The Conservation of Circular Disc Sector space.

It is my contention that spheres and circular discs formed a prior philosophy upon which Thales drew and taught many concepts of proportion or Logos Analogos relationships of space. However to demonstrate certain transformations of spatial boundaries as being dual requires the flexibility found in material space as not being created or destroyed. The conservation of matter is a common everyday occurrence that it is taken for granted, but in fact material mediums as all alchemists know do not conserve there shape texture and even volume during and after a chemical reaction.

It was a bold proposal that states that the quantity of matter is conserved in a chemical reaction. While it is not drawn attention to this quantity of matter is an Alchemical concept used and defined by Newton as a measure related to the ratio of motives of material and air, and the measure of the volume of that ratio for the bulk of each object.

Enclosing an object in a sturdy glass container allowed one to assume that all quantity of matter in that volume was isolated. . No matter what was in that volume a relative density was assigned to it via the prescribed calculation. For this reason material was not distinguished and became called Mass.

However careful chemists were able to use the mass as a stepping stone to tabulate pure materials and so characterise them. Then the reacting of several materials together in a sealed container could be shown not to alter this mass characteristic, despite the materials being utterly transformed!

The quantity of matter is part of a chain of concepts Newton established to describe a centripetal/ centrifugal measurement system.. It related every part of an isolated system through these force measures

Conservation of space however has a astrological use, where it is assumed that space is absolute, isolated and still. . With such a conception a boundary change does not affect space. In that regard space passes Tintoretto and out of any dynamic boundary, at least absolute space does. Fractal space behaves differently, and do fractal geometry is different.

Suppose now a circle is squashed, then the space that was inside now stands outside the new topological boundary. However for a ” real” object that space would be deformed within the new boundary , possibly acting to restore the boundary to its initial position.

Using absolute space can I demonstrate that a sector is dual to a half of a rectangle formed by the circle radius and the sector arc length?

It is possible to establish this fairly simply providing absolute space is used, and a specific case involving the arc length equal to the circle diameter is used.

The concept requires also a secure definition of a good or true line sometimes confused with a straight line in other contexts where it is not necessarily the case. This good line must be the line of dual seemeia, or indicators of where arcs cross if drawn from 2 fixed centres , using the dual radii for each centre..

Given this good line a circular sector with arc length equal to I diameter of its circle is placed on the line and rolled so that every point on the arc is brought into contact with only one point on the line.. The centre or vertex of this sector moves one diameter tracing out a rectangle with the radius as the other side.

Conservation of space or absolute space means that the space in this rectangle passes through and or is contained within the arc sector.. Thus the rectangle contains some of all the space swept out by the arc sector. In addition all space has passed symmetrically through this rectangular figure, with space entering and leaving the arc at the same rate.relative to this rectangle.

At the end of this role a symmetrical figure represents the whole process. What we note is this symmetry allows us to half all the spaces in the diagram.the rectangle is created by the sector rolling, thus the whole space in the sector has passed into an through this rectangular space.. We see that there is as much outside this space at the beginning as there is at the end. . This rectangular space therefore has transferred its space into the rectangle . At one stage it was wholly inside the complete rectangle to be. So the space in the rectangle is 2 times the space within the sector. If any space was compressed into it the shape would not be symmetrical . It also took all of its fixed boundary o create this shape and mark out the rectangle..

A legitimate question is how do you know it is transformed into the rectangle? The answer is the arc sector is not transformed into the rectangle . It sweeps through the rectangle, creating the rectangle, thus it’s space places itself everywhere in the rectangle..the rectangle thus must be at least one of the 2 sectors in the symmetric form . If it was just less than 2 the sector would would not extend beyond symmetrically. If more than 2 again it would over extend. Precisely 2 retains symmetry and maintains conservation of space.

It is worth establishing this point with several reasonable or proportional examples, after which we may establish the discovery of Archimedes that an object must displace its own space in order to occupy a different space, or more dynamically an object rolling through space must displace multiples of its own space or multiples of its own space must pass through it.. In the case of a circular disc we may then establish a multiple factor of 1/4 the rectangle it cuts out to quantify its space. In the case of a sphere this reduces to 4/24 of the cuboid it cuts out.

