Esoteric Science

In this diagram Kircher arranges 18 objects in two vertical columns and then determines the number of arrangements in which they can be combined. By the same method Kircher further estimates that fifty objects may be arranged in 1,273, 726,838,815,420,339, 851,343,083, 767,005,515,293, 749,454,795,473,408,000,000, 000,000 combinations. From this it will be evident that infinite diversity is possible, for the countless parts of the universe may be related to each other in an in-calculable number of ways. MPH

Pythagoras, the First Philosopher

From Historia Deorum Fatidicorum.

During his youth, Pythagoras was a disciple of Pherecydes and Hermodamas, and while in his teens became renowned for the clarity of his philosophic concepts. The influence of this great soul over the those about him was such that a word of praise from Pythagoras filled his disciples with ecstasy, while one committed suicide because the Master became momentarily irritated over some-thing he had done. Pythagoras was so impressed by this tragedy that he never again spoke unkindly to or about anyone. MPH

The Symmetrical Geometric Solids

To the five symmetrical solids of the ancients is added the sphere (1), the most perfect of all created forms. The five Pythagorean solids are: the tetrahedron (2) with four equilateral triangles as faces; the cube (3) with six squares as faces; the octahedron (4) with eight equilateral triangles as faces; the icosahedron (5) with twenty equilateral triangles as faces; and the dodecahedron (6) with twelve regular pentagons as faces. MPH

Number related to Form

Pythagoras taught that the dot

symbolized the power of the number 1,

the line the power of the number 2,

the surface the power of the number 3,

and the solid the power of the number 4. MPH

The Tetractys

Theon of Smyrna declares that this array of ten dots, the tetractys of Pythagoras, was a symbol of the greatest importance, to the discerning mind it revealed the mystery of universal nature. MPH

The "Cube" and the Star

By connecting the ten dots of the tetractys, nine triangles are formed. Six of these are involved in the forming of the "cube". The same triangles, when lines are drawn between them, also reveal the six pointed star with a dot in the center. Only seven dots are used in forming the "cube" and the star. Qabbalistically, the three unused corner dots represent the threefold, invisible causal universe, while the seven dots involved in the "cube" and the star are the Elohim—the Spirits of the seven creative periods. The Sabbath, or seventh day, is the central dot. MPH

The Numerical Values of the Hebrew, Greek, and Samaritan Alphabets

Columns from left to right:

1-Names of the Hebrew letters. 2-Samaritan letters. 3-Hebrew and Chaldean letters.

4-Numerical equivalents of the letters. 5-Capital and small Greek letters. 6-The letters marked with asterisks are those brought to Greece from Phoenicia by Cadmus. 7-Names of the Greek letters. 8-Nearest English equivalents to the Hebrew, Greek, and Samaritan letters. Note. When used at the end of a word, the Hebrew Tau has the numerical value of 400, Caph 500,, Mem 600, Nun 700, Pe 800, Tzadi 900. A dotted Alpha and a dashed Aleph have the value of 1,000. MPH

The Sieve of Eratosthenes

This sieve is a mathematical device originated by Eratosthenes about 230 B.C. for the purpose of segregating the composite and incomposite odd numbers. All the odd numbers are first arranged in their natural order in the second panel from the bottom, designated Odd Numbers. Every third number (beginning with 3) is divisible by 3, every fifth number (beginning with 5) is divisible by 5, every seventh number (beginning with 7) is divisible by 7, every ninth number (beginning with 9) is divisible by 9, every eleventh number (beginning with 11) is divisible by 11, and so on to infinity. This system finally sifts out what the Pythagoreans called the "incomposite" numbers, or those having no divisors other than themselves and unity [one]. These will be found in the lowest panel, designated Primary and Incomposite Numbers. In his History of Mathematics, David Eugene Smith states that Eratosthenes was one of the greatest scholars of Alexandria and was called by his admirers "the second Plato." Eratosthenes was educated at Athens, and is renowned not only for his sieve but for having computed, by a very ingenious method, the circumference and diameter of the earth. His estimate of the earth’s diameter was only 50 miles less than the polar diameter accepted by modern scientists. In the third century before Christ the Greeks not only knew the earth to be spherical in form but could also approximate, with amazing accuracy, its actual size and distance from both the sun and the moon. MPH