The latest tax assessment available at the time of writing gives the realty for the borough of Manhattan as $3,820,754.181. This is estimated to be 78% of the actual value, making the actual value a little more than $4,898,400,000.
The amount of the Indians’ money would therefore be more than the present assessed valuation but less than the actual valuation.—White, W. F.
A Scrap-book of Elementary Mathematics (Chicago, 1908), pp. 47-48.
[2131]. See Mystery to Mathematics fly!—Pope, Alexander.
The Dunciad, Bk. 4, line 647.
[2132]. The Pythagoreans and Platonists were carried further by this love of simplicity. Pythagoras, by his skill in mathematics, discovered that there can be no more than five regular solid figures, terminated by plane surfaces which are all similar and equal; to wit, the tetrahedron, the cube, the octahedron, the dodecahedron, and the eicosihedron. As nature works in the most simple and regular way, he thought that all elementary bodies must have one or other of those regular figures; and that the discovery of the properties and relations of the regular solids must be a key to open the mysteries of nature.
This notion of the Pythagoreans and Platonists has undoubtedly great beauty and simplicity. Accordingly it prevailed, at least to the time of Euclid. He was a Platonic philosopher, and is said to have wrote all the books of his Elements, in order to discover the properties and relations of the five regular solids. The ancient tradition of the intention of Euclid in writing his elements, is countenanced by the work itself. For the last book of the elements treats of the regular solids, and all the preceding are subservient to the last.—Reid, Thomas.
Essays on the Powers of the Human Mind (Edinburgh, 1812), Vol. 2, p. 400.
[2133]. In the Timæus [of Plato] it is asserted that the particles of the various elements have the forms of these [the regular] solids. Fire has the Pyramid; Earth has the Cube; Water the Octahedron; Air the Icosahedron; and the Dodecahedron is the plan of the Universe itself. It was natural that when Plato had learnt that other mathematical properties had a bearing upon the constitution of the Universe, he should suppose that the singular property of space, which the existence of this limited and varied class of solids implied, should have some corresponding property in the Universe, which exists in space.—Whewell, W.
History of the Inductive Sciences, 3rd Edition, Additions to Bk. 2.