Leonardo DaVinci's drawing, "The Proportions of Man", demonstrates the rational structure and geometrical proportions of the human body. Shown below is the drawing of "Trinitary Man". It conforms to the basic circle and square of DaVinci's "Man", but Trinitary Man has an added triangle, as well as mathematics, and geometry, to make Trinitary Man more significant than DaVinci's Man :
The Horizontal-Curved-Vertical lines of the drawing can make all letters of the alphabet, that is the basis of words. Also, the Circle-Triangle-Square is the basis of designs, including that of Trinitary Man.
All lines extending from the basic Circle-Triangle-Square of Trinitary Man intersect on focal points of his body. This is more apparent if the erased lines on his body are drawn in. Each focal point on the body has Horizontal-Diagonal-Vertical line passing thru it. The focal points are the eyes, nose, mouth, shoulders, nipples, solar plexus, belly button, groin, knees, etc.. The focal points are also acupuncture and Shakra points.
Conforming to the points of the Circle-Triangle-Square, the non-extended limbs of Trinitary Man are shorter than when extended. This is consistent with anatomy when the joints are moved into the body and when extended. Also, anatomically, when the arms are bent at the elbow, they follow triangular lines to meet at the groin.
If horizontal and vertical lines are drawn thru the focal points of the Trinitary body, rectangles are made that are similar to those shown by ABCD and abcd in the drawing. Each rectangle is a "Golden Rectangle", that is an architectural ideal of beauty. Each rectangle is a mathematical "Golden Ratio" (1/2, 2/3, 5/8 ....), "Golden Proportion" (1:.618), and "Golden Section" (.618, 1.618). The Golden Ratios are also "Fibonacci Ratios" that are found in the mathematical, geometrical order of organic and inorganic Nature; as in crystals, spiraling plants, shells, in the rate of animal reproduction, etc. .
The Golden Triangle of Trinitary Man and the logarithmic spiral may be constructed from the Golden Rectangle; that is constructed from the Square and the Golden Ratio of Phi, that are in the Fibonacci series of ratios. The phi (1.816) and pi (1.34) of Trinitary Man's circle are irrational, infinite numbers that are found in the geometrical designs of man and nature. They represent the irrational disorder that is in the rational order of whole numbers, or the irrational disorder in the rational order of free-willed man and in quantum mechanics.
As the curving spiral can be made from the angular Golden Rectangle, it reflects the rational, coherent unity between the diversity of artistic and natural designs . Separately, the spiral symbolizes the free-willed, free-wheeling, irrational disorder of art; while the triangle symbolizes the rigidity of the stable, rational order of scientific structures. Trinitary Man symbolizes the harmonious unity between flexible art and rigid science.
The whole drawing of Trinitary Man, as an extension of its mathematical, geometrical parts, is composed of 5 vertical rows and 8 horizontal rows of Golden Rectangle. The parts make the greater whole of a Golden Rectangle. The Golden Rectangles; with their Golden Proportions, Ratios, and Sections, may be found by sub-dividing larger rectangles into smaller ones, or by combining smaller rectangles into larger ones. Thus, Golden Sections may be found in sub-divisions like the neck, arms, wrist-joint, knuckle-spacing, etc. The principle of the whole, applying to the part is evident in Trinitary Man's face (See below), where the same principles of the Circle-Triangle-Square apply:
Many different geometrical forms may be made from the lines that extend from the basic Circle-Triangle-Square to the focal points on the body of Trinitary Man. A sample of these geometrical forms is shown below on the drawing of Trinitary Man. These forms include the triangle, pentagram, pentagon, hexagram, and octagon:
Other geometrical forms, as well as other triangular and rectangular lines, have been omitted from this drawing to permit the geometrical forms to be more clearly seen.
Other creatures in nature are designed around a circle, triangle, square, or other geometrical forms; like the pentagram, pentagon, hexagon, octagon, or other geometrical form. Only Trinitary Man is designed around a synthesized unity of diverse forms made from the basic Circle-Triangle-Square.
