=1805.= Form and size constitute the foundation of all search for truth.--PARKER, F. W. _Talks on Pedagogics (New York, 1894), p. 72._ =1806.= At present the science [of geometry] is in flat contradiction to the language which geometricians use, as will hardly be denied by those who have any acquaintance with the study: for they speak of finding the side of a square, and applying and adding, and so on, as if they were engaged in some business, and as if all their propositions had a practical end in view: whereas in reality the science is pursued wholly for the sake of knowledge. Certainly, he said. Then must not a further admission be made? What admission? The admission that this knowledge at which geometry aims is of the eternal, and not of the perishing and transient. That may be easily allowed. Geometry, no doubt, is the knowledge of what eternally exists. Then, my noble friend, geometry will draw the soul towards truth, and create the mind of philosophy, and raise up that which is now unhappily allowed to fall down.--PLATO. _Republic [Jowett-Davies], Bk. 7, p. 527._ =1807.= Among them [the Greeks] geometry was held in highest honor: nothing was more glorious than mathematics. But we have limited the usefulness of this art to measuring and calculating. --CICERO. _Tusculanae Disputationes, 1, 2, 5._ =1808.= Geometria, Through which a man hath the sleight Of length, and brede, of depth, of height. --GOWER, JOHN. _Confessio Amantis, Bk. 7._ =1809.= Geometrical truths are in a way asymptotes to physical truths, that is to say, the latter approach the former indefinitely near without ever reaching them exactly.--D’ALEMBERT. _Quoted in Rebière: Mathématiques et Mathématiciens (Paris, 1898), p. 10._ =1810.= Geometry exhibits the most perfect example of logical stratagem.--BUCKLE, H. T. _History of Civilization in England (New York, 1891), Vol. 2, p. 342._ =1811.= It is the glory of geometry that from so few principles, fetched from without, it is able to accomplish so much.--NEWTON. _Philosophiae Naturalis Principia Mathematica, Praefat._ =1812.= Geometry is the application of strict logic to those properties of space and figure which are self-evident, and which therefore cannot be disputed. But the rigor of this science is carried one step further; for no property, however evident it may be, is allowed to pass without demonstration, if that can be given. The question is therefore to demonstrate all geometrical truths with the smallest possible number of assumptions.