Stahl:

(1659-1734) German chemist, physician & philosopher, supporter of vitalism, his work on phlogiston were accepted for many decades.  Although he did not support the views of iatro-mechanists, he believed that all non-living creatures were mechanical as were living things (to a certain degree); non-living things did not rapidly change over time whereas living things are subject to change & decomposition; this led to his work with fermentation.  He believed that chemistry could not be reduced to mechanistic views; he accepted atoms but did not believe they alone could describe the chemical processes.  Atoms could not be isolated individually & that they join together to form elements. He took an empirical approach when establishing his descriptions of chemistry.

 

Phlogiston theory:

superseded scientific theory that postulated the existence of a fire-like element (phlogiston), found in combustible bodies & released during combustion; first proposed in 1667 by JJ Becher & addressed formally by Georg Ernst Stahl; attempted to explain processes such as combustion & rusting (oxidation); abandoned late 18th century following experiments by Lavoisier & others; these experiments ultimately led to the discovery of oxygen.

 

Paracelsus: * see EndNote<A>

(1493-1541) Swiss physician, alchemist, lay theologian & philosopher of the German Renaissance; pioneer in the "medical revolution" of the Renaissance, emphasizing the value of observation in combination with received wisdom.  Considered the "father of toxicology".  He also had a substantial impact as a diviner, his "Prognostications" being studied by Rosicrucians in the 1600s. 

 

Robert Boyle: * see EndNote<B>

(1627-1691) Anglo-Irish natural philosopher, chemist, physicist & inventor, founder of modern experimental scientific method.  He is best known for Boyle's law, describing the inversely proportional relationship between the absolute pressure and volume of a gas, if the temperature is kept constant within a closed system.  Among his works, The Sceptical Chymist is seen as a cornerstone book in the field of chemistry.  A devout and pious Anglican, noted for his writings in theology.

 

the Element:

In chemistry, a pure substance which cannot be broken down by chemical means or transformed into other chemical elements by chemical processes.  They were until 1913 identified by their atomic weight.  In 1661, Robert Boyle proposed his theory of corpuscularism which favoured the analysis of matter as constituted by irreducible units of matter (atoms), favouring neither Empedocles or Paracelsus.  The first modern list of chemical elements was given in Lavoisier's 1789 Elements of Chemistry, which listed 33 including light and caloric.  By 1818, Jöns Jakob Berzelius had determined atomic weights for 45 of the 49 elements. By 1869 Dmitri Mendeleev had expanded this to 66.

 

Lavoisier:

(1743-1794) French nobleman & chemist, actor in the 18th-century chemical revolution, also impacted biology.  His accomplishments in chemistry occurred when he moved it from a qualitative study to a quantitative one.  Most noted for his discovery of the role oxygen plays in combustion. He recognized & named oxygen (1778) and hydrogen (1783), and opposed the phlogiston theory.  He helped construct the metric system, wrote the first extensive list of elements, and helped to reform chemical nomenclature.  He predicted the existence of silicon (1787) & discovered that, although matter may change its form or shape, its mass always remains the same.  A powerful member of several aristocratic councils & administrator of the hated Ferme générale (whose profits funded his scientific research).  During the French Revolution he was guillotined.

 

elements of Empedocles: * see EndNote<C>

see above page 383

 

elements of Lavoisier: * see Endnote<C>

In 1789 Lavoisier published his Elementary Treatise on Chemistry, the first modern chemical textbook.  It defines an element as a single substance that can't be broken down by chemical analysis and from which all chemical compounds are formed.  The book contains 33 elements (of which 23 are considered modern elements).  The book also contains Lavoisier’s law of conservation of mass (Lavoisier's Law): "Nothing is lost, nothing is created, everything is transformed."

 

Lavoisier (his combustion theory):

His studies in combustion were his most significant contribution to science. In late 1772 he began tests & reported results of his first experiments to the Academy in October, stating that when phosphorus burned, it combined with a large quantity of air to produce acid spirit of phosphorus, the phosphorus increased in weight on burning.  Later he extended his observations & conclusions to the burning of sulfur and went on to add that "what is observed in the combustion of sulfur and phosphorus may well take place in the case of all substances that gain in weight by combustion and calcination: and I am persuaded that the increase in weight of metallic calces is due to the same cause."

 

isolation of oxygen (1771):

it is commonly believed oxygen was discovered by the Swedish pharmacist Carl Wilhelm Scheele who produced oxygen gas by heating mercuric oxide (HgO) & various nitrates in 1771–2.  He called the gas "fire air" as it was then the only known agent to support combustion.  He wrote an account of this discovery in a manuscript titled Treatise on Air and Fire, published in 1777.

 

[Many historians credit Michael Sendivogius with the discovery of oxygen.  Between 1598 and 1604 he performed various experiments & published his results in his De Lapide Philosophorum Tractatus duodecim e naturae fonte et manuali experientia depromti (1604); he described a substance contained in air, referring to it as 'cibus vitae' (food of life).]

