Archytas of Tarentum found the two mean proportionals by a very striking construction in three dimensions, which shows that solid geometry, in the hands of Archytas at least, was already well advanced. The construction was usually called mechanical, which it no doubt was in form, though in reality it was in the highest degree theoretical. It consisted in determining a point in space as the intersection of three surfaces: (a) a cylinder, (b) a cone, (c) an "anchor-ring" with internal radius = 0.
Thomas Little HeathRelated topics
cone construction cylinder degree doubt found form geometry intersection least mean mechanical point radius reality solid space striking three well handsRelated quotes
To the cosmic corpuscles we should find it natural to attribute an individual radius of action as limited as their dimensions. We find, on the contrary, that each of them can only be defined by virtue of its influence on all around it. Whatever space we suppose it to be in, each cosmic element radiates in it and entirely fills it. However narrowly the heart of an atom may be circumscribed, its realm is co-extensive, at least potentially, with that of every other atom. This strange property we will come across again, even in the human molecule.
Pierre Teilhard de Chardin
At the roots of all our judgments there are a certain number of essential ideas which dominate all our intellectual life; they are what philosophers since Aristotle have called the categories of the understanding: ideas of time, space, class, number, cause, substance, personality, etc. They correspond to the most universal properties of things. They are like the solid frame which encloses all thought: this does not seem to be able to liberate itself from them without destroying itself.
Émile Durkheim
When two identical He atoms collide... the interference is destructive. Particles that behave like He atoms are called fermions, short for "particles obeying Fermi–Dirac statistics." ...while bosons imitate one another... the "identity force" between fermions acts like a repulsion, and the probability of finding a fermion at some point in space is reduced if some of its identical siblings are nearby. ...It is the repulsive identity forces between electrons that support white dwarf stars... against their own gravity.
Frank Wilczek
A point of great importance would be first to know: what is the capacity of the earth? And what charge does it contain if electrified? Though we have no positive evidence of a charged body existing in space without other oppositely electrified bodies being near, there is a fair probability that the earth is such a body, for by whatever process it was separated from other bodies - and this is the accepted view of its origin - it must have retained a charge, as occurs in all processes of mechanical separation.
Nikola Tesla
In ancient times there was no public education, except that of the forum, the theater, and the street, and the general degree of illiteracy was very high.... the early men of science were left very much to themselves and such a phrase as "the scientific culture of Alexandria in the third century B. C." does not cover any reality. In a sense, this is still true today; the real pioneers are so far ahead of the crowd (even a very literate crowd) that they remain almost alone...
George Sarton