The mechanistic basis of Trinitary Man is manifested in the fact that he may be drawn on a 3-angled isometric underlay sheet that is used to make standard engineering blueprints. Shown below are some of the geometrical forms that may be made from focal points on the body of Trinitary Man:
If a dozen different geometrical forms are drawn on separate clear plastic sheets; and if these forms are placed atop each other, it will be apparent that all of the lines of all of the forms intersect at the same focal points. This may seem natural and normal, but if a drawing of Trinitary Man is placed on the bottom of these collective forms, all of the intersecting points of the different forms will be seem to coincide with the focal points on the body of Trinitary Man. Could the evolution of man make this synthesis of so many geometrical forms by chance? Could the design of Trinitary Man be made on a rock by the natural erosion of wind and water erosion?
The design of Trinitary Man is the essence of classical Greek idealism and aesthetics as expressed by Aristotle's Golden Mean of Moderation, and as applied in Classical Greek art, architecture, and design. It is based on rational Classical principles of Unity, Harmony, Balance, Proportion, Symmetry, Form, Coherence, etc.
The sharp angular lines of Trinitary Man apply to male beauty. A softening or rounding of the angular points on the body makes the drawing an ideal standard for female beauty, for "Trinitary Woman". On the same principle, the soft circle symbolizes the female, the hard square symbolizes the male, and the triangle is their synthesis. All three interrelate to make the harmonious unity of a diversity of trinities.
The Circle-Triangle-Square relates Trinitary Man to the Trinitarian philosophy and its ultimate principles, purposes, perfections, premises, perspectives, and structures. The trinity is a unifying symbol to manifest the stabilized, ideal, harmonious unity that should be in all natural and human diversity.
Could the mathematical geometry that is inherent in the form of Trinitary Man be evolved over millions of years without any distortion? If one makes a photo-copy of a face, and recopies each copy many times, each new copy will lose some of its original essence in beauty and form. This does not seem to have occurred in the geometry of Trinitary Man as he has evolved over changing generations.
What would happen to the design of Trinitary Man if one of his basic forms changed just a fraction? This may be demonstrated by horizontally moving some of the coinciding layers of geometrical forms printed on clear plastic that overlay a picture of Trinitary Man. Would it be like moving the steel framework of a building a fraction, as in an earthquake, to destroy it? Nature has not changed the design of Trinitary Man, but will man's genetic engineering change it?
How can Trinitary Man be evolving if he has reached a point of mathematical, geometrical perfection? To evolve beyond a point of perfection is to devolve to imperfection. What will his devolution become? Will it be a regression back to the ape? A circle, triangle, or square cannot be advanced to be better without destroying it. Is the design of Trinitary Man any different?
If the design of Trinitary Man could be destroyed in a moment in time, could it have been created in a moment in time? If evolving human beings are lined up to show their transition from ape to Trinitary Man, at what point in this evolutionary time did Trinitary Man reach his geometrical perfection? If there is no progressive natural evolution in the making of Trinitary Man, what can we say about his creation? If Trinitary Man did not evolve to his present mathematical, geometrical perfection to be better, what does this say about him being created, about Darwin's Theory of Evolution?
The design principles of Trinitary Man apply only to free-willed human beings, not to other creatures. Conversely, Darwin's Theory applies to other natural creatures who lack in free -willed self-control and self-determination. His theory may apply to man's physical body, but subject to man's rational free will. Thus a free-will man may be born to be thin in hot Africa and fat in a cold polar regions, but his free will may choose to be otherwise. Darwin's theory of evolution, with its natural selection and survival of the fittest, may explain how man adapts to his environment to change the design and parts of his body, but are not all these adaptive changes in his body within the moderating limits of the design of Trinitary Man?
A computer can design complex mathematical, geometrical designs, but could it start from a single point, or from the trinity of the Circle-Triangle-Square, to design Trinitary Man without someone to feed data into it? If man evolved from primordial slime to become an ape, that evolved to become a free-willed human being, then there must have been a purpose that directed this evolution to become the mathematical, geometrical form of Trinitary Man. If so, then who or what guided this evolutionary purpose?
Trintary Man may not be mathematically accurate to the nth degree, but is it not mathematically and geometrically accurate enough to affirm that the design of Trintary Man's body is based on rational, mathematical and geometrical structures?