History And Transcendence: This demonstration is equivalent to proving that the Euclidean problem of the quadrature of the circle is impossible, and closes in this generation a question that has occupied mathematicians for 4,000 years. The long and difficult proofs of Hermite and Lindemann have been much simplified, first by Weierstrass (Berliner Berichte, 1885), and in particular by Hil-bert, Hurwitz and Gordon (Mathematische Annalen, Vol. XLIII). The questions involved treated without requiring a knowledge of the calculus have become familiar to English mathematicians through the translation by Beman and Smith of Klein's 'Famous Problems of Elementary Geometry' (1897). Consult also the chapter on 'The History and Transcendence ol i", in 'Monographs on Topics in Modern Mathematics' (New York 1911), by D. E. Smith. J. BRACE CHITTENDEN, PH.D.
The seeking of God or spiritual transcendence is hardly something that we could expect pupils to engage in on their own (or even necessarily in company) and those who do engage in this task generally do so from an exalted level of spiritual awareness, within a sophisticated spiritual frame of reference and commitment. Thus the exploration of the spiritual might be seen to necessarily involve consideration of the social dimension. Spirituality says something about human relationships and it is unlikely that we will identify the spiritual outside the context of moral development.
His History of Ionian Philosophy(1821) ; History of the Pythagorean Philosophy (1826), and Notes on the Philosophy of the Megarean School in the Rheinisches Museum, are models of historical investigation on the principles of Schleiermacher. His historical masterpiece is the History of Philosophy (1829-53), which deals with general history up to the time of Kant. It was supplemented by a Review of the History of German Philosophy from the Time of Kant (1853).
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