The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 2
... greater than a right angle . XII . An acute angle is that which is less than a right angle . Obtuse . Acute . XIII . A term or boundary is the extremity of any thing . XIV . A figure is that which is enclosed by one or more boundaries ...
... greater than a right angle . XII . An acute angle is that which is less than a right angle . Obtuse . Acute . XIII . A term or boundary is the extremity of any thing . XIV . A figure is that which is enclosed by one or more boundaries ...
Σελίδα 4
... greater than its part . X. Two straight lines cannot enclose a space . XI . All right angles are equal to one another . XII . If a straight line meets two straight lines , so as to make the two interior angles on the same side of it ...
... greater than its part . X. Two straight lines cannot enclose a space . XI . All right angles are equal to one another . XII . If a straight line meets two straight lines , so as to make the two interior angles on the same side of it ...
Σελίδα 5
... greater . It is required to cut off from a b , the greater , a part equal to c , the less . From the point a draw ( i . 2 ) the straight line a d equal to c ; and from the centre a , and at the distance a d , describe ( 3 post . ) the ...
... greater . It is required to cut off from a b , the greater , a part equal to c , the less . From the point a draw ( i . 2 ) the straight line a d equal to c ; and from the centre a , and at the distance a d , describe ( 3 post . ) the ...
Σελίδα 6
... 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 one equal to two sides of the other , each to each ; and have ...
... 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 one equal to two sides of the other , each to each ; and have ...
Σελίδα 7
... greater than the other : let ab be the greater ; and from it cut ( i . 3 ) off db equal to a c , the less , and join dc ; therefore , because in the triangles dbc , acb , db is equal to a c , and bc common to both , the two sides , db ...
... greater than the other : let ab be the greater ; and from it cut ( i . 3 ) off db equal to a c , the less , and join dc ; therefore , because in the triangles dbc , acb , db is equal to a c , and bc common to both , the two sides , db ...
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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