The shapes of space formed when working directly with the circle disc or sphere I call Shunyasutras. The ” rectilineal” shapes are distinct because the good or true line is precisely good or true to itself. This good line is defined however by a property of circles that intersect because they are centred at precisely 2 centres.the point of intersection are called dual points. The dual points that define a good line or a true line are intersections of identical radial displacements from the 2 centres. Shapes of space with a true line fit together along those lines precisely or they don’t.. If they do not the shapes are not dual! It is this powerful notion of duality that is carried through from point to curve to line to shape of space as surface or volume.this notion of duality applies to the Shunyasutras, where a curved arc sector if it is dualed is also a good or true curve!

The straight line however has taken a dominant position in our psyche, despite the fact that it is never found in nature. It is a formal construct that dominates human evaluation schemes. This was not always the case. The circle played a deeper magical role in the past particularly in its rivalry with the spiral.

The absolute empirical dominance of the “spiral” shape and dynamic of space is remarkable when one realises how it is obscured from general metrical perception. In distant times past the circle grew to dominate magical lore and triumphed when it was believed to contain or constrain the spiral. Both these. We’re represented as dragons or serpents

However to measure with the circle always required skill and precise application. The precision of dual points as circle reference points came to dominate the practice of measuring with the circle. The straight lined ruler based on a right angled triangle within a semi circle became an indispensable tool of architecture. The lore of circles that underpins it was soon pushed out of the common thought and left for experts and philosophers to investigate. . Thus I have no intuition of duality of the Shunya ultras, how one shape may be used with a transformed one, and what topological constraints are required to declare duality or fit”.

In the case of arc sectors I can show how the rectangle formed between the arc rolled out ant the diameter contains 2 overlapping arc sectors. The question is does the overlap fit the space mot overlapped?to answer that question I have to employ symmetry observations and exhaustive comparisons, which call upon the notion of ” fit” I have established for the straight line.

The circular gnomon and Lunes play a historical part in the metrication of the Shunyasutras

 

http://mathworld.wolfram.com/Arbelos.html

 

Centripetal and Centrifugal force

I am undone! Woe is me !

However it is not as bad as that. Reading the Astological principles further in order to understand the introduction of centrifugal force, I find that Newton ascribes its description to the excellent mr Halleys work on hoological oscillation! Of course he mentions Huygens and Wren.

The first reveal was newtons scholium on the astrological definitions of various quantities and measures and the general relativity of these terms snd ideas. In so doing he describes certain absolutes as concepts the reader is expected to accept without question, either as astrological or commonly accepted among philosophers. Thus without being immersed in his times it is easy to miss certain subtexts implied by certain ideas.

The second reveal is the absolute geometrical nature of the theorems and corollaries by which he derives the centripetal force . In so doing the reader is drawn away from the heavens to geometrical figures. Having demonstrated in corollaries certain ” mathematical” relations, he asks why they may not now be applied to the motions of orbits in space!

Well the reason is, in my opinion that the construction of the curves is so evidently geometrical that one must also suppose that this is how god does it in the heavens! . This is evidently not a sustainable assumption, except if one be a believer in god. Yet I caution that the god who this might be attributed to states plainly that he will not allow this assumption!

The more reasonable circumstance is to say that this method is a geometrical model which must prove itself by empirical observation to be useful, and nothing more. This utilitarian view avoids the difficulties arising from the models short comings.

Now we may see how Newton models a centripetal force , drawing a body from a rectilinear course ( potentially) continually into a curve..mthat the rectilineal motion is but a device is evident by Newtons process of eliminating it to the curve, and stating certain laws in terms of the arcs, not the tangents or chords of them.. And yet there are sod who insist on the rectilineal as the true motion, denying the curve of the orbit.

Now as a second but contrary proof Newton refers to Halleys centrifugal force. This is the force imparted to a curved or circular boundary by an object constrained within it! Thus the object by impulses on the circular boundary transmits a centrifugal force, o which the boundary responds so that the object is turned into such sn orbit as might be considered circumnavigating. Newton observes that the force that expands the circle outwards is equal and opposite to his centripetal force, by which the centre attracts an object into an orbit..

Thus the curved orbit is constrained within 2 encasing methods which both agree in the evaluation of the force required to turn a moving obje with certain velocity into a curved orbit.

