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 ページ
レビュー - レビューを書く
ABCD Addenda altitude base bisector bisects centre of similitude chord circum-circle circumf circumference coincide collinear common concurrent concyclic concyclic points corners cross-ratio cyclic quadrilateral diagonals diam diameter divided draw equal angles equiang Euclid external find the Locus fixed circle fixed point given circle given line given point harmonic conjugates inscribed intersection inverse Join Let ABC line is drawn magnitudes meet mid point mid pt Note—The Note—Use opposite sides orthocentre pair parallel parallelogram pedal triangle perpendicular polygon PROBLEM—To produced Prop Proposition Proposition 13 Ptolemy's Theorem quad radical axis radii radius ratio rect rectangle rectilineal figure respectively right angles segments segt Similarly simr Simson's Line square straight line tang tangents Theorem THEOREM—If thro touch triangle ABC variable
255 ページ - 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.
154 ページ - 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.
95 ページ - 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.
86 ページ - 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.
37 ページ - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
44 ページ - 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.
88 ページ - 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.
22 ページ - Any two sides of a triangle are together greater than the third side.