"The respective and relative motion of three gravitating bodies revolving together and about each other, is as four to three, or one and one-third of one primary circumference."

First Proportion: As one primary circumference of a circle is to the moon's time about the earth, so is the moon's time about the earth to the earth's time about the sun.

Second Proportion: The square of the diameter of the moon is to the square of the diameter of the earth, as the moon's time around the earth is to the earth's time round the sun,-- the time here meant being circular time, as before.
 

"The moon's orbit (or moon's time) round the earth in a sidereal lunation, over the value of a complete circle, is one and one-third of one primary circumference."

"The earth's time round the sun over the value of a complete circle in space is as four to three, or one and one-third the moon's time round the earth over the value of a complete circle in space."

First Proportion: As one primary circumference of a circle is to the moon's time about the earth over the value of a complete circle in space, so is the moon's time round the earth to the earth's time round the sun over the value of a complete circle in space.

Second Proportion: The square of the diameter of the moon is to the square of the diameter of the earth, as the moon's time round the earth over the value of a complete circle in space, is to the earth's time round the sun over the value of a complete circle in space.

"The mean distance of the sun's center from the center of the earth, or that at which the earth would revolve, if the area or plane of her elliptical orbit were made the area of a circle, is eleven thousand six hundred and sixty four diameters of the earth, neither more nor less; admitting, therefore, that the earth's diameter is 7,912 English miles (which no doubt is pretty nearly), then the sun's center is distant from the earth's center as above 92,285,568 English miles, and neither one mile more or less."

Axioms as proven herein and as self-evident:

First: The circle is the basis or beginning of all magnitude or area. (Prop. III See GEOMETRY)

Secondly: Any expression of numbers in relation to material things is also an expression of magnitude. (Prop. XVIII See GEOMETRY)

Third: A point is therefore a magnitude when considered as one. (Prop. XVIII See GEOMETRY)

Fourth: A point in reference to space or extension on all sides of it, is therefore a molecule or globe, and in reference to a plane, it is a circle. (Prop. XVIII See GEOMETRY)

For greater details See GEOMETRY and (Quadrature of the Circle)

"One of the relative properties between straight lines and a perfect curve or circle is such, that all regular shapes formed of straight lines and equal sides, have their areas equal to half the circumference multiplied by the least radius which the shape contains (which is always the radius of an inscribed circle) than which every other radius contained in the shape is greater, and the circle has its area equal to half the circumference multiplied by the radius, to which every other radius contained in the circle is equal."

"The circumference of any circle being given, if that circumference be brought into the form of a square, the area of that square is equal to the area of another circle, the circumscribed square of which is equal in area to the area of the circle whose circumference is first given."

"The circle is the natural basis or beginning of all area, and the square being made so in mathematical science, is artificial and arbitrary."

"The circumference of any circle being given, if that circumference be brought into any other shape formed of straight lines and of equal sides and angles, the area of that shape is equal to the area of another circle, which circle being circumscribed by another and similar shape, the area of such shape circumscribing the last named circle is equal to the area of the circle whose circumference is given."

"The circumference of a circle by the measure of which the circle and the square are made equal, and by which the properties of straight lines and curved lines are made equal, is a line outside of the circle, wholly circumscribing it, and thoroughly enclosing the whole area of the circle, and hence, whether it shall have breadth or not, forms no part of the circle."

"The circumference of a circle, such that its half being multiplied by radius, to which all other radii are equal, shall express the whole area of the circle, by the properties of straight lines, is greater in value in the sixth decimal place of figures than the same circumference in any polygon of 6144 sides, and greater also than the approximation of geometers at the same decimal place in any line of figures."

"Because the circle is the primary shape in nature, and hence the basis of area; and because the circle is measured by, and is equal to the square only in ratio of half its circumference by the radius, therefore, circumference and radius, and not the square of diameter, are the only natural and legitimate elements of area, by which all regular shapes are made equal to the square, and equal to the circle."

"The equilateral triangle is the primary of all shapes in nature formed of straight lines, and of equal sides and angles, and it has the least radius, the least area, and the greatest circumference of any possible shape of equal sides and angles."

"The circle and the triangle are opposite to one another in all the elements of their construction, and hence the fractional diameter of one circle, which is equal to the diameter of one square, is in the opposite duplicate ratio to the diameter of an equilateral triangle whose area is one."