Precisely how this is done is not here discussed, but how it may be modelled by infinitely reducing triangular areas containing the curve is. Once again this is a model process we are asked to apply to the behaviours in space, whose mysterious actions remain mysterious, unless you believe this model process to be actually how Nature does it!

Density

Density in the Newtonian system of quantities within an absolute vis system is the ratio of a given volume of air to the same volume of any other substance or matter, compound or aggregate as to : how far each stretches a spring balance, or how much is required in adjustment to achieve a balance of moments. Density is thus the ratio of motive vis of a standard volume of air to a volume of any substance or matter required to balance.

Because density is a ratio of motive vis, it is physically dimensionless, but this is a mathematical nicety. Density is clearly a force! Within the Newtonian force or vis system it could be no other. Due to the Abdolute nature of these force or vis systems it is clear that pressure , and the distribution of pressure , the pressure gradients etc are a better conceptualisation of vis than the hijacked term force,

Density is a substance pressure, and it presses toward the centre of an absolute system. Substances thus separate by the pressures involved with densities leading to regionalisation, stratification dynamic interactions between and around densities.

The Quantity of Motion and the Quantity of Matter

The first time I came upon the definition of the quantity of motion I felt that in some way it embodied all the motion of the parts, particles or ” atoms ” of matter. I had no idea that it was a complex vector summation. I almost immediately looke back to understand the definition of the quantity f matter. This is when I came upon the mystery of density. However I finally resolved this as an allusion to the Archimedes principle of displacement of volume of watersllied to the Bouyancy of the immersed material less dense material floated in water and displaced enough water to balance against their weight. Items that sank displaced an equal volume to the item but that volume of water did not balance , thus the item was denser than water.

It became clear that density was an obscured force or pressure. Density pushed less density to one side and occupied the lowest position. It thus behaves precisely like the Newyonial motive force. But volume of density or bulk of density also determined the amount of centripetal force , quantity of matter was alike to the definition of the quantity of motive.

The quantity of motion is a quantitative bridge between the quantity of matter and the motive vis measure. Thus it becomes apparent that Newton leads the reader into the complex quantitative system he adduced from the Galilean principle. This principle itself was adduced from observations he made of the Jovian system. In addition Galileos observations of the planet Venus allowed him to set out a convincing empirical basis to the fancy of Copernicus that the sun was the centre of the universe.

In the Dialogo he sets out amusingly his ideas in a discourse, so that the pros and cons, the propositions and objections, the arguments and counter arguments are set forth. Here in words supported by a diagram he sets out the Galilean principle as a fractal structure of local space. For it to convince his peers it was necessary for each part of the fractal system to be absolute. This meant that the Jovian system was independent of the solar system, and so the system moved around the sun as if the parts were not drawn to the sun but solely to the planet Jupiter.

Similarly the planet Venus moved about the sun as if drawn to the sun but not drawn to the earth. Thus his diagram reveals on what principle this might happen, and this is the Galilean principle that centres of vis are absolute in there influence on local regions of space, by imparting the velocity of the centre to every part of the local region. In this way the local region behaves as a sole or absolute quantity that may be itself drawn to a larger centre.

Newton adduced a quantitative vis system based on. Triumvirate of vis: absolute vis, accelerative vis and motive vis. The absolute vis is that quantity of vis that is the total or entire within an isolated system. The accelerative vis is how that total vis is quantitatively and regionally distributed in the local space as observed by how it affects the velocity over time of the parts of the total throughout the region of local influence. The motive vis is how those parts of the system are individually and proportionally being drawn toward the systems centre. This was each parts centre tench and is defined precisely as a parts weight by Newton. Thus he enables motives to be compared empirically by a spring balance or by a balance of moments.

These motives are dependent on their location within the regional accelerative vis distribution, as well as the quantity of the part and the velocity change over time of the part..btoday we naturally call the distribution of vis a field, but in fact the idea of a field is not natural at all. In great part it is a concept due to the empirical observations, diagrams and philosophy of Faraday. Newton here shows a conceptual quantity distribution which acts on bodies within its influence as an absolute system, that is very much akin to a field concept, but in fact it based on an unspecified distribution law. Later he would demonstrate the inverse square law, which is a familiar field distribution that defines a modern field essentially.

