The first six books of the Elements of Euclid, with numerous exercises |
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Seite 2
A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter .
A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter .
Seite 47
I. EQUAL circles are those of which the diameters are equal , or from the centres of which the straight lines to the circumferences are equal . This is not a definition , but a theorem , the truth of which is evident ; for , if the ...
I. EQUAL circles are those of which the diameters are equal , or from the centres of which the straight lines to the circumferences are equal . This is not a definition , but a theorem , the truth of which is evident ; for , if the ...
Seite 48
The angle of a segment is that which is contained by the straight line and the circumference . VIII . An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the ...
The angle of a segment is that which is contained by the straight line and the circumference . VIII . An angle in a segment is the angle contained by two straight lines drawn from any point in the circumference of the segment to the ...
Seite 49
If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . LET abc be a circle , and a , b any two points in the circumference ; the straight line drawn from a to b ...
If any two points be taken in the circumference of a circle , the straight line which joins them shall fall within the circle . LET abc be a circle , and a , b any two points in the circumference ; the straight line drawn from a to b ...
Seite 51
If any point be taken in the diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is ...
If any point be taken in the diameter of a circle which is not the centre , of all the straight lines which can be drawn from it to the circumference , the greatest is that in which the centre is , and the other part of that diameter is ...
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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.