The first six books of the Elements of Euclid, with numerous exercisesIngram, Cooke, 1853 - 147 sider |
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Side 36
... rectangles af , ce ; and a e is the square of a b ; and af is the rectangle con- tained by ba , a c ; for it is contained by da , a c , of which ad is equal to ab ; and ce is contained by ab , bc , for be is equal to ab ; therefore the ...
... rectangles af , ce ; and a e is the square of a b ; and af is the rectangle con- tained by ba , a c ; for it is contained by da , a c , of which ad is equal to ab ; and ce is contained by ab , bc , for be is equal to ab ; therefore the ...
Side 37
... rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of a b ... ad or be , and through g draw hk parallel to ab or de . And because cf is parallel to a d , and b'd falls upon them ...
... rectangle contained by the parts . LET the straight line ab be divided into any two parts in c ; the square of a b ... ad or be , and through g draw hk parallel to ab or de . And because cf is parallel to a d , and b'd falls upon them ...
Side 38
Euclides. and into two unequal parts at the point d ; the rectangle a d , db , together with the square of c d , is ... a d , db , for dh is equal ( ii . 4. cor . ) to db ; and df together with ch is the gnomon cmg ; there- fore the ...
Euclides. and into two unequal parts at the point d ; the rectangle a d , db , together with the square of c d , is ... a d , db , for dh is equal ( ii . 4. cor . ) to db ; and df together with ch is the gnomon cmg ; there- fore the ...
Side 39
Euclides. angle a d , db , together with the square of cb , is equal to the gnomon cmg , and the figure 18 ; but the gnomon cmg and 1g make up the whole figure cefd , which is the square of cd ; therefore the rectangle ad , db , together ...
Euclides. angle a d , db , together with the square of cb , is equal to the gnomon cmg , and the figure 18 ; but the gnomon cmg and 1g make up the whole figure cefd , which is the square of cd ; therefore the rectangle ad , db , together ...
Side 40
... rectangle ck is equal ( i . 36 ) to bn , and gr to rn ; but ck is equal ( i . 43 ) to rn , because they are the ... a d : therefore four times the rectangle ab , bc , together with the square of a c , is equal to the square of a d , that ...
... rectangle ck is equal ( i . 36 ) to bn , and gr to rn ; but ck is equal ( i . 43 ) to rn , because they are the ... a d : therefore four times the rectangle ab , bc , together with the square of a c , is equal to the square of a d , that ...
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Almindelige termer og sætninger
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
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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.