 

 

Statics: * see EndNote<D>

fundamental examination of the effects of forces upon objects (primary discipline in Engineering Mechanics), explores the behaviour of bodies that are at rest or move at a constant velocity, an analysis of loads acting on physical systems that do not experience acceleration but rather are in static equilibrium with their environment.  Archimedes (287–212 BC) pioneered work in statics.

Spengler is asserting here that Statics is Apollonian physics, with characteristics specific to their Culture.

 

Chemistry: * see EndNote<D>

Spengler is actually referring to Alchemy, precursor to Faustian Chemistry, that Chemistry, or Alchemy, is Magian physics, with characteristics specific to their Culture.  Alchemy comes from an Arabic word; the Islamic world was a melting pot for alchemy, Platonic & Aristotelian thought was assimilated during the late 7th & early 8th centuries through Syriac translations & scholarship.  In the late 8th century, Jābir ibn Hayyān (died 816 AD) or "Geber", initiated approaches based on scientific methodology & experimentation in the lab; his clear description of the processes, alchemical apparati & methodical classification of the substances mark an experimental spirit far removed from the Greeks.  Early Islamic chemists contributed key chemical discoveries, such as the muriatic (hydrochloric acid), sulfuric & nitric acids, the discovery that aqua regia (nitric mixed with hydrochloric acids) could dissolve gold; they contributed to hermeticism, in particular Geber, whose goal was the artificial creation of life (including, human life).  His elemental system consisted of 7 elements (5 classical elements (aether, air, earth, fire, water) plus 2 chemical elements sulphur & mercury.

 

Dynamics: * see EndNote<D>

branch of physics developed in classical mechanics concerned with the study of forces & their effects on motion; it look at how a physical system might develop or alter over time, & studies the causes of those changes.  Newton first established the fundamental physical laws which govern dynamics in (non-relativistic) physics.  Dynamics is closely related to his 2nd law of motion, though all 3 of Newton’s laws of motion must be considered as all are interrelated in any given observation.  Dynamics falls under 2 categories: linear and rotational.  Linear pertains to objects moving in a line & involves concepts such as: force, mass/inertia, displacement, velocity, acceleration & momentum.. Rotational dynamics pertains to objects rotating or moving in a curved path, & involves concepts such as torque, moment of inertia/rotational inertia, angular displacement, angular velocity, angular acceleration & angular momentum.  Objects often exhibit both linear & rotational motion.  Spengler is asserting here that dynamics is Faustian physics, with characteristics specific to their Culture.

 

Euclidean geometry: * see EndNote<E>

branch of mathematics that studies the shapes, positions  & dimensions of 2D (plane geometry-squares, circles & triangles) & 3D (cubes, cones & spheres) objects; Euclid (an Alexandrian Greek) formalized this study in his textbook Elements (300 BC), which provided the axiomatic system & gave examples of formal proof; his work however was a compilation of propositions based on books by earlier Greek mathematicians, notably Eudoxus, Theaetetus, Hippocrates of Chios & Pythagoras

 

Algebra: * see EndNote<E>

from the Arabic al-jabr, study of mathematical symbols & the rules for manipulating these symbols; includes everything from elementary equation solving to the study of abstractions such as groups, rings & fields.  Algebra uses abstractions, such as letters (e.g. X) to stand for numbers that are either unknown or allowed to take on many values.  Such symbols include unknowns, constants, and variables.  It provides methods for writing formulas & solving equations that are clearer & easier than text

​

Higher Analysis: * see EndNote<E>

branch of mathematics dealing with limits & related theories (eg differentiation, integration, measure, infinite series, analytic functions) usually studied in the context of real & complex numbers and functions; evolved from calculus, which involves the elementary concepts & techniques of analysis; can be applied to any space of mathematical objects having a topological space) or a metric space.

 

art of the statue: * see EndNote<F> 

Apollonian sculpture was notable for its development of naturalistic but idealized depictions of the human body, nude male figures generally the focus of innovation; stylistic development between about 750 & 300 BC was remarkable, moving from frontal, flat figures culminating in fully 3D sculpture

 

art of the arabesque: * see EndNote<F>

surface decorations based on rhythmic linear patterns of scrolling and interlacing foliage, tendrils" or plain lines, often combined with other elements, typically using leaves, derived from stylised half-palmettes, were combined with spiralling stems, consisting of a single design 'tiled' or seamlessly repeated as many times as desired; Islamic art promoted non-figurative work & arabesque was prominent in its art, in particular the decoration of architecture; although a fundamental element of Islamic art, arabesque was already a long tradition before Islam.

 

art of the fugue; * see EndNote<F >

​systematic imitation of a principal theme (the subject) in simultaneously sounding melodic lines (counterpoint).  With its mathematical intricacy, formality, symmetry & variety, it was a focus of interest for Faustian composers.

​

motion: * see EndNote<G>

each of the 3 Cultures defines & perceives motion in its own peculiar way