Euclid's Book on Divisions of Figures: ... with a Restoration Based on Woepcke's Text and on the Practica Geometriae of Leonardo Pisano |
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Common terms and phrases
angle Arabian Archimedes auxiliary propositions Baldassarre Boncompagni book On Divisions Books of Euclid's British Museum CANTOR catalogue circle Commandinus construction Cottonian Library discussion divide a given divide the triangle divides the quadrilateral divisionibus Divisions of Figures Draw the line edition enunciations Euclid's book Euclid's Elements Favaro Federico Commandino Figuren fraction Géométrie Geschichte given point situated given quadrilateral given ratio given trapezium given triangle Heath Heiberg Heron Heron of Alexandria J. L. Heiberg John Dee Join Kästner Leipzig Leonardo Pisano Let abcd line parallel London Machomet Math Mathematik Muhammed Bagdedinus Ofterdinger one-third Pappus parallel sides parallel to bg parallelogram Paris Porisms Practica Geometriae problem Proclus proof Prop Proposition 19 quadl quadri quadrilateral ac rectangle reference Similarly solution square Steinschneider straight line drawn Suter Tartaglia three equal translation treatise triangle abg vertex Vorlesungen Woepcke Woepcke's
Popular passages
Page 31 - The area of a triangle is equal to one-half the product of its base and altitude.
Page 62 - If a straight line be bisected, and a straight line be added to it in a straight line, the square on the whole with the added straight line...
Page 50 - TO a given straight line to apply a parallelogram equal to a given rectilineal figure...
Page 18 - 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 52 - Bisect AB in D, and if the square upon AD be equal to the square upon C, the thing required is done : But if it be not equal to it, AD must be greater than C, according to the determination : Draw DE at right angles to AB, and make it equal to C : produce ED to F...
Page 10 - Moreover the treatise is no fragment, but finishes with the words " end of the treatise," and is a well-ordered and compact whole. Hence we may safely conclude that Woepcke's is not only Euclid's own work but the whole of it. A restoration of the work, with proofs, was attempted by Ofterdinger3, who however does not give Woepcke's props.
Page 2 - Marinus his Preface. Also a Treatise of the Divisions of Superfices, ascribed to Machomet Bagdedine, but published by Commandine, at the Request of John Dee, of London. Published by the Care and Industry of John Leeke and George Serle, Students in the Mathematics.
Page 26 - A'M to A'M. Proposition 3. (Problem.) To cut a given sphere by a plane so that the surfaces of the segments may have to one another a given ratio. Suppose the problem solved. Let AA' be a diameter of a great circle of the sphere, and suppose that a plane perpendicular to A A...
Page 50 - The marvellous ingenuity of the solution is indeed worthy of the " godlike men of old," as Proclus calls the discoverers of the method of "application of areas"; and there would seem to be no reason to doubt that the particular solution, like the whole theory, was Pythagorean, and not a new solution due to Euclid himself.
Page 52 - To apply a rectangle, which shall be equal to a given square, to a given straight line, deficient by a square : but the given square must not be greater than that upon the half of the given line. Let AB be the given straight line, and let the square upon the given straight line C, be that to which the rectangle to be applied must be equal, and this square by the determination is not greater than that upon half of the straight line AB.