Cabeo (magnetic theory):

His work Philosophia magnetica (1629) was based on work done by William Gilbert a pioneer in understanding magnetism.  Gilbert deduced that the Earth's magnetic field is equivalent to that of a uniformly magnetized sphere but knew that declinations (deviation off true North) were not consistent with this.  He theorized the continents (owing to their topography), formed centres of attraction leading to the deviation.  Cabeo showed if the topography was on the correct scale the tiny differences between the highs & lows would not be enough to affect the deviation.  Cabeo did not accept its motion as the cause of the magnetic field as he (like Aristotle) thought the Earth immobile.  He described electrical attraction in terms of electrical effluvia (vapour), released by rubbing certain materials together.  These bodies pushed into the surrounding air displacing it.  When the air returned it carried light bodies with it making them move towards the attractive material.  This has some affinity with theories developed by Aristotelians to explain why an arrow continues to fly through the air after it has left the bow, namely that an arrow creates a vacuum in its wake, into which air rushes, pushing it from behind.

and see above page 414

 

Michelangelo (late architecture):

(1475-1564) appointed architect of St. Peter's in 1546, an on-going project of 50 years; it was his last great commission.  His impact is seen at the chancel end with its dome.  He reduced the defined geometric forms of Bramante (a square with square projections) & Raphael (a square with semi-circular projections).  The geometry is blurred by giving the external masonry massive proportions & filling in every corner with a small vestry or stairwell.  This creates a continuous wall-surface folded at different angles, lacking right-angles (which define change of direction at the corners).  The exterior is surrounded by giant Corinthian pilasters set at slightly different angles in keeping with the ever-changing angles of the wall's surface.  Above them the huge cornice ripples in a continuous band, keeping the whole building in a state of compression.  The ovoid dome thrusts upwards because of the apparent pressure created by flattening the building's angles & restraining its projections.  The design creates visual tension & compression.  While Michelangelo abandoned the Classicism of the Renaissance, he prefigured the Baroque.

 

Vignola:

see above page 412, Jesuit style (architecture, physics, mathematics)

 

Michelozzo:

(1396-472) Italian architect & sculptor, pupil of Ghiberti, collaborator with Donatello, favoured by the Medici.  Palazzo Medici in Florence (built 1444-1484) was Michelozzo's most well-known project & led to the development of a new architectural type: the Florentine Renaissance palace.  In 1436 he began the complete rebuilding of the ruined monastery of San Marco (completed 1443) in Florence.  His elegant library here became the model for subsequent libraries throughout 15th-century Italy.  In 1444–45 he directed similar reconstruction of the large complex of church buildings at Santissima Annunziata (Florence).  Despite these successes & his Medici patronage he was overshadowed by Donatello in sculpture & Brunelleschi in architecture.   He was one of the most influential, yet unknown, architects of the Early Renaissance.

 

Raphael:

(148-1520 ) Italian artist famous for his painting; in 1514 he was named architect of the new St Peter's & was briefly the most important architect in Rome.  His design used massive piers all the way down the nave, like an alley making the interior darker.  His nave had 5 bays, with complex apsidal chapels off the aisles.  This made the squareness of the exterior walls more defined by reducing the size of the towers, and the semi-circular apses more defined by encircling each with an ambulatory.  None of these alterations survived his death or Michelangelo’s changes.  Pope Julius created several new thoroughfares in Rome & turned to Raphael to fill these streets with palaces.  One of these was the design for the Palazzo Branconio dell'Aquila.  His design included an unusually richly decorated façade using both painted panels on the top story & sculpture on the middle one.  Like his work for St Peters, this was also pulled down & only drawings survive.  He also designed the Villa Madama, one of the most sophisticated villas in Italy, which influenced later developments & was the only modern building in Rome which Palladio made a measured drawing.  However it had to be finished by Antonio da Sangallo the Younger.

 

dynamics:

see above page 412

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Boscovich (I758. theory):

(1711-1787) physicist, astronomer, mathematician, philosopher, diplomat, poet, theologian, Jesuit priest from the Republic of Ragusa, studied, lived & published in Italy & France; he produced a precursor to atomic theory & made several contributions to astronomy (determining a planet’s orbit as well as its equator).  His famous work, Theory of Natural philosophy derived to the single Law of forces which exist in Nature (published in Vienna 1758) contained his atomic theory & theory of forces.  He uses physical terms, like position, velocity, direction & centre of mass.  He correctly suggests that the continuity of force is a necessary assumption for determinism, & he presented it in a strict mathematical form.  He anticipates Laplace’s demon with his image of a super-powerful calculating intelligence, which if it knew the precise location & momentum of every particle in the universe, could calculate the history & future of every particle.

