The first six books of the Elements of Euclid, with numerous exercises |
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Seite 48
Similar segments of a circle are those in which the angles are equal , or which contain equal angles . Definition XI . PROPOSITION I. - PROBLEM . To find the centre of a given circle . LET abc be the given circle ; it is required to ...
Similar segments of a circle are those in which the angles are equal , or which contain equal angles . Definition XI . PROPOSITION I. - PROBLEM . To find the centre of a given circle . LET abc be the given circle ; it is required to ...
Seite 62
Upon the same straight line and upon the same side of it , there cannot be two similar segments of circles not coinciding with one another . d b If it be possible , let the two similar segments of circles , viz .
Upon the same straight line and upon the same side of it , there cannot be two similar segments of circles not coinciding with one another . d b If it be possible , let the two similar segments of circles , viz .
Seite 63
And because the segment acb is similar to the segment a db , and that similar segments of circles contain ( iii . def . 11 ) equal angles ; the angle acb is equal to the angle adb , the exterior to the interior , which is im- possible ...
And because the segment acb is similar to the segment a db , and that similar segments of circles contain ( iii . def . 11 ) equal angles ; the angle acb is equal to the angle adb , the exterior to the interior , which is im- possible ...
Seite 64
But similar segments of circles upon equal straight lines are equal ( iii . 24 ) to one another ; therefore the segment bac is equal to the segment edf . But the whole circle abc is equal to the whole def ; therefore the remaining ...
But similar segments of circles upon equal straight lines are equal ( iii . 24 ) to one another ; therefore the segment bac is equal to the segment edf . But the whole circle abc is equal to the whole def ; therefore the remaining ...
Seite 73
Given a segment of a circle and a straight line , to describe on the line another segment of a circle which shall be similar to the given segment . 9. Given a point , a straight line , and a point in the line , to . describe a circle ...
Given a segment of a circle and a straight line , to describe on the line another segment of a circle which shall be similar to the given segment . 9. Given a point , a straight line , and a point in the line , to . describe a circle ...
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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.