The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 sider |
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Side 34
... triangle have its exterior angle and one of its opposite interior angles double of ... twice the line joining the vertex and the middle of the base . 21. Each ... rectangle are equal to one another . 25. If any number of parallelograms be ...
... triangle have its exterior angle and one of its opposite interior angles double of ... twice the line joining the vertex and the middle of the base . 21. Each ... rectangle are equal to one another . 25. If any number of parallelograms be ...
Side 37
... twice the rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of a b is equal to the squares of a c , cb , and to twice the rectangle con- tained by a c , cb . a مع с b k f e Upon ...
... twice the rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of a b is equal to the squares of a c , cb , and to twice the rectangle con- tained by a c , cb . a مع с b k f e Upon ...
Side 39
... twice the rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of a b , b c are equal to twice the rectangle ...
... twice the rectangle contained by the whole and that part , together with the square of the other part . LET the straight line ab be divided into any two parts in the point c ; the squares of a b , b c are equal to twice the rectangle ...
Side 43
... rectangle cf , fa , together with the square of a e , is equal to the squares of ba , ae : take away the square of ... twice the rectangle contained by the side upon which , when produced , the perpendicular falls , and the straight line ...
... rectangle cf , fa , together with the square of a e , is equal to the squares of ba , ae : take away the square of ... twice the rectangle contained by the side upon which , when produced , the perpendicular falls , and the straight line ...
Side 44
... twice the rectangle contained by either of these sides , and the straight line inter- cepted between the ... twice the rectangle cb , bd . First , let ad fall within the triangle abc ; and because the straight b d c c cb , ba are equal ...
... twice the rectangle contained by either of these sides , and the straight line inter- cepted between the ... twice the rectangle cb , bd . First , let ad fall within the triangle abc ; and because the straight b d c c cb , ba are equal ...
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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 passager
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.