The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 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 ...
Página 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 ...
Página 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 .
Página 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 ...
Página 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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Términos y frases comunes
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 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 ILLUSTRATED LONDON inscribe less LET abc LET the straight likewise multiple opposite angle parallel parallelogram pentagon perpendicular Q. E. D. PROPOSITION rectangle a d rectangle contained remaining angle right angles segment shewn square of a c square of eg straight line a b straight line ab straight line bc tiple touches the circle triangle abc triangle def twice the rectangle
Pasajes populares
Página 2 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another : XVI.
Página 42 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 21 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Página 29 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 38 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of...
Página 15 - 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 other two sides of the triangle, but shall contain a greater angle. Let...
Página 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 4 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Página 126 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.