It is logically clear that if motive is to be the weight of a part of an absolute system, that is the quantitative measure of that parts tendency to the centre,that a measure of tha quantity of motion is needed. This measure makes explicit the velocity of the part that is to be changed over time. But if the part has its velocity explicit the part of space within the system was also explicit. This part of the system he defined as the quantity of matter,

The quantity of matter is therefore and necessarily a part of an absolute system, and not a universal constant at all.

The concept of a quantity of matter is relative to an absolute system. It is a regional part of that system capable of changing its velocity as a whole or sole object especially in centriole tench, or propensity to move toward the systems centre. To quantify this part Newton brings it down to a geometrical measure called a volume. . But a volume clearly dies not model the differences between weight of volumes as measured by balances. In fact this problem, as Newton knew was solved by Archimedes using the displacement of water as a way to describe quantitatively the inference between volumes of parts of the absolute system. This difference as a measure was called density. It is a ratio,and it is a ratio of compared motives.

Now I always thought that Archimedes used water as the standard substance, whose motive is used by volume to quantify every part of an absolute system.. If water as used then it is a substance found everywhere on earth and thus makes it a good local standard. If it can be found everywhere in the universe it makes it a useful universal substance to be used within each absolute system as a standard for this quantitative purpose.

However it suddenly becomes apparent that Newton based his concept of a standard substabpnce not on water but on air!air too can be found everywhere on earth, but there is clearly a naive hope that it might extend out into the system of the earth and the moon!. Newton thus considered the earth moon system to be measurable in terms of density ratios of Air.

Considering this, I must assume that Newton expected the earth and moon to have such large quantities of matter that the air between them would be a negligible part of the system in terms of quantity of motion. Substantially then the centre tench of the moon to the earth and the earth to the moon reside mainly within the relative weights of these bodies. The effect of any intervening air would be negligible. This is important because the resistive force of air as wind was well known. Thus objections of the moon and earth being blown off course by respective winds are made implausible! Nevertheless Newton expected over very long times the motion between the earth and moon would be retarded by this air leading to the moon eventually falling from the sky!

Heat as a Vibratory State of Matter

There is long 17 th century tradition that heat was a vibratory state or condition of matter. It is found particularly among the Alchemical writings of philosophers and especially amongst the writings of Newton. However, when heat began to be studied, Fourier in particular adopted the analogy of a fluid.

It is said that he used Newtons observation that heat( a fluid) flows from a high temperature to a low temperature, from hot to cold. However since Newton expressed heat as a vibration he did not concur with this notion!

The higher state of vibration corresponded to the higher temperature, thus a higher vibratory state passes into a lower vibratory state.

There are several observations at superconducting temperatures where cold is observed to flow into heat! This seems anomalous except when you realise that it is a relative statement if vibration passes into lower vibration one may equally say that lower vibration passes into higher vibration
However empirical observation reveals the following. Heat is associated with lower densities of a material. Thus a warm front is associated with low pressure circulation cells, cold temperatures are associated with higher densities, thus anticyclones spread out into warmer lower density air bringing a chill.

We say high density spirals out into lower density, but this is cold flowing into heat! In addition we say heat convicts or radiates into cold , but give no thought to cold converting or radiating into heat.

If we look at convection in a metal bar, the high temperature Is associated ith a less dense volume of material, expanding and highly radiative . But consider for a moment that the cold material is attempting to radiate into this less dense region , that it is converting from its stays of higher density spreading into a region of lower density. In this case the lower temperature and lower vibratory system is nevertheless more highly effective in pushing a lower vibratory state onto a higher one.

The situation is not the simplified hot flowing into cold energy flow or even high temperature flowing to lower temperature, it is a high temperature low density high vibrational radiating and expanding state which is being penetrated by a low temperature high density low vibration radially contracting low radiation state”

Thus warm air does not rise, rather cold air pushes the less dense air up.

In terms of the znewtonian absolute system this makes perfect sense, as the quantity of motion , and the motive measure of the cold air has a greater cntipetency than the less dense warm air.

Absolute.

