
The Ethic of Freethought (Mar 6, 1883)
Source: Mathematical Thought from Ancient to Modern Times (1972), p. 175
The Ethic of Freethought (Mar 6, 1883)
On the genesis of two of his historical and autobiographical works.
The Education of Henry Adams (1907)
Context: Any schoolboy could see that man as a force must be measured by motion, from a fixed point. Psychology helped here by suggesting a unit — the point of history when man held the highest idea of himself as a unit in a unified universe. Eight or ten years of study had led Adams to think he might use the century 1150-1250, expressed in Amiens Cathedral and the Works of Thomas Aquinas, as the unit from which he might measure motion down to his own time, without assuming anything as true or untrue, except relation. The movement might be studied at once in philosophy and mechanics. Setting himself to the task, he began a volume which he mentally knew as "Mont-Saint-Michel and Chartres: a Study of Thirteenth-Century Unity." From that point he proposed to fix a position for himself, which he could label: "The Education of Henry Adams: a Study of Twentieth-Century Multiplicity." With the help of these two points of relation, he hoped to project his lines forward and backward indefinitely, subject to correction from any one who should know better. Thereupon, he sailed for home.
Source: Mathematical Thought from Ancient to Modern Times (1972), p. 57
Context: The Greeks failed to comprehend the infinitely large, the infinitely small, and infinite processes. They "shrank before the silence of the infinite spaces."
Introduction
Higher Mathematics for Chemical Students (1911)
Vol. I, Ch. 10, as translated by R. B. Haldane
The World as Will and Representation (1819; 1844; 1859)
Context: Correct and accurate conclusions may be arrived at if we carefully observe the relation of the spheres of concepts, and only conclude that one sphere is contained in a third sphere, when we have clearly seen that this first sphere is contained in a second, which in its turn is contained in the third. On the other hand, the art of sophistry lies in casting only a superficial glance at the relations of the spheres of the concepts, and then manipulating these relations to suit our purposes, generally in the following way: — When the sphere of an observed concept lies partly within that of another concept, and partly within a third altogether different sphere, we treat it as if it lay entirely within the one or the other, as may suit our purpose.
Hartshorne (1958) "The concept of geography as a science of space, from Kant and Humboldt to Hettner" in: Annals of the Association of American Geographers Vol 48 (2). p. 97
Dictionary of National Biography, art. "William Shakespeare"
“Parallel lines have a common end point at an infinite distance.”
Brouillion project (1639) as quoted by Harold Scott MacDonald Coxeter, Projective Geometry (1987)
Source: Why We Fail as Christians (1919), p. 19