On the lecture slate The circle rounded under female hands With flawless demonstration. --TENNYSON. _The Princess, II, l. 493._ =1844.= It is plain that that part of geometry which bears upon strategy does concern us. For in pitching camps, or in occupying positions, or in closing or extending the lines of an army, and in all the other manœuvres of an army whether in battle or on the march, it will make a great difference to a general, whether he is a geometrician or not.--PLATO. _Republic, Bk. 7, p. 526._ =1845.= Then nothing should be more effectually enacted, than that the inhabitants of your fair city should learn geometry. Moreover the science has indirect effects, which are not small. Of what kind are they? he said. There are the military advantages of which you spoke, I said; and in all departments of study, as experience proves, any one who has studied geometry is infinitely quicker of apprehension.--PLATO. _Republic [Jowett], Bk. 7, p. 527._ =1846.= It is doubtful if we have any other subject that does so much to bring to the front the danger of carelessness, of slovenly reasoning, of inaccuracy, and of forgetfulness as this science of geometry, which has been so polished and perfected as the centuries have gone on.--SMITH, D. E. _The Teaching of Geometry (Boston, 1911), p. 12._ =1847.= The culture of the geometric imagination, tending to produce precision in remembrance and invention of visible forms will, therefore, tend directly to increase the appreciation of works of belles-letters.--HILL, THOMAS. _The Uses of Mathesis; Bibliotheca Sacra, Vol. 32, p. 504._ =1848.= Yet may we not entirely overlook The pleasures gathered from the rudiments Of geometric science. Though advanced In these inquiries, with regret I speak, No farther than the threshold, there I found Both elevation and composed delight: With Indian awe and wonder, ignorance pleased With its own struggles, did I meditate On the relations those abstractions bear To Nature’s laws. * * * * *