The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 páginas |
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Página 31
... square upon a given straight line . LET ab be the given straight line ; it is required to describe a square upon a b . From the point a draw ( i . 11 ) ac at right angles to a b ; and make ( i . 3 ) a d equal to a b , and through the ...
... square upon a given straight line . LET ab be the given straight line ; it is required to describe a square upon a b . From the point a draw ( i . 11 ) ac at right angles to a b ; and make ( i . 3 ) a d equal to a b , and through the ...
Página 32
... square gb is double of the trian- gle fbc , because these also are upon the same base fb , and between the same ... ac : wherefore the square upon the side bc is equal to the squares upon the sides ba , a c . Therefore , in any right ...
... square gb is double of the trian- gle fbc , because these also are upon the same base fb , and between the same ... ac : wherefore the square upon the side bc is equal to the squares upon the sides ba , a c . Therefore , in any right ...
Página 36
... square a deb , and through c draw ( i . 31 ) cf , parallel to a d or be . Then ae is equal to the rectangles af , ce ; and a e is the square of ab ; and af is the rectangle con- tained by ba , a c ; for it is contained by da , a c , of ...
... square a deb , and through c draw ( i . 31 ) cf , parallel to a d or be . Then ae is equal to the rectangles af , ce ; and a e is the square of ab ; and af is the rectangle con- tained by ba , a c ; for it is contained by da , a c , of ...
Página 37
... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts . LET the straight line a b be divided into any two parts in c ; the square of a b is equal to the squares of a c ...
... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by the parts . LET the straight line a b be divided into any two parts in c ; the square of a b is equal to the squares of a c ...
Página 38
... square of c d , is equal to the square of cb . a 1 k h d b Upon cb describe ( i . 46 ) the square cefb , join be ... a c is equal to cb ; therefore also al is equal to df . To each of these add ch , and the whole ah is equal to d f and ...
... square of c d , is equal to the square of cb . a 1 k h d b Upon cb describe ( i . 46 ) the square cefb , join be ... a c is equal to cb ; therefore also al is equal to df . To each of these add ch , and the whole ah is equal to d f and ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 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.
Página 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.
Página 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...
Página 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...
Página 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 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...
Página 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.