"The fractional diameter of one circle which is equal to the diameter of one square being in the opposite ratio to the diameter of the equilateral triangle whose area is one, equals 81."

"The fractional area of one square which is equal to the area of one circle, equals 6561; and the area of the circle inscribed in one square equals 5153."

"The true ratio of circumference to diameter of all circles, is four times the area of one circle inscribed in one square for the ratio of circumference, to the area of the circumscribed square for the ratio of diameter. And hence the true and primary ratio of circumference to diameter of all circles is 20612 parts of circumference to 6561 parts of diameter."

"The line approximated by geometers as the circumference of a circle is a line coinciding with the greatest limit of the area of the circle, but not enclosing or containing it."

"An infinity in minuteness is always such, that it is capable of increase; therefore, in material things, an infinity equals one ultimate particle of matter, such, that in the nature of the material or thing under consideration, it cannot be less."

AXIOMS as proven herein and self evident:

First: The circumference of a circle is a line outside of the circle thoroughly enclosing it, and of itself forms no part of the area of the circle. (Prop. V)

Second: The line approximated by geometers, if it could be correctly determined, is a line coinciding with the greatest limit of the area of the circle, but not enclosing it. (Prop. I)

Third: The line approximated by geometers is consequently the circumference of a circle whose diameter is less than one in its relative value to the area of a circle. (Prop. I, III, IV & XIII)

Fourth: The difference between a line coinciding with the greatest limit of the area of any circle and a line enclosing the same circle, is an infinity, such that it cannot be less. (Prop. XIV)

Fifth: In material things an infinity equals one ultimate particle of whatever material or thing is under consideration, such that it cannot be less. (Prop. XIV)

Sixth: An infinity is a value, such that it is always capable of increase. (Prop. XIV)

"The value of that infinity which is the difference between the inscribed and circumscribed lines (axiom 4th), and which is omitted by geometers, is increased in the process of bisection of a circumference, so that at some great number of sides of a polygon it will always equal one or more in the sixth decimal place, and may be increased, until it shall equal circumference itself."

AXIOMS as proven herein and as self-evident:

First: Space is infinitely divisible. (Prop. XIV)

Second: Any imaginary line (not a material line), which shall have breadth, is equal to the same portion of space.

Third: Any such imaginary line is, therefore, infinitely divisible.

Fourth: Any such imaginary line may, therefore, be divided, until each part or division is less than any magnitude which is, or can be, developed to our senses.

Fifth: At whatever point the division of such a line may be arrested, because the sum of all the parts is equal to the whole; therefore, each part must have breadth, though the breadth of each part may be such, that no conceivable number of them form a developed magnitude.

Sixth: One line cannot occupy two places at the same time; neither can two lines be in one and the same place, at the same time.

Seventh: Two lines without breadth, cannot exist with no breadth between them.

Eighth: The existence of shape signifies limit; hence, no shape can exist without a boundary line definitely located, which forms no part of the shape itself, which boundary is its circumference."

"No two lines lying in the same plane, parallel to each other, and between two other straight lines, which are at an angle to each other, can possibly coincide, and be equal, except they shall be- come one and the same line."

"All lines which have a fixed and definite locality must have breadth, whether they be lines of circumference, or lines of division."

"The circle inscribed and circumscribed about an equilateral triangle, is in duplicate ratio to the circle inscribed and circumscribed about a square."

AXIOMS as proven herein and as self-evident:

First: Circumference and radius (and not the square of diameter) are the only natural and legitimate elements of area by which all regular shapes may be measured alike and made equal to one another. (Prop. VII)

Second: The equilateral triangle and the circle are exactly opposite to one another in the elements of their construction, which are circumference and radius. (Prop. VIII & IX)

Third: The equilateral triangle is the primary of all shapes in nature formed of straight lines and of equal sides and angles (Prop. III), and has the least number of sides of any shape in nature formed of straight lines, and the circle is the ultimatum of nature in the extension of the number of sides.
PROPOSITION XIX

"In all the elements of their construction which serve to increase or diminish area, the equilateral triangle and the circle are exactly opposite to one another in respect to the greatest and the least of any shapes in nature, and hence they are opposite to one another in ratio of the squares of their diameters, or in duplicate ratio."

