The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 sider |
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Side 89
... said to have to the last of them the ratio compounded of the ratio which the first has to the second , and of the ratio which the second has to the third , and of the ratio which the third has BOOK V. DEFINITIONS . 89 Definitions.
... said to have to the last of them the ratio compounded of the ratio which the first has to the second , and of the ratio which the second has to the third , and of the ratio which the third has BOOK V. DEFINITIONS . 89 Definitions.
Side 90
... 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 to f ; and b ... compounded of ratios which are the same with the ratios of e to f , g to h , and k to l . And the same thing is to ...
... 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 to f ; and b ... compounded of ratios which are the same with the ratios of e to f , g to h , and k to l . And the same thing is to ...
Side 112
... compounded of the same ratios are the same with one another . LET a be to b as d to e ; and b to c as e to f : the ratio which is com- pounded of the ratios of a to b , and b to c , which by the de- a b c finition of compound ratio , is ...
... compounded of the same ratios are the same with one another . LET a be to b as d to e ; and b to c as e to f : the ratio which is com- pounded of the ratios of a to b , and b to c , which by the de- a b c finition of compound ratio , is ...
Side 113
... compounded of ratios which are the same with the first ratios , each to each , is the same with the ratio compounded of ratios which are the same with the other ratios , each to each . a b c . d . LET a be to bas e to f ; and c to d as ...
... compounded of ratios which are the same with the first ratios , each to each , is the same with the ratio compounded of ratios which are the same with the other ratios , each to each . a b c . d . LET a be to bas e to f ; and c to d as ...
Side 114
... compounded of ratios which are the same with the first ratios , each to each , is the same with the ratio compounded of ratios which are the same , each to each , with the last ratios ; and if one of the first ratios , or the ratio ...
... compounded of ratios which are the same with the first ratios , each to each , is the same with the ratio compounded of ratios which are the same , each to each , with the last ratios ; and if one of the first ratios , or the ratio ...
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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.