The pure geometry of position is mainly distinguished, according to Professor Reye's definition,[56] from the geometry of ancient times and from analytical geometry, in that it makes no use of the idea of measurement. Nothing is said in it "about the bisection of segments of straight lines, about right angles and perpendiculars, about ratios and proportions, about the computation of areas, and just as little about trigonometric ratios and the algebraic equations of curved lines, since all these subjects of the older geometry assume measurement.... We shall be concerned as little with isosceles and equilateral triangles as with right-angled triangles; the rectangle, the regular polygon, and the circle are likewise excluded from our investigations, except in the case of these applications to metric geometry. We shall treat of the center, the axes, and the foci of so-called curves of the second order, or conic sections, only as incidental to the general theory; but, on the other hand, shall become acquainted with many properties of these curves, more general and more important than those to which most text-books upon analytical geometry are restricted." Of all the other branches of geometry, the descriptive is the most helpful in facilitating the study of the geometry of position; and perspective or central projection plays an important part in it. It stands in a certain antithetical relation to analytical geometry on account of its method, which is synthetic, and whence it is sometimes known as synthetic geometry. Since metric relations are not considered in it, its theorems and problems are very general and comprehensive. As presented in von Standt's complete work, it is regarded by the author as an excellent aid to the exercise and development of the imagination; and the important graphical methods with which Professor Culmann has enriched the science of engineering in his work on graphical statistics, being based for the most part upon it, a knowledge of it has become important for students of that science. In the present work, the outgrowth of his lectures, Professor Reye has attempted to supply the want of a text-book which shall offer to the student the necessary material in a concise form.