There is perhaps no question that occupies, comparatively, a larger space in the history of Greek geometry than the problem of the Doubling of the Cube. The tradition concerning its origin is given in a letter from Eratosthenes of Cyrene to King Ptolemy Euergetes quoted by Eutocius... "Eratosthenes to King Ptolemy greeting. "There is a story that one of the old tragedians represented Minos as wishing to erect a tomb for Glaucus and as saying, when he heard that it was a hundred feet every way,Too small thy plan to bound a royal tomb. Let it be double; yet of its fair form Fail not, but haste to double every side.But he was clearly in error; for when the aides are doubled, the area becomes four times as great, and the solid content eight times as great. Geometers also continued to investigate the question in what manner one might double a given solid while it remained in the same form.
Thomas Little HeathRelated topics
bound content cube double doubling eight error fail fair feet form four geometry given great haste history hundred king letter might perhaps plan problem question saying side small space story times way while yet aides ptolemyRelated quotes
For The United States, the leading space faring nation for nearly half a century, to be without carriage to low Earth orbit and with no human exploration capability to go beyond Earth orbit for an indeterminate time into the future, destines our nation to become one of second or even third rate stature. While the President's plan envisages humans traveling away from Earth and perhaps toward Mars at some time in the future, the lack of developed rockets and spacecraft will assure that ability will not be available for many years.
Without the skill and experience that actual spacecraft operation provides, the USA is far too likely to be on a long downhill slide to mediocrity. America must decide if it wishes to remain a leader in space. If it does, we should institute a program which will give us the very best chance of achieving that goal.
Neil Armstrong
Every artificial excavation-every well and cellar-every cut for a fort, common road, railway, or canal-every quarry-every tunnel through a mountain-and every pit and gallery of a mine bored into the solid earth, furnish means of investigating its interior. Still more do the inland precipices, and the rocky promontories and headlands along the rivers, lakes, seas, and oceans; the naked mountain-sides ribbed with strata, that bound the defiles, gorges, and valleys; the ruins accumulated at the feet of lofty pinnacles and barriers, and those that have been transported and scattered, far and wide, over the earth; present us with striking features of the internal structure of our planet. Most of all, do the inclined strata push up their hard edges, in varied succession, and thus faithfully disclose the form and substance of the deep interior, as it exists many miles and leagues beneath the observer's feet.
Gideon Mantell
A million and a half of people spread over the Atlantic seaboard might be thought no great number; but it was a new thing in the world. ...which had in fact been carefully noted by Benjamin Franklin in a pamphlet on The Increase of Mankind, Peopling of Countries, etc.-that within three-quarters of a century the population of the continental colonies had doubled every twenty-five years, whereas the population of Old England during a hundred years past had not doubled once and now stood at only some six and a half millions. ...With these facts in mind, one might indeed say that a people with so much vitality and expansive power was abundantly able to pay taxes; but perhaps it was also a fair inference, if any one was disposed to press the matter, that unless it was so minded, such a people was already, or assuredly soon would be, equally able not to pay them.
Carl L. Becker
The recurrent problem of civilization is to define the male role satisfactorily enough ... so that the male may in the course of his life reach a solid sense of irreversible achievement, of which his childhood knowledge of the satisfactions of child-bearing have given him a glimpse. In the case of women, it is only necessary that they be permitted by the given social arrangements to fulfil their biological role, to attain this sense of irreversible achievement. If women are to be restless and questing, even in the face of child-bearing, they must be made so through education.... Each culture--in its own way--has developed forms that will make men satisfied in their constructive activities without distorting their sure sense of their masculinity. Fewer cultures have yet found ways in which to give women a divine discontent that will demand other satisfactions than those of child-bearing.
Margaret Mead
Few people seem to perceive fully as yet that the most far-reaching consequence of the establishment of the common origin of all species is ethical; that it logically involved a readjustment of altruistic morals, by enlarging, as a necessity of rightness, the application of what has been called the 'Golden Rule' from the area of mere mankind to that of the whole animal kingdom. Possibly Darwin himself did not quite perceive it. While man was deemed to be a creation apart from all other creations, a secondary or tertiary morality was considered good enough to practise towards the 'inferior' races; but no person who reasons nowadays can escape the trying conclusion that this is not maintainable. And though we may not at present see how the principle of equal justice all round is to be carried out in it entirety, I recognize that the League is grappling with the question.
Thomas Hardy
