The Continuum from Euclid to Pythagoras to Newton, and including the theocratic contention with Galileo in particular, and also in consideration of Copernicus and others, is evident. From origin point to the 360degree circle divided into 90degree quadrants, which serve as the origin of Pythagorean mathematics, variabilities lead to understandings from dead reckoning to square rule carpentry and even onwards to Newtonian scholiums regarding elipses and orbits of heavenly bodies within the heavens… a series of topics which makes both progression towards and a return through time to Galileo, and his inquisition regarding the diurnality of the heavens, pertinent.

Euclidean, Pythagorean or Newtonian?


From a dead reckoning origin point within the compasses’ 360degrees and relative to the known fixes upon the cardinal directions North, South, East and West, proximal aspects are discerned by eastern sunrise and western sunset and relativities of all directions and including the north star (inclinated according to one’s latitude). Euclidian and Pythagorean mathematics specify a perimeter of sets around, and trigonometric valuations pertaining to, the quadrants. From there, Newtonian ellipses and functions of calculus spin inward and outward (In mathematic’s historical trajectory) as functions relative to the origin and sets upon the euclidian perimeter. Calculus one is initially taught in what equates to the northeastern quadrant where both the ordinal and abscissal (x,y,) values are positive. Also, elevations and declinations from this plane as with a simple transit yield altitudinal and depth related imagery and coordinates to geographic information systems perspectives and descriptive mathematics.

Transit, Armillary, Sextant
Hamlet and the Ghost
Instrumentation for Measure and Proximal Assessment

Pythagorean Square Rule Trigonometric Carpentry