The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 sider |
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Resultat 1-5 av 58
Side 6
... base b c shall coincide with the base ef , because the point b coinciding with e , and c with f , if the base b c does not coincide with the base e f , two straight lines would enclose a space , which is impossible ( 10 ax . ) . Therefore ...
... base b c shall coincide with the base ef , because the point b coinciding with e , and c with f , if the base b c does not coincide with the base e f , two straight lines would enclose a space , which is impossible ( 10 ax . ) . Therefore ...
Side 7
... base fc is equal ( i . 4 ) to the base gb , and the triangle afc to the triangle a gb ; and the remaining angles of the one are equal ( i . 4 ) to the remaining angles of the other , each to each , to which the equal sides are opposite ...
... base fc is equal ( i . 4 ) to the base gb , and the triangle afc to the triangle a gb ; and the remaining angles of the one are equal ( i . 4 ) to the remaining angles of the other , each to each , to which the equal sides are opposite ...
Side 8
... base equal to one another , and likewise those which are terminated in the other extremity . Ir it be possible , let there be two triangles a c b , a d b , upon the same base a d bcd ; much greater Again , because cb is angle bcd ; but ...
... base equal to one another , and likewise those which are terminated in the other extremity . Ir it be possible , let there be two triangles a c b , a d b , upon the same base a d bcd ; much greater Again , because cb is angle bcd ; but ...
Side 9
... base bc coincides with the base ef , but the sides ba , ca do not coincide with the sides ed , fd , but have a different situation , as eg , fg , then upon the same base ef , and upon the same side of it , there can be two triangles ...
... base bc coincides with the base ef , but the sides ba , ca do not coincide with the sides ed , fd , but have a different situation , as eg , fg , then upon the same base ef , and upon the same side of it , there can be two triangles ...
Side 10
... base dfis equal to the base ef ; therefore the angle dcf is equal ( i . 8 ) to the angle But , when the adjacent angles ecf ; and they are adjacent angles . which one straight line makes with another straight line are equal to one ...
... base dfis equal to the base ef ; therefore the angle dcf is equal ( i . 8 ) to the angle But , when the adjacent angles ecf ; and they are adjacent angles . which one straight line makes with another straight line are equal to one ...
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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.