For greater details see Quadrature of the Circle.

Rudolf Steiner stated in 1913: "The science of the future will be based on sympathetic vibration." However, he forgot to mention sympathetic vibration is just another way of saying Unconditional Love. Love has been the base of most religions from the dawn of time and is the basis for the New Age. Unfortunately science and society, in the western world, has wandered far astray from this basic and most powerful of forces. This is being reversed! There is now a major and massive worldwide movement back to the place where it is okay for love to enter into our lives, homes and sciences. This is happening right now, before our very eyes, in our very hearts.

When two objects are in harmony with each other on multiple harmonic levels the vibrations acting between the two are as a communication of intent and quality of BEingness of each to the other. The vibrations emitted by one are perfectly received and assimilated (understood) by the other. The two individualized objects begin to resonate AS ONE. This special kind of vibration is called a Sympathetic Vibration. This definition coincides perfectly with that of Unconditional Love. Just as the New Age is the establishment of Love between people and throughout society the New Science is the adaptation of dynamic love to science, technology and engineering via sympathetic vibration. (It's about time!) The Musical Dynasphere is the first example of these devices using this subtle yet powerful force as its underlying principle of construction, BEing and operation.

This Spiritual Science was originally developed (as far as we are concerned) more than 100 years ago in Philadelphia by John Worrell Keely (1827-1898). His work is now being redeveloped for general advantage and betterment of Humankind. With the development of this powerful force and its science and philosophy, we are being enabled once again to rediscover what and who we really are. Little by little this renewal of self awareness and consequently self-identity develops into the state of I AM or being ONE WITH Creation and the Creator. This New Science loves, respects and cooperates with Nature on all levels instead of arrogantly forcing it to address purposes on strictly the material level. Being in harmony with Nature is a joy and a celebration as opposed to discord, destruction and death. This New Technology also allows us to develop seemingly miraculous products and processes when applied to diverse fields such as health and healing, psychology and personal growth.

As the world awakens to this emerging New Age of increased self identity (based on Love) the reigning social structure (based on Fear) is being remodeled. The underlying feeling or motivation of change is Love. The letting go of fear and apprehension can be scary to some. Allowing one's self to be in a state of Love (wide open and seemingly defenseless) can be just as scary. Whether one acts or reacts in love or fear is a personal and conscious choice. As the new awareness of love permeates one's consciousness they begin to experience feelings they may never have felt before or as powerfully. If living in a fear mode they instinctively react to these new feelings in the old fashioned (and no longer useful) way - with fear and all of its effort intensive mechanisms of reactionary self-defense, flight or fight, guilt, calumnies and condemnations of self, others and pretty near all else. Reacting out of fear also leads to desire for control and passive-aggressive behavior - all being destructive to coincidental action or harmony.

On the positive side there are those ready and willing to embrace the newness of the experience of Love and consequentially enter into a celebration of the changes they sense coming over them as they ease into and flow with the exhilarating currents of love, brotherhood and mutual appreciation. This usually manifests as joy. This welling up of Love for one's self, neighbors and that which is called God/dess or Creator is the cloak, mantle or attitude of Unconditional Love. There is a yielding or surrendering to Spirit in this very personal, uplifting and transformative state of BEing. This, coincidentally, was the only commandment, as the Law of One, ever given by Christ who epitomized BEing in Unconditional Love. As we each learn to consciously act in Love this then is the coming of Christ Consciousness to earth, building, as it were, the Kingdom of Love or Heaven. To be as Christ or to be One With Him, in the moment, NOW and PRESENT, is to be in the dynamic state of Unconditional Love and Lovingness.

The New Science based on Sympathetic Vibration uplifts all in hope. It is not deprecatory or predatory like the old polluting and costly ways. Nor is it reserved to the rich or elite. This New Knowledge and Awareness is the sharing of Love into ALL aspects of our lives. After all, how can we love ourselves and neighbors one instant then pollute the air, water and food the next? Or how does one love some but hate or fear others? Our mission (should we choose to accept it) is loving those people, things and situations we fear or are seemingly unlovable. The trick is to transmute the lead of fear (illusion) into the gold of love (truth). The giving of Unconditional Love is all encompassing, all of the time and in all ways without demand, condition or reservation.

Unconditional Love is happening, right here and right now. Celebrate in your choice!