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 4
... straight line may be produced to any length in a straight line . III . And that a circle may be described from any ... ab be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre a , at ...
... straight line may be produced to any length in a straight line . III . And that a circle may be described from any ... ab be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre a , at ...
Σελίδα 5
... ab ; therefore ca , cb , are each of them equal to ab ; but things which are equal to the same are equal to one another ... straight line c is likewise equal C d a e b to ad ; whence ae and c are each of them equal to ad ; therefore the ...
... ab ; therefore ca , cb , are each of them equal to ab ; but things which are equal to the same are equal to one another ... straight line c is likewise equal C d a e b to ad ; whence ae and c are each of them equal to ad ; therefore the ...
Σελίδα 6
Euclides. line a e is equal ( 1 ax . ) to c , and from a b , the greater of two straight lines , a part ae has been cut off equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the ...
Euclides. line a e is equal ( 1 ax . ) to c , and from a b , the greater of two straight lines , a part ae has been cut off equal to c the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the ...
Σελίδα 9
... a b , and from ac cut ( i . 3 ) off ae equal to ad ; join de , and upon it describe ( i . 1 ) an equilateral triangle def ; then join af ; the straight line af bisects the angle bac Because ad is equal to a e , and af is common to the ...
... a b , and from ac cut ( i . 3 ) off ae equal to ad ; join de , and upon it describe ( i . 1 ) an equilateral triangle def ; then join af ; the straight line af bisects the angle bac Because ad is equal to a e , and af is common 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