The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Σελίδα 1
... magnitude . II . A line is length without breadth . III . The extremities of a line are points . IV . A straight line is that which lies evenly between its extreme points . V. A superficies is that which hath only length and breadth ...
... magnitude . II . A line is length without breadth . III . The extremities of a line are points . IV . A straight line is that which lies evenly between its extreme points . V. A superficies is that which hath only length and breadth ...
Σελίδα 4
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . * IX . The whole is greater than its part . X. Two straight lines cannot enclose a space . XI . All right angles are ...
... Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one another . * IX . The whole is greater than its part . X. Two straight lines cannot enclose a space . XI . All right angles are ...
Σελίδα 88
... to one half of a side of the other triangle . 12. If a square be inscribed in a circle , it shall be double the square of the radius of the circle . BOOK V. DEFINITIONS . I. A LESS magnitude is said 88 THE ELEMENTS OF EUCLID .
... to one half of a side of the other triangle . 12. If a square be inscribed in a circle , it shall be double the square of the radius of the circle . BOOK V. DEFINITIONS . I. A LESS magnitude is said 88 THE ELEMENTS OF EUCLID .
Σελίδα 89
... magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have ...
... magnitudes of the same kind to one another , in respect of quantity . IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have ...
Σελίδα 90
... magnitude . For example , if a , b , c , d be four magnitudes of the same kind , the first a is said to have to the last d the ratio compounded of the ratio of a to b , and the ratio of b to c , and the ratio of c to d ; or , the ratio ...
... magnitude . For example , if a , b , c , d be four magnitudes of the same kind , the first a is said to have to the last d the ratio compounded of the ratio of a to b , and the ratio of b to c , and the ratio of c to d ; or , the ratio ...
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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