Cauchy:

(1789 -1857) French mathematician & physicist, pioneered analysis; one of the first to state & prove theorems of calculus rigorously, rejecting the heuristic principle of the generality of algebra of earlier authors; he founded complex analysis & the study of permutation groups in abstract algebra.  He had great influence over his contemporaries & successors; famous for development of complex function theory (first pivotal theorem proved by him, known as Cauchy's integral theorem).

Gothic wall statuary of German cathedrals: * see Endnote 45

originated in the Saxon sculptures who carved the 13th century figures for Magdeburg, Bamberg & Naumburg cathedrals.  They show signs typical of Germanic Romanesque art; the persistence of this style delayed full adoption of Gothic art in the Germanic regions of the Holy Roman Empire.  The new Gothic style came up against a strong local tradition & older traditions (Byzantine). In only a few exceptional cases were facades receptive to the great sculptured programs.

​

Gothic condition:

relating to a Cultural Springtime, before full maturity, prior to the highest creative genius of a Culture

​

Dipylon pottery: * see Endnote 46

amphora (750 BC) large painted vase, grave marker at the Dipylon cemetery, Athens by  the Dipylon Master; the outer surface bears horizontal bands of painted decoration in the Late Geometric style, single, double & triple meanders; the tall cylindrical neck includes friezes of repeated stylised deer & goats; a panel on one side depicts the lying in of a draped dead woman on a bier, with a checkered shroud above the body, stylised figures of male & female mourners to either side.

​

Baghdad 9th & 10th centuries intellects:

center of the Arab caliphate during the Golden Age of Islam; largest city worldwide early 10th century. Science, economic development & culture flourished.  Inaugurated by Abbasid caliph Harun al-Rashid (786 to 809) with creation of the House of Wisdom (in Baghdad); scholars from across the world with different cultural backgrounds brought together to translate the world's classical knowledge into Arabic.  Khwārizmī plays major role in the developing algebra, algorithms & Hindu-Arabic numerals.