The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 15
... straight lines to a point within the triangle , these shall be less than the ... given straight lines , but any two whatever of these must be greater than ... line de terminated at the point d BOOK I. PROPS . XXI . , XXII . 15.
... straight lines to a point within the triangle , these shall be less than the ... given straight lines , but any two whatever of these must be greater than ... line de terminated at the point d BOOK I. PROPS . XXI . , XXII . 15.
Σελίδα 16
Euclides. Take a straight line de terminated at the point d , but unlimited towards e , and make ( i . 3 ) df equal ... given straight lines a , b , c . Which was to be done . PROPOSITION XXIII . - PROBLEM . At a given point in a given ...
Euclides. Take a straight line de terminated at the point d , but unlimited towards e , and make ( i . 3 ) df equal ... given straight lines a , b , c . Which was to be done . PROPOSITION XXIII . - PROBLEM . At a given point in a given ...
Σελίδα 17
... given point a in the given straight line a b , the angle fag is made equal to the given rectilineal angle dce . Which was to be done . PROPOSITION XXIV . — THEOREM . If two triangles have two sides of the one equal to two sides of the ...
... given point a in the given straight line a b , the angle fag is made equal to the given rectilineal angle dce . Which was to be done . PROPOSITION XXIV . — THEOREM . If two triangles have two sides of the one equal to two sides of the ...
Σελίδα 22
Euclides. PROPOSITION XXXI . — PROBLEM . To draw a straight line through a given point parallel to a given straight line . LET a be the given point , and bc the given straight line ; it is required to draw a straight line through the point ...
Euclides. PROPOSITION XXXI . — PROBLEM . To draw a straight line through a given point parallel to a given straight line . LET a be the given point , and bc the given straight line ; it is required to draw a straight line through the point ...
Σελίδα 28
... a parallelogram that shall be equal to the given triangle a bc , and have one of its angles equal to d Bisect ( i . 10 ) bc in e , join a e , and at the point e in the straight line ec make ( i . 23 ) the angle cef equal to d ; and through ...
... a parallelogram that shall be equal to the given triangle a bc , and have one of its angles equal to d Bisect ( i . 10 ) bc in e , join a e , and at the point e in the straight line ec make ( i . 23 ) the angle cef equal to d ; and through ...
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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