The first six books of the Elements of Euclid, with numerous exercises |
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Σελίδα 56
THEOREM , 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 a bc in more points than one , and first on the inside ...
THEOREM , 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 a bc in more points than one , and first on the inside ...
Σελίδα 59
From this it is manifest , that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it , touches the circle ; and that it touches it only in one point , because if it did meet the circle in ...
From this it is manifest , that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it , touches the circle ; and that it touches it only in one point , because if it did meet the circle in ...
Σελίδα 60
If a straight line touches a circle , the straight line drawn from the centre to the point of contact shall be perpendicular to the line touching the circle . LET the straight line de touch the circle a b c in the point c ; take the ...
If a straight line touches a circle , the straight line drawn from the centre to the point of contact shall be perpendicular to the line touching the circle . LET the straight line de touch the circle a b c in the point c ; take the ...
Σελίδα 68
If a straight line touches a circle , and from the point of contact a straight line be drawn cutting the circle , the angles made by this line with the line touching the circle shall be equal to the angles which are in the alternate ...
If a straight line touches a circle , and from the point of contact a straight line be drawn cutting the circle , the angles made by this line with the line touching the circle shall be equal to the angles which are in the alternate ...
Σελίδα 69
17 ) the straight line e f touching the circle a b c in the point b , and at the point b , in the straight line bf , make ( i . 23 ) the angle fb c equal to the angle d : therefore , because the straight line ef touches the circle a b c ...
17 ) the straight line e f touching the circle a b c in the point b , and at the point b , in the straight line bf , make ( i . 23 ) the angle fb c equal to the angle d : therefore , because the straight line ef touches the circle a b c ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
abcd angle a b c angle bac applied base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given rectilineal given straight line greater half ILLUSTRATED inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 4 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 13 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 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...
Σελίδα 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.