The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 14
... Q. E. D. PROPOSITION XVIII . — THEOREM . The greater side of every triangle is opposite to the greater angle . d LET abc be a triangle , of which the side ac is greater than the side a b ; the angle abc is also greater than the angle ...
... Q. E. D. PROPOSITION XVIII . — THEOREM . The greater side of every triangle is opposite to the greater angle . d LET abc be a triangle , of which the side ac is greater than the side a b ; the angle abc is also greater than the angle ...
Σελίδα 15
... Q. E. D. PROPOSITION XXII . — PROBLEM . To make a triangle of which the sides shall be equal to three given straight lines , but any two whatever of these must be greater than the third ( i . 20. ) . LET a , b , be the three given ...
... Q. E. D. PROPOSITION XXII . — PROBLEM . To make a triangle of which the sides shall be equal to three given straight lines , but any two whatever of these must be greater than the third ( i . 20. ) . LET a , b , be the three given ...
Σελίδα 17
... Q. E. D. PROPOSITION XXV . - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , but the base of the one greater than the base of the other ; the angle also contained by the sides of ...
... Q. E. D. PROPOSITION XXV . - THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , but the base of the one greater than the base of the other ; the angle also contained by the sides of ...
Σελίδα 18
... Q. E. D. PROPOSITION XXVI . - THEOREM . If two triangles have two angles of the one equal to two angles of the other , each to each , and one side equal to one side , viz . either the sides adjacent to the equal angles , or the sides ...
... Q. E. D. PROPOSITION XXVI . - THEOREM . If two triangles have two angles of the one equal to two angles of the other , each to each , and one side equal to one side , viz . either the sides adjacent to the equal angles , or the sides ...
Σελίδα 19
... Q. E. D. PROPOSITION XXVII . - THEOREM . If a straight line falling upon two other straight lines makes the ... PROP . XXVII . 19.
... Q. E. D. PROPOSITION XXVII . - THEOREM . If a straight line falling upon two other straight lines makes the ... PROP . XXVII . 19.
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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