The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 8
Euclides. PROPOSITION VII . — THEOREM . Upon the same base , and on the same side of it , there cannot be two trian ... PROPOSITION VIII . — THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to ...
Euclides. PROPOSITION VII . — THEOREM . Upon the same base , and on the same side of it , there cannot be two trian ... PROPOSITION VIII . — THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to ...
Σελίδα 9
... PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal angle , it is required to bisect it . Take any point d in a b , and from ac cut ( i . 3 ) ...
... PROPOSITION IX . - PROBLEM . To bisect a given rectilineal angle , that is , to divide it into two equal angles . LET bac be the given rectilineal angle , it is required to bisect it . Take any point d in a b , and from ac cut ( i . 3 ) ...
Σελίδα 10
... PROPOSITION XI . - PROBLEM . To draw a straight line at right angles to a given straight line , from a given point in the same . de LET a b be a given straight line , and c a point given in it ; it is required to draw a straight line ...
... PROPOSITION XI . - PROBLEM . To draw a straight line at right angles to a given straight line , from a given point in the same . de LET a b be a given straight line , and c a point given in it ; it is required to draw a straight line ...
Σελίδα 11
... PROPOSITION XIII . — THEOREM . The angles which one straight line makes with another upon one side of it are either two right angles , or are together equal to two right angles . LET the straight line ab make with cd , upon one side of ...
... PROPOSITION XIII . — THEOREM . The angles which one straight line makes with another upon one side of it are either two right angles , or are together equal to two right angles . LET the straight line ab make with cd , upon one side of ...
Σελίδα 12
... PROPOSITION XIV . - THEOREM . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the ...
... PROPOSITION XIV . - THEOREM . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and 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