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The Elements of Plane Geometry ...
Association for the improvement of geometrical teaching
Uten tilgangsbegrensning - 1884
ABCD according alternate altitude angle ABC angle ACB angle BAC arc HK base bisects called centre chord circle whose centre circumference circumscribed coincide common construction Conversely corresponding described diagonal diameter difference distance divided draw drawn equal equal circles externally extremities fall figure four given circle given point given straight line greater half Hence identically equal inscribed internally intersect joining kind less lies line joining locus magnitudes manner meet middle point minor arc multiple opposite sides parallel parallelogram passes perpendicular polygon Prob produced proportional Prove quadrilateral radii radius ratio rectangle contained rectilineal figure regular respectively right angles segment Shew side side BC similar square stands straight line drawn taken tangent THEOR Theorem third triangle ABC whole Нур
Side 41 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 182 - 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.
Side 67 - 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.
Side 167 - 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.
Side 32 - Any two sides of a triangle are together greater than the third side.
Side 34 - Of all the straight lines that can be drawn to a given straight line from a given point outside it, the perpendicular is the shortest.
Side 23 - The lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal.
Side 63 - If there are three or more parallel straight lines, and the intercepts made by them on any straight line that cuts them are equal, then the corresponding intercepts on any other straight line that cuts them are also equal.
Side 39 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Side 106 - 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.