=1866.= We must, then, admit ... that there is an independent science of geometry just as there is an independent science of physics, and that either of these may be treated by mathematical methods. Thus geometry becomes the simplest of the natural sciences, and its axioms are of the nature of physical laws, to be tested by experience and to be regarded as true only within the limits of error of observation--BÔCHER, MAXIME. _Bulletin American Mathematical Society, Vol. 2 (1904), p. 124._ =1867.= Geometry is not an experimental science; experience forms merely the occasion for our reflecting upon the geometrical ideas which pre-exist in us. But the occasion is necessary, if it did not exist we should not reflect, and if our experiences were different, doubtless our reflections would also be different. Space is not a form of sensibility; it is an instrument which serves us not to represent things to ourselves, but to reason upon things.--POINCARÉ, H. _On the Foundations of Geometry; Monist, Vol. 9 (1898-1899), p. 41._ =1868.= It has been said that geometry is an instrument. The comparison may be admitted, provided it is granted at the same time that this instrument, like Proteus in the fable, ought constantly to change its form.--ARAGO. _Oeuvres, t. 2 (1854), p. 694._ =1869.= It is essential that the treatment [of geometry] should be rid of everything superfluous, for the superfluous is an obstacle to the acquisition of knowledge; it should select everything that embraces the subject and brings it to a focus, for this is of the highest service to science; it must have great regard both to clearness and to conciseness, for their opposites trouble our understanding; it must aim to generalize its theorems, for the division of knowledge into small elements renders it difficult of comprehension.--PROCLUS. _Quoted in D. E. Smith: The Teaching of Geometry (Boston, 1911), p. 71._