Search results

integer, and integer solutions are sought for x and y. In Cartesian coordinates, the equation is represented by a hyperbola; solutions occur wherever the...

Plotinus, the second emanation represents an uncreated second cause (see Pythagoras' Dyad). Plotinus sought to reconcile Aristotle's energeia with Plato's...

musica universalis or "music of the spheres", which had been studied by Pythagoras, Ptolemy and others before Kepler; in fact, soon after publishing Harmonice...

integer solutions. (i.e., Diophantine equations for which there are no integer solutions, since, given a Diophantine equation with at least one solution, the...

Books. ISBN 1-57863-203-X. Dudley, Underwood (1997). Numerology, Or, What Pythagoras Wrought. Cambridge University Press. ISBN 0-88385-524-0. DuQuette, Lon...

used to describe the order in nature. This was noted and advocated by Pythagoras, Plato, Galileo, and Newton. Some theorists, like Hilary Putnam and Penelope...

has been defended by C.J. de Vogel, Pythagoras and Early Pythagoreanism (1966), pp. 97–102, and C. Riedweg, Pythagoras: His Life, Teaching, And Influence...

with the circle and denote the length CH as h. Then, using Thales' theorem and, as in the proof of Pythagoras' theorem by similar triangles, triangle...

1, or 0 positive solutions corresponding to the number of possible triangles given the data. It will have two positive solutions if b sin γ < c < b...

for integer solutions, the equation a2 + b2 = c2 is a Diophantine equation. Thus Pythagorean triples are among the oldest known solutions of a nonlinear...

} which can be obtained by two consecutive applications of Pythagoras' theorem. The Euclidean transformations or Euclidean motions are the (bijective)...

{\displaystyle {\tfrac {1}{2}}ah_{a}={\tfrac {1}{2}}bh_{b}={\tfrac {1}{2}}ch_{c}} , the triangle inequality a < b + c {\displaystyle a<b+c} implies 1 h...

used to find solutions to metaphysical problems, especially the discovery of the foundations of morality. Kant claimed that these solutions could be found...

and modern philosophy. Formal philosophy was introduced to Italy by Pythagoras, founder of the Italian school of philosophy in Crotone. Italian philosophers...

orthonormal basis for our coordinates; then the squared distance to P, by Pythagoras, is d 2 ( O , P ) = ‖ p ‖ 2 = ∑ r = 1 n p r 2 {\displaystyle d^{2}(O,P)=\|\mathbf...

gave two solutions, one of which uses 8 pieces. In the late 17th century Jacques Ozanam came back to this issue and in the 19th century, solutions using...

England: Samuel Jallasson. p. 104. From p. 104: 'In the like Manner Pythagoras ow'd the Invention of Musik to the noise of the Hammer of a Blacksmith...

Particles?". These solutions cut and pasted Schwarzschild black holes to make a bridge between two patches. Because these solutions included spacetime...

that they somehow purified the blood and so cured all manner of illness.: Ch.6  The first such preparation that is known to use the term "panacea" for...

inventor, Alexander Friedmann. The solutions for R(t) depend on k and Λ, but some qualitative features of such solutions are general. First and most importantly...