When first I came upon Newtons absolute time, I took it to mean that non relative time which rests with his God. But now I must examine his use of this word, it’s etymology at least from the Latin if not the Greek prior philosophy , to the translators use in the English version of his great Natural Philosophy of Astrological Principles!

The occasion of this research has been the reading of Galileos Dilogo , in part, the apprehension of the Galilean fractal principle contained therein and Newtons use of the same in his triumvirate of Vis, under the heading of the Centrioetency of force, that is the Centripetal Force.

I hope , by these means to reveal the backwards structural arrangement of Newtons definitions, and why the measure that is the quantity of motion is placed as a foundational or initial definition.

Search:
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
absolute (adj.)
late 14c., “unrestricted; complete, perfect;” also “not relative to something else” (mid-15c.), from Middle French absolut (14c., Old French asolu, Modern French absolu), from Latin absolutus, past participle of absolvere “to set free, make separate” (see absolve).

Most of the current senses also were in the Latin word. Sense evolution was “detached, disengaged,” thus “perfect, pure.” Meaning “despotic” (1610s) is from notion of “absolute in position.” Absolute monarchy is recorded from 1735 (absolute king is recorded from 1610s); scientific absolute magnitude (1902), absolute value (1907) are from early 20c. In metaphysics, the absolute “that which is absolute” is from 1809.

http://en.m.wiktionary.org/wiki/absolute

It may be seen that in this context and at the time Newton wrote that he meant to convey the idea of ” non relative” ” non dependant” and ” isolated” in regard to the observations and deductions Galileo had made of the Jovian system. Thus in this system the absolute vis was evident as a separate system from that of the earth moon system. In quantitative terms this had to be the whole or totality of that quantity of vis.

Through the telescope this sense of isolation is profound, and the sight of the moons of Jupiter and the realisation that they are ” independently ” rotating around Jupiter was the deepest possible shock to the system men and women of those days could experience!

It takes a mind that measures to see this system as an absolute quantity! In the sense that a triangle is a different absolute quantity o a hexagon, say. Only by seeing these as Arithmoi, pebbles or mosaic chips can the profound quantitative analogy be understood. For a picture may capture that which takes a thousand words to describe the extensive properties and propensities of, but that same picture cut into a mosaic gives a quantitative and relative encoding of each part in the Arithmos. Each Arithmos is as an absolute quantity, complete and entire to itself.

That such properties of vis, namely centripetal vis should be so evidently associated to this quantity or Arithmos is a revelation! However to use the quantitative apprehension with the vis some rule of relation must be observed. For example this absolute quantity of force might be divided uniformly though the isolated system. . However by this time, sufficient evidence and deduction had been gathered as to suggest that the rule of relationship was an inverse square law. So this quantity of vis was distributed so as to act differently at different distances from the centre. This notion was not absolute therefore as it depended on the absolute quantity of the system however it was measured by the accelerative effect this distribution of vis had throughout the system thus Newton called this measure the acclerative vis. It is a dependent subdividing of the isolated or indent quantity of vis in the system. Thus while encoding the same regional quantity, so that the total should be the same, the distribution of the summation should reflect the greater sum where the greater concentration of vis is and vice versa.

How might this be achieved quantitatively? This requires that there be another subdivision of the vis such that the greater acceleration is embodied in the greater part of the whole or if necessary the greater acceleration being in the smaller part, the force being small yet the time of application is longer. That being the requirement means that the accelerative vis must impinge a change in velocity of parts dependent on time! It is thus the measure of that velocity change over time. This is agin a definition of acceleration given by Galileo, but here the proportion of the system, ie it’s relative” bulk” or mass compared to he Abdolute, affects the quantity of vis in that part.

But then, should a part be moved centripetally as a whole then that part is a measure of motive vis in the following precise sense: if it is opposed by a spring or by the parts acting as moments to a balance! Thus a part or a summation of parts may now be given a motive as a multiple of some standard notive or weight, and balanced accordingly on a pair of scales.

Thus has Newton brought down from the starry heavens, by Alikening to a system of measures that quantify the absolute systems of planets by their motions over time and by their bulk in the heavens or yet within each absolute system.