 

Galileo (motion):

(1564-1642) The Discourses and Mathematical Demonstrations Relating to Two New Sciences (published 1638), his final book & scientific testament; written partly in Italian & partly in Latin.  His work was empirical & his theories expressed geometrically.  He questioned Aristotle, most notably that bodies fell at a speed proportional to weight.  Galileo posits that in a vacuum all bodies, large or small, would fall at the same speed through air or water providing they are of the same density.  Shape also matters as even a piece of gold leaf floats through the air & a bladder filled with air falls much more slowly than lead. Galileo also considered the motion of projectiles & air resistance, which he observes affects less dense bodies more & which offers greater resistance to faster bodies. His experiments derived the correct kinematical law for the distance travelled during a uniform acceleration starting from rest which is proportional to the square of the elapsed time. 

 

Leibniz (living force):

Proposed by Leibniz between 1676 &1689, vis viva or "living force" was the first recorded description of kinetic energy in an early formulation of the principle of conservation of energy. Leibniz realized that the total energy would be conserved in certain mechanical systems & considered it an innate motive characteristic of matter.  His mathematical formulation of his observation, mass x velocity squared (mv2) was seen as a rival theory to the conservation of momentum championed by Newton (England & Descartes (France).  Consequently academics in those countries neglected Leibniz's vis viva.   In reality, both energy and momentum are conserved, so the two approaches are equally valid.

 

quantitative number:

numbers used to measure magnitude & multitude, to show a measurable quantity, such as length, mass, temperature & time.

 

functional number:

a binary relation between 2 sets that associates to each element of the first set exactly one element of the second set: each element x of a set X (the domain of the function), to a single element y of another set Y (the codomain of the function).  Originally they expressed how a varying quantity depends on another quantity (e.g. the position of a planet is a function of time).  The concept was elaborated with the infinitesimal calculus late 17th century.  It was formalized late 19th century in terms of set theory which greatly enlarged the domains of application of the concept.

 

Galileo (mass as volume):

Galileo’s experiments were focused on weight of objects & did not include gravity as a force.  He made significant advances in the concept of weight & proposed a way to measure the difference between the weight of a moving object & one at rest.  He concluded weight was proportionate to the amount of matter of an object (not the speed of motion as supposed by Aristotelian Physics).

 

Kepler (mass as volume):

Using Tycho Brahe's observations of Mars, he spent 5 years developing his own method for planetary motion.  He focused on area & distance of the orbit.  Between 1609 & 1619 he published his 3 observations, explaining how the planets orbit the Sun in elliptical orbits (not circular) with the Sun at a focal point of the ellipse.  He discovered the square of the orbital period is directly proportional to the cube of the semi-major axis of its orbit.  Voltaire was the first to refer to Kepler’s observations as “laws.

 

Newton (mass as function):

The bridge between Kepler's gravitational mass & Galileo's gravitational acceleration was discovered by Newton who found the relationship between both observations.  In 1684, Newton sent a paper titled "On the motion of bodies in an orbit" to Halley, who then presented it to the Royal Society of London.  Newton went onto record his ideas in 3 books titled Mathematical Principles of Natural Philosophy (the Principia), which were received by the Royal Society between 1685 & 1687.  Newton’s work showed that mass is a function of weight divided by gravitational force. The force gravity was made manifest in Newton’s universal law of gravitation.

 

Archimedes (form):

(287-212 BC), his 2 books On Floating Bodies (250 BC), in Greek, is a work on hydrostatics, a field established by Archimedes.  His aim was to determine the positions that various solids will assume when floating in a fluid, according to their form & the variation in their specific gravities.  It elaborates his displacement principle which allows the buoyancy of any floating object partially or fully immersed in a fluid to be calculated. The book contains a detailed investigation of the stable equilibrium positions of floating right paraboloids (an idealization of the shapes of ships' hulls) of various shapes & relative densities, when floating in a fluid of greater specific gravity, according to geometric and hydrostatic variations.

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Nonent:

see page 398 above

 

contrapuntal notion:

a musical term referring to the relationship between 2 or more musical lines or voices) which are harmonically interdependent yet independent in rhythm and melodic contour.  In European classical tradition it was found in Medieval music & began developing In the Renaissance, becoming a common practice period, in the Baroque.

 

un-plastic notion:

plastic art forms are capable of receiving form & involve the physical manipulation of a medium by moulding or modelling (e.g. sculpture or ceramics).  Materials used include those that can be carved or shaped (e.g. stone, wood, concrete, glass or metal).  Spengler identifies such art (sculpture) as the prime symbol for the Apollonian Culture.  Non-plastic art would include music or literature; Spengler identifies music as the prime symbol for the Faustian Culture.