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.
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 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 a...
Euclid and his Modern Rivals (1879), both literary and mathematical in style Symbolic Logic Part ILewis Carroll, 1885. Euclid and his Modern Rivals . London: Macmillan, repr. New York: Dover, 1973.TEIXEIRA, R. M. Euclid and his Modern Rivals (1879), de Lewis Carroll:Traducao e Critica....
(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 ...
In fact, ‘toolbox’ comes close to the surface meaning of the Greek word stoicheia,‘Elements’. The etymology and usage are complex, but the relevant focal use of stoicheia is clearly in reference to the letters of the alphabet (Burkert Citation1959). To refer, in Greek, to stoicheia...
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...
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) #...
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 ...