The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 sider |
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Side 89
... Ratio is a mutual relation of two 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 ...
... Ratio is a mutual relation of two 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 ...
Side 90
... 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 of a to d is said to be compounded of the ratios of a to b , b to c , and c to d : And if a has to b the same ratio which e has ...
... 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 of a to d is said to be compounded of the ratios of a to b , b to c , and c to d : And if a has to b the same ratio which e has ...
Side 93
... ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of the second and fourth , viz . the equimultiple of the first shall have the ...
... ratio to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the same ratio to any equimultiples of the second and fourth , viz . the equimultiple of the first shall have the ...
Side 94
... ratio to the second and fourth . And in like manner , the first and the third have the same ratio to any equimultiples whatever of the second and fourth . Let a the first have to b the second , the same ration which the third c has to ...
... ratio to the second and fourth . And in like manner , the first and the third have the same ratio to any equimultiples whatever of the second and fourth . Let a the first have to b the second , the same ration which the third c has to ...
Side 95
... ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also greater than the fourth ; and if equal , equal ; if less , less . TAKE any equimultiples of each of them , as the doubles of ...
... ratio which the third has to the fourth ; then , if the first be greater than the second , the third is also greater than the fourth ; and if equal , equal ; if less , less . TAKE any equimultiples of each of them , as the doubles of ...
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The first six books of the Elements of Euclid, with numerous exercises Euclides Uten tilgangsbegrensning - 1853 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 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.
Side 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 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.
Side 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.
Side 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...
Side 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...
Side 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 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...
Side 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.