The first six books of the Elements of Euclid, with numerous exercises |
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Seite 47
I. EQUAL circles are those of which the diameters are equal , or from the centres of which the straight lines to the ... A straight line is said to touch a circle when it meets the circle , and being produced does not cut it . III .
I. EQUAL circles are those of which the diameters are equal , or from the centres of which the straight lines to the ... A straight line is said to touch a circle when it meets the circle , and being produced does not cut it . III .
Seite 51
Wherefore , if in a circle , & c . ... LET the two circles a b c , cdg cut one another in the points b , c ; they have not the same centre . ... If two circles touch one another internally , they shall not have the same centre .
Wherefore , if in a circle , & c . ... LET the two circles a b c , cdg cut one another in the points b , c ; they have not the same centre . ... If two circles touch one another internally , they shall not have the same centre .
Seite 54
If a point be taken within a circle , from which there fall more than two equal straight lines to the circumference , that point is the centre of the circle . ... THEOREM . If two circles touch 54 THE ELEMENTS OF EUCLID .
If a point be taken within a circle , from which there fall more than two equal straight lines to the circumference , that point is the centre of the circle . ... THEOREM . If two circles touch 54 THE ELEMENTS OF EUCLID .
Seite 55
If two circles touch each other internally , the straight line which joins their centres being produced shall pass through the point of contact . LET the two circles abc , a de touch each other internally in the point a , and let f be ...
If two circles touch each other internally , the straight line which joins their centres being produced shall pass through the point of contact . LET the two circles abc , a de touch each other internally in the point a , and let f be ...
Seite 56
One circle cannot touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle e bf touch the circle abc in more points than one , and first on the inside , in the ...
One circle cannot touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle e bf touch the circle abc in more points than one , and first on the inside , in the ...
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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.