Faust II:

tragedy by Goethe (1832), the 2nd part of his earlier work Faust; owing to its complexity in form and content, it is not as was well known as Faust I.

 

“mothers”:

characters in Faust Part 2: Act I (A Dark Gallery); Faust & Mephisto talk, the Emperor asks Faust to invoke the spirits of Paris & Helen of Troy; Faust needs Mephisto for this but he cannot help & suggests Faust visit the "Eternal Mothers," mysterious spirits, living in a grotto deep in the earth.  They are cosmic forces symbolizing the mystical essence of life, existing before man & making his creation possible; source of all form & being; they are feminine spirits, creative & generative force of the universe allowing man & Nature to exist, reflected in all human & natural phenomena.

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Leibnitz: 

see Introduction page 42

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the Calculus (Leibnitz): * see Endnote 35

mathematical discipline focused on limits, functions, derivatives, integrals & infinite series;  discovered by Newton & Leibniz independently mid-17th century.  Leibniz saw the tangent as a ratio but declared it as the ratio between ordinates & abscissas.  He stated that the integral was the sum of the ordinates for infinitesimal intervals in the abscissa, the sum of an infinite number of rectangles. 

 

analysis situ (Leibnitz):

(archaic name for topology) developed as a field of study out of geometry & set theory, through analysis of concepts such as space, dimension, and transformation; these ideas go back to Gottfried Leibniz, who in the 17th century envisioned the geometria situs (Greek-Latin for "geometry of place") and analysis situs (Greek-Latin for "picking apart of place").

 

Ausdehnungslehre (Grassman):

The Theory of Linear Extension, a New Branch of Mathematics  (aka A1)- 1844 by Grassman (1809-1877); German polymath, mathematician; undistinguished student until university in 1827; studied Humanities though interested in maths; in 1831 (while preparing to sit exam to teach maths) wrote essay referencing linear algebra & notion of a vector space, the first known reference.  Later he showed that geometry, as expressed in his algebraic form, was not limited to 3 spatial dimensions, but was  unbounded.

 

Leibniz (and the divine principle):

Leibniz held a profound believe in God; his principle- sufficient reason-stated there is adequate reason to account for existence & nature of everything, in all cases the ultimate sufficient reason is the free choice of God; planetary motion depended on the action of a spirit (God).  In On the Ultimate Origin of Things he developed a cosmological argument for God, proving ultimate origin must be God.  In Theodicy justified imperfections of the world claiming that it is the optimal among all possible worlds, as an all-powerful knowing God, would not to create an imperfect world.