The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 σελίδες |
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Αποτελέσματα 1 - 5 από τα 23.
Σελίδα 4
... double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
... double of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space , are equal to one ...
Σελίδα 24
... double ( i . 34 ) of the triangle bdc ; and they are there- fore equal to one another . But , if the sides ad , ef ( see second and third figures ) , opposite to the base bc of the parallelograms a b c debcf , be not terminated in the ...
... double ( i . 34 ) of the triangle bdc ; and they are there- fore equal to one another . But , if the sides ad , ef ( see second and third figures ) , opposite to the base bc of the parallelograms a b c debcf , be not terminated in the ...
Σελίδα 27
... be upon the same base and between the same parallels , the parallelogram shall be double of the triangle . LET the parallelogram abcd and the triangle ebc be upon the same a d b e base bc , and between the BOOK I. PROPS . XL . , XLI . 27.
... be upon the same base and between the same parallels , the parallelogram shall be double of the triangle . LET the parallelogram abcd and the triangle ebc be upon the same a d b e base bc , and between the BOOK I. PROPS . XL . , XLI . 27.
Σελίδα 28
... double of the tri- angle e bc . Join ac ; then the triangle abc is equal ( i . 37 ) to the triangle ebc , because they are upon the same base bc , and between the same parallels bc , ae . But the parallelogram abcd is double ( i . 34 ) ...
... double of the tri- angle e bc . Join ac ; then the triangle abc is equal ( i . 37 ) to the triangle ebc , because they are upon the same base bc , and between the same parallels bc , ae . But the parallelogram abcd is double ( i . 34 ) ...
Σελίδα 32
... double k ( i . 41 ) of the triangle abd , because they are upon the same base bd , and be- tween the same parallels bd , al ; and the square gb is double of the trian- gle fbc , because these also are upon the same base fb , and between ...
... double k ( i . 41 ) of the triangle abd , because they are upon the same base bd , and be- tween the same parallels bd , al ; and the square gb is double of the trian- gle fbc , because these also are upon the same base fb , and between ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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 perpendicular Q. E. D. PROPOSITION rectangle a b 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
Δημοφιλή αποσπάσματα
Σελίδα 40 - 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.
Σελίδα 2 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 19 - 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.
Σελίδα 27 - To describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 36 - 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...
Σελίδα 13 - 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...
Σελίδα 11 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 2 - 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...
Σελίδα 124 - 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.