The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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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 abc , or cba ; that which is contained by ab ...
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 abc , or cba ; that which is contained by ab ...
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... 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 . d 3 c b From the ...
... 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 . d 3 c b From the ...
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... straight line ab . Which was to be done . PROPOSITION II . — PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the given point , and be the given straight line ; it is required to draw from ...
... straight line ab . Which was to be done . PROPOSITION II . — PROBLEM . From a given point to draw a straight line equal to a given straight line . LET a be the given point , and be the given straight line ; it is required to draw from ...
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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 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 the less . Which was to be done . PROPOSITION IV . - THEOREM . If two triangles have two sides of the ...
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... ab , 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 . a Because ad is equal to ae , and af is common to the ...
... ab , 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 . a Because ad is equal to ae , and af is common to the ...
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ac is equal adjacent angles alternate angles angle abc angle acb angle bac angle edf angle equal base bc bisected centre circle abc diameter double draw duplicate ratio equal angles equal straight lines equal to f equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given rectilineal figure given straight line gnomon greater ratio greater than f ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram perpendicular produced Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle shewn side bc similar and similarly square of ac straight line ab straight line ac straight line drawn THEOREM tiple touches the circle triangle abc triangle def twice the rectangle