I now turn to Abdolute time. This is not an observed property of the Jovian system, but rather an addiction by Newton, that if a system may be absolute, that is isolated and entire, that time might also be absolute. In fact it was necessary to use earth based times to discuss the changes in the Jovian system, yet it is evident that if Jupiter has moons then it has it’s own system for recording Tymes! That being the point explicitly made within the first chapter of genesis as regards the function of a moon!

Given then that each absolute system has its own absolute time, that makes time a relative concept! But that was unacceptable or that way lies confusion! Thus absolute that is independent time was the solution. Such a time may well exist with god, but it’s conception was more mathematically adduced than for any other reason. If such a time is not demanded how will 1 second be measured any where in the universe never mind on the planet earth.

Absolute time represents a simple knee jerk reaction to the difficulty of quantitatively measuring acceleration and velocity in these absolute systems. Later Einstein would point the way to how to relate all these relative measures together in a system based exactly on Galileos principle of uniform motion of reference frames.

Returning now to the motive, it is clearly a quantity that is proportional to the bulk or mass of a part and the velocity of a part under accelerative vis. It is exactly a quantity of motion. What we find is that Newton defines such a measure almost as the first of his definitions before defining vis or acceleration or velocity. These are assumed to be known from Galileo’s work.

The quantity of motion is thus his final definition of motive, placed first to emphasise it as a fundamental unit within a centripetally acting absolute vis system, with an accelerative bis rule.

This is. Newtons exposition of the Galilean principle in a form amenable to quantitative measures.

Newton’s Centripetal Force

Newtons definition of centripetal force precedes his application of the Galilean principle which he reduces to 3 sorts or kinds of vis as a centripetal force.the absolute, the accelerative and the motive.

It is to be noted that in defining centripetal force the first presentations describe it as drawing a body away from its natural or innate rectilinear motion, that being the propensity of its innate force. However this is rather a stronger notion than the original Greek idea of a ” good” or “straight ” line allows. Such a good line if it be true to its nature in the motion may in fact be a curve! In any case the assumption that motion is naturally rectilinear is hardly empirical by any degree!

Supposing now that the innate motion merely attempts to continuously recede from the centre which impels it from its recession hardly spoils the plot, but in fact enhances it in the many and congenial examples he gives of a centripetal force in action, or behaving as he wishes it to be described.

We may also have missed the import of his second example, that such a force is as an example magnetic, and as a third example but of an unknown force, gravitational!. So in proposing this definition it is not to define gravity but all kinds of force that tend the motion of a body continually to ward a centre, and so doing by altering the bodies innate velocity Leo, as well as its general recessive course, we’re it to be viewed from the vantage of the pulling force centre!

There is then a ballistic discussion mediated on the introduction of the idea that the velocity of a body is altered by a centripetal force, in which the relative view is again switched as the explosive power of gunpowder now impels a body to some velocity which gives it increasing range , until at last a velocity should be reached by which the projectile completes one orbit! The argument being so clear and logical that it has been remarked that it alone was sufficient to convince his peers that he knew whereof hew rote. But it should be noted that with increasing peed the missile was said to pass out of orbit to continue into gods universe unhindered. . This vision was clearly advanced so that he might bring the moon into his discussion forthwith and deny ny argument that the moon was drawn out of its way by the same centripetal gravity that governed the ballistics of the projectile.

This having been advanced he leaves it to the mathematicians( that is the qualified astrologers) to determine this exact velocity , and the intensity of this centripetal force so that any body in orbit might just remain so , falling so as to miss the earth continually, but not to come crashing down onto the earth, nor yet to fly away.

Now some have read this and failed to see the complexity of what Newton set out to do. As a consequence they have not grasped the complex nature of the orbital problem in particular, the many forces as impulses or resistive forces or impelling or expelling forces that are herein described and employed to convey the conceptual framework he thn goes on to address. Therefore ome have rejected his later more careful description of circular and orbital motion in which centrifugal force is admitted to the description. It is empirically obvious to all that such a force is needed to account fully for observed behaviours, but some have sought to make velocity the source of this centrifugal force. The changes in in the tension on a string would properly imply both a centripetal and centrifugal force, which when removed by swinging a projectile in an elliptical arc results in the projectile crashing to the ground under no centripetal orce by the string! Thus the string not only must supply centripetal force but also centrifugal force to keep the projectile in that correct attitude to orbit.. The velocity itself if it was solely rectilinear would behave tangentially in breaking loose of the projectile, but instead it behaves as if it has another velocity imparted by a centrifugal force compounded with the supposed rectilineal one ( by those who would argue that rectilinear is a straight tangential velocity instantaneous to the orbital curve).

