The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 Seiten |
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Seite 89
... multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a ... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ...
... multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a ... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ...
Seite 91
... multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION I. - THEOREM . If any number of magnitudes be equimultiples of as many others , each of each ; what multiple soever any one of ...
... multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION I. - THEOREM . If any number of magnitudes be equimultiples of as many others , each of each ; what multiple soever any one of ...
Seite 92
... multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . LET ab the first , be the same multiple ...
... multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . LET ab the first , be the same multiple ...
Seite 93
... multiple of b , that gl is of d . For the same reason , kf is the same multiple of b , that 1h is of d ; and so , if there be more parts in ef , gh , equal to a , c because , therefore , the first ek is the same multiple of the second b ...
... multiple of b , that gl is of d . For the same reason , kf is the same multiple of b , that 1h is of d ; and so , if there be more parts in ef , gh , equal to a , c because , therefore , the first ek is the same multiple of the second b ...
Seite 94
... multiple of a , that 1 is of c ( v . 3 ) . For the same reason , m is the same multiple of b , that n is of d and because , as a is to b , so is c to d ( hypoth . ) , and of a and c have been taken certain equimultiples k , l : and of b ...
... multiple of a , that 1 is of c ( v . 3 ) . For the same reason , m is the same multiple of b , that n is of d and because , as a is to b , so is c to d ( hypoth . ) , and of a and c have been taken certain equimultiples k , l : and of b ...
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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.