Euclidean geometry:

see Introduction page 42

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Archimedes:

(287-212 BC) Greek mathematician, physicist, engineer, inventor& astronomer; a leading scientists & greatest mathematician of the Classical world; anticipated modern calculus & analysis by applying concepts of infinitesimals & method of exhaustion to derive & rigorously prove many geometrical theorems (area of a circle, surface area & volume of a sphere, area under a parabola); first to apply mathematics to physical phenomenon, founding hydrostatics, statics & explaining the lever.

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Gauss:

(1777-1855) German mathematician, contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, geodesy, geophysics, mechanics, electrostatics, magnetic fields, astronomy, matrix theory, and optics.  Gauss ranked as one of history's most influential mathematicians.

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Infinitesimal Calculus:

archaic for Calculus (both differential  & integral calculus); branches of mathematical analysis connected with the concept of an infinitely small function.  The method of "infinitely smalls" was employed by the scientists of Greece & Europe in the Middle Ages to solve problems in geometry & natural science, but only exactly defined in the 19th century.

 

sum of human knowledge:

Kant posits that all knowledge is either a priori (valid from necessity, e.g. 1 + 1 = 2) or a posteriori (validated by experience); Kant also argues that this knowledge is unalterable and universal for all humanity; universal validity is a 17th Century Enlightenment idea.