The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 11
... straight line of an unlimited length , from a given point without it . LET a b be the given straight line , which may be produced to any length both ways , and let c be a point without it . It is required to draw a straight line ...
... straight line of an unlimited length , from a given point without it . LET a b be the given straight line , which may be produced to any length both ways , and let c be a point without it . It is required to draw a straight line ...
Σελίδα 12
... straight line . Ar the point b in the straight line a b , let the two straight lines bc , bd b a d upon the opposite sides of a b , make the adjacent angles abc , abd equal together to two right angles , bd is in the same straight line ...
... straight line . Ar the point b in the straight line a b , let the two straight lines bc , bd b a d upon the opposite sides of a b , make the adjacent angles abc , abd equal together to two right angles , bd is in the same straight line ...
Σελίδα 15
... a b . two sides , & c . Q. E. D. than ca , and b Therefore any ల PROPOSITION XXI . - THEOREM . If from the ends of the side of a triangle there be drawn two straight lines to a point within the triangle , these shall be less than the ...
... a b . two sides , & c . Q. E. D. than ca , and b Therefore any ల PROPOSITION XXI . - THEOREM . If from the ends of the side of a triangle there be drawn two straight lines to a point within the triangle , these shall be less than the ...
Σελίδα 16
Euclides. Take a straight line de terminated at the point d , but unlimited towards e , and make ( i . 3 ) df equal ... a b C and from the centre g , at the distance gh , describe ( 3 post . ) another circle hlk ; and join kf , kg ; the ...
Euclides. Take a straight line de terminated at the point d , but unlimited towards e , and make ( i . 3 ) df equal ... a b C and from the centre g , at the distance gh , describe ( 3 post . ) another circle hlk ; and join kf , kg ; the ...
Σελίδα 17
... 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 other , each to each , but ...
... 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 other , each to each , but ...
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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