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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson with ...
No preview available - 2014
ABCD Algebraically angle A CB angle ABC angle BA angle equal Apply Euc axiom base BC chord circle ABC constr demonstrated describe a circle diagonals diameter divided double draw equal angles equiangular equilateral triangle equimultiples Euclid Euclid's Elements exterior angle Geometrical given circle given line given point given straight line given triangle gnomon hypotenuse inscribed intersection isosceles triangle less Let ABC lines be drawn meet the circumference multiple opposite angles opposite sides parallelogram pentagon perpendicular Porisms problem produced Prop proportionals proved Q.E.D. PROPOSITION quadrilateral quadrilateral figure radius rectangle contained rectilineal figure remaining angle right angles right-angled triangle segment semicircle shew shewn similar similar triangles square on AC squares on AB tangent THEOREM touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle wherefore
Page 54 - If two triangles have two sides of the one equal to two sides of the...
Page 38 - Let ABCD be the given rectilineal figure, and E the given rectilineal angle. It is required to describe a parallelogram equal to ABCD, and having an angle equal to E.
Page 144 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Page 18 - Any two angles of a triangle are together less than two right angles.
Page 266 - 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.
Page 152 - 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.
Page 7 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line; it is required to draw from the point A a straight line equal to BC.
Page 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Page 96 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side...