The first six books of the Elements of Euclid, with numerous exercises |
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Seite 31
... wherefore the figure a deb is rectangular , and it has been demonstrated that it is equilateral ; it is therefore a ... side subtending the right angle is equal to the squares described upon the sides which contain the right angle .
... wherefore the figure a deb is rectangular , and it has been demonstrated that it is equilateral ; it is therefore a ... side subtending the right angle is equal to the squares described upon the sides which contain the right angle .
Seite 35
I. EVERY right - angled parallelogram is said to be contained by any two of the straight lines which contain one of ... If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the ...
I. EVERY right - angled parallelogram is said to be contained by any two of the straight lines which contain one of ... If there be two straight lines , one of which is divided into any number of parts , the rectangle contained by the ...
Seite 36
by a , bc , is equal to the several rectangles contained by a , bd , and by a , de , and also by a , ec . ... LET the straight line ab be divided into any two parts in the point c ; the rectangle contained by ab , bc , together with the ...
by a , bc , is equal to the several rectangles contained by a , bd , and by a , de , and also by a , ec . ... LET the straight line ab be divided into any two parts in the point c ; the rectangle contained by ab , bc , together with the ...
Seite 37
If a straight line be divided into any two parts , the 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 ...
If a straight line be divided into any two parts , the 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 ...
Seite 38
and into two unequal parts at the point d ; the rectangle a d , db , together with the square of c d , is equal to the ... To each of these add ch , and the whole ah is equal to d f and ch : but ah is the rect- angle contained by a d ...
and into two unequal parts at the point d ; the rectangle a d , db , together with the square of c d , is equal to the ... To each of these add ch , and the whole ah is equal to d f and ch : but ah is the rect- angle contained by a d ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 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.
Seite 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.
Seite 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...
Seite 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...
Seite 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Seite 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...
Seite 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.