The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected
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ABCD base bisected bisectors called centre chord circumference circumscribed common Constr construct DEFINITION describe Describe a circle diagonals diameter difference divided draw drawn equal equilateral EXERCISES external extremities figure find the locus fixed formed four given circle given point given straight line greater half Hence inscribed intersect Join length less Let ABC magnitude meet middle point NOTE opposite sides parallel parallelogram pass perp plane point of contact polygon PROBLEM produced proof proportional PROPOSITION prove quadrilateral radius ratio rect rectangle contained regular remaining respectively right angles segment shew shewn sides similar Similarly square straight line drawn tangent THEOREM third touch triangle ABC twice vertex vertical angle whole
Page 333 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 45 - 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.
Page 142 - In every triangle, the square on the side subtending an acute angle, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall on it from the opposite angle, and the acute angle.
Page 148 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Page 377 - 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 308 - From this it is manifest, that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the...
Page 3 - 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 73 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Page 7 - Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.