also coin- cide with the ...
Σελίδα 10
... straight line cd ab is cut into two equal parts in the point d . Because a c is equal to c b , and cd common to the two triangles acd , bcd ; the two sides a c , cd are equal to bc , cd , each to each ; and the angle acd is equal to the ...
... straight line cd ab is cut into two equal parts in the point d . Because a c is equal to c b , and cd common to the two triangles acd , bcd ; the two sides a c , cd are equal to bc , cd , each to each ; and the angle acd is equal to the ...
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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