Smith, James, Young, Augustus, 8 : 25 :: 1 : 3.125 1 : 3√32 :: 1 : 3.1748020+ William Harbord makes the ratio to be a perfect square number, or :: 1 : π Constant Terry makes the ratio to be a perfect square number, or 1: 1.77635683940025046467781066894531252 Theodore Faber makes his area, diameter, and circumference all to be perfect square numbers. His ratio is both a square and a biquadrate: 13, or (1)2=6; and 13, or (6)2= 256, or 3.16049382671, or 1 : (1.7777777777)2 (1)2. Circumference :: 1 : π Diameter = The recurring decimal of Mr. Faber's ratio contains the digits, excepting the digit 5; while his area contains them, excepting the 8. Thomas P. Stowell has produced from the digits in the form of a common fraction a value of π, now generally in use, as follows: 273883.1416. John Bounoulli says that the sum of the following series of fractions, which has unity for numerators and the squares of the natural numbers for denominators, is finite, and equal to the square of the circumference of the circle divided by 6; or the orthodox value of #: 3.14159265358979323+2 1+1+1+18+28+88 +49 +84 +81, &c. = 6 Wallis, in his Arithmetic of Infinites, 1655, gives the following; 4X 2.4.4.6.6.8.8.10.10.12.12, etc. = 3.141592653589794632384626+ The Integral Calculus gives the following simple expression in terms of a definite integral: π ∞ dx = 1.5707963267948976619231326691+ Prof. Benjamin Peirce, in his work, " Linear Associative Algebra," Washington, D. C., 1870, adopted a new symbol for the root of the imaginary quantity V(-1), and produces a result which he terms "the mysterious formula," as follows: J = √(−1) € = 2.7182818285+. 3.1415926535+ The Solar Equation. In astronomical works the Greek letter, the initial of the word parallaxis, is also used to represent the solar equation: #8".86226925+ The parrallactic equation here given is called "the Latimer Solar Equation," from the late Charles Latimer, Cleveland, Ohio, who produces it from the orthodox value of (the ratio), as follows: Parallactic = 5 Peripheric π. 8".862269255/3.14159265358+ This value, it will be observed, is ten times the side of a square equal to the area of a circle of diameter one: 8".86226925+ 10.785398163397448309+ = The different calculations of the sun's parallax in modern times as found in works on astronomy, are as follows; The sum of all is This table gives the results of 29 calculations. 257".0109+, which divided by 29, gives a mean value for the "solar equation," 8".862+; thus far it coincides with the Latimer value. John Taylor, in "The Great Pyramid, Why was it Built?" 1859, says the Pyramid was built for a - Pyramid. He finds its vertical height is to twice the breadth of its base as diameter to circumference, 486.2567 763.81×2 : : 1 3.1415926535+ St. John V. Day, author of " Purpose and Primal Condition of the Great Pyramid of Jeezeh," 1868, computes the area of the Pyramid's right section to the area of the base as 1 to 3.14159265358979+, and adds that it is indeed most singular that the mathematical symbol π (pi) for the ratio, is the first letter of the two Greek words periphieia and pyramis, and intimates that the symbol was probably derived from the latter word because that ratio enters into its several proportions. Samuel Beswick, in his monograph on "The Sacred Cubit of the Great Pyramid and Solomon's Temple," 1878, says the builders took the circular measure, 3.14159265358979+, and called it a square, and took one side of this square for the first element in the scale of length. √3.1485926535897932+=1.77245385+ geometrical units. That the common cubit was ten times these units, or 17.7245385+ geometrical inches; that the royal cubit was 20.6786286+ geometrical inches; that the geometrical inch is 1.00118+ British inches. = The varied length of some of the cubit-rods is best seen for comparison, as follows: Mr. Beswick says the above approximations of the cubit-rods show they were all intended to represent the same measure, and that their makers had but one standard for a guide. An interesting illustrated paper on Solomon's Temple by Mr. Beswick will be found in Scribner's Monthly, December, 1875, pp. 257-272. |