Euclid: Greek mathematician who applied the deductive principles of logic to geometry, thereby deriving statements from clearly defined axioms. His Elements remained influential as a geometry textbook until the 19th century.
more and more propositions, the outstanding feature of the rules of inference being that they are purely formal, i.e., refer only to the outward structure of the formulas, not to their meaning, so that they could be applied by someone who knew nothing about mathematics, or by a machine....
namely in terms of the cutting-in-half of the angle on one side of a line: “when a straight line standing on a straight line makes the adjacent angles equal to one another, each of the equal angles isright.” That is to say, a right angle is...
There have been several attempts to reconstruct the Porisms, but controversy still rages over the mere meaning of the title, making discussion of content difficult. It is generally agreed, however, that the work was in the realm of higher mathematics. ...
The astronomer Rheticus tried to confer meaning to this number according to a Pythagorean understanding: For the number six is honoured above all the others in the sacred prophecies of God and by the Pythagoreans and the other philosophers. What is more agreeable to God's handiwork than this ...
The literal translation “let it have been postulated” sounds awkward in English, but more accurately captures the meaning of the Greek. 8. Remind that the concepts of infinite straight line and infinite half-line (ray) are absent from Euclid’s geometry; thus the result of OP2 is always ...
(APPEND CMAKE_MODULE_LINKER_FLAGS " ${OpenMP_LINKER_FLAGS}") endif() else() # Typically avoid adding flags as defines but we can't # pass OpenMP flags to the linker for static builds, meaning # we can't add any OpenMP related flags to CFLAGS variables # since they're passed to ...
From Gaussian integers to propositional logic, Stillwell delves into arithmetic, computation, algebra, geometry, calculus, combinatorics, probability, and logic. He discusses how each area ties into more advanced topics to build mathematics as a whole. Through a rich collection of basic principles, vi...
Today, philosophy is understood as a discipline of generalized concepts about the world and the place occupied by human beings in it. It is an attempt to understand the reality and the essence of the things of life and of the human being, to comprehend the meaning and purpose of existence....
Then, for any q∈Z>0 and all sufficiently large X>0 (with the meaning of “sufficiently large” possibly depending on q), we have (1) #{x∈Z∩[1,X]:(f(x),q)=1 and f(x)∈T∞}≫qX; (2) #{x∈Z∩[1,X]:(f(x),q)=1 and f(x)∈T13}≫qX(logX)3; (3) #...