The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 Seiten |
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Seite 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 ...
Seite 90
Euclides. third , and of the ratio which the third has to the fourth , and so on unto the last 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 ...
Euclides. third , and of the ratio which the third has to the fourth , and so on unto the last 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 ...
Seite 91
... magnitudes are equal to one another . II . Those magnitudes of which the same or equal magnitudes are equimultiples are equal to one another . III . A multiple of a greater magnitude is greater than the same mul- tiple of a less . IV . That ...
... magnitudes are equal to one another . II . Those magnitudes of which the same or equal magnitudes are equimultiples are equal to one another . III . A multiple of a greater magnitude is greater than the same mul- tiple of a less . IV . That ...
Seite 92
... fourth . a 1.1 . d b- k . g g h h c 1 f Because ab is the same multiple of c , that de is off ; there are as many magnitudes in ab equal to c , as there are in de equal to f . In like manner , as many as there are in bg equal to c , so ...
... fourth . a 1.1 . d b- k . g g h h c 1 f Because ab is the same multiple of c , that de is off ; there are as many magnitudes in ab equal to c , as there are in de equal to f . In like manner , as many as there are in bg equal to c , so ...
Seite 93
... fourth d . If , therefore , the first , & c . Q. E. D. e bg c d PROPOSITION IV . - THEOREM . If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the ...
... fourth d . If , therefore , the first , & c . Q. E. D. e bg c d PROPOSITION IV . - THEOREM . If the first of four magnitudes has the same ratio to the second which the third has to the fourth ; then any equimultiples whatever of the ...
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Häufige Begriffe und Wortgruppen
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 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 straight line drawn tiple touches the circle triangle abc triangle def twice the rectangle
Beliebte Passagen
Seite 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.
Seite 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.
Seite 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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.
Seite 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.
Seite 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...
Seite 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...
Seite 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 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...
Seite 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.