The Elements of Euclid: The errors, by which Theon, or others, have long ago vitiated these books, are corrected and some of Euclid's demonstrations are restored. Also, to this second edition is added the book of Euclid's Data. In like manner corrected
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AC is equal adjacent angles angle ABC angle ACB angle BAC base BC BC is given bisected Book circle ABCD circumserence cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid faid fame altitude fame manner fame multiple fame plane fame ratio fame reason fame straight line fides fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon join less Let ABC parallel parallelogram perpendicular plane angles polygon prisms proportionals Proposition pyramid Q^E. D. PROP ratio of AE rectangle contained rectilineal figure right angles segment shewn sides similar sirst solid angle solid parallelepiped square of AC straight line BC THEOR third tiple triangle ABC vertex wherefore
Page 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 48 - 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 in the point C; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square of AC.
Page 73 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn from the extremity between that straight line and the circumference, so as not to cut the circle...
Page 105 - 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. either the sides adjacent to the equal...
Page xv - 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.
Page 167 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Page 54 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 47 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.