Euclid Revised: Containing the Essentials of the Elements of Plane Geometry as Given by Euclid in His First Six Books, with Numerous Additional Propositions and Exercises
Clarendon Press, 1890 - 400 σελίδες
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ABCD Addenda altitude angle axis base bisector bisects Book called centre chord circumference coincide collinear common concurrent constant construction contained conversely corners corresponding cyclic describe diagonals diameter difference distance divided draw drawn equal Euclid Exercise external extremities figure fixed circle fixed point four given given line greater harmonic inscribed internal intersection inverse Join length Let ABC Locus magnitudes maximum mean meet mid point Note opposite sides pair parallel parallelogram perpendicular placed polar position produced Prop proportional Proposition prove quadrilateral radius ratio rect rectangle rectilineal respectively right angles segments similar Similarly simr square straight line taken tangents THEOREM third touch triangle triangle ABC true variable
Σελίδα 251 - 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 150 - If a straight line touch a circle, and from the point of contact a chord be drawn, the angles which this chord makes with the tangent are equal to the angles in the alternate segments.
Σελίδα 91 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.
Σελίδα 82 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Σελίδα 37 - 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 44 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 84 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Σελίδα 22 - Any two sides of a triangle are together greater than the third side.