Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books and the First Twenty-one Propositions of the Eleventh Book ...

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T. Stevenson, 1845 - 199 σελίδες
 

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Σελίδα 12 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Σελίδα 143 - 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.
Σελίδα 69 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Σελίδα 20 - 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 the two straight lines BD.
Σελίδα 102 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times
Σελίδα 44 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 71 - The opposite angles of any quadrilateral figure described in a circle, are toe/ether equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD : any two of its opposite angles are together equal to two right angles.
Σελίδα 66 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 83 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

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