That being said we must now proceed past the moon to the Jovian system observed by Galileo to follow newtons establishment of his force triumvirate.

Centripetal force is of 3 kinds, and each kind is a measure/ Metron or measured quantity the absolute vis measure is a quantitative appreciation of a central agency. His example is the many kinds of lodestones nd their corresponding intensity. Thus should we specify a particular lodestone, or even Jupiter, that is a particular absolute vid.. Thus absolute means an isolated or specific potency under investigation, and the sole cause of all that is considered in following discussions.. It is defined as acting from the centre.

Later Newton adds that this absolute vis is the cause or central causative agentin the system. I have taken that to mean in the universal system god, but in a local system, clearly it is a specified quantitative object.it has to be quantitative because he is establishing a quantitative fractal system as designed by Galileo.

The accelerative vis is next defined. There are more examples of how the accelerative vis varies around the specified object or centre.. Thus if we isolate a quantity from an extensive magnitude, that is only the beginning. We must now examine that quantity carefully snd specify som sub quantity measure!in other words, taking the object as a whole we must now divide it into multiple parts..in this case taking the intensity of the absolute vis we must now render it into its behavioural parts. In this case , as he later shows, he desires to establish an inverse square proportionality as the parts. This is his taccrlerative vis proportion, which he will later empirically and geometrically and astrologically establish.

He quotes one observation of Galileo directly, that accelerative vis imparts the same velocity regardless of mass at the sae height or distance from the accelerative bis centre.. But the absolute force for each identified system will be different, so the subsystem accelerative force will have a different value but the same law of calculating the measures..

Now I took the accelerative vis to be an instance of a universal vis, an absolute vis, but clearly it is a scale of behavioural action centred on the centre of the absolute vis.. Thus in the universal view accelerative vis describes how the various parts of the universe should behave relative to the centre. Immediately it becomes apparent that this system cannot have a universal application! No one knows where the centre of the universe might be!thus despite its general applicability it is not a universal system but a local empirical one.

In that regard, yhe recent expositions on dark matter seem premature. If we choose a galaxy as an object we can use this system to estimate whether an inverse square law pplirs to the galactic syste, the galaxy is assumed as the absolute vis nd an accelerative vis is designed for it from the galactic centre. When this is done, it apparently does not work! So dark matter was invented o explain this” anomaly”. This ord Anomally means infringement of alas, but it is us who imposed this law on the galaxy in the first place, clearly our law is not a correct description for galactic systems! We do not need to invent dark matter, we just need to get the correct law, which may beone of the other laws Newton tried throughout his astrological principles.

Finally he describes the motive vis measure or Metron. This basically allows the observer to sum up the behaviour of masses or parts of a system which are being impelled by the accelerative vis to move toward or about the centre. In very particular, at the same level one mass may be blanced on a weighing device against not her. Thus the motive vis measures parts against parts under the influence of the same accelerative vis and uses the balance or ahookes spring to establish proportionalmeasures like mass, weight etc.

Again Newton relates this to the astrological Jovian system, in which the moons might now be weighed against each other within the one accelerative force of the absolute Jovian system

There is no as yet direct statement that the accelerative force if the centre itself is in motion imparts this additional motion to the parts it. Accelerates, but this will be advanced later.

The Galilean Principle

The Galilean principle is mentioned in passing. That an object within a carriage sealed from visual contact with the outside will be seen by an observer in that carriage to move as it should. Thus it is indistinguishable Whether the object is in a moving carriage or not.

The movement of the carriage is conveyed to the object and to the air within the carriage! We must take this further. Whatever is within that carriage is moved in concert with the carriage, thus whatever medium or aether or property by which some physical power exhibits itself is also moved.mthus we say the laws of physics hold in any uniformly moving frame of reference. By this we mean that that motion of the frame is imparted to any phenomenon within that frame.

How then do some say and teach that the speed of light is a universal constant? That nothing travels faster than the speed of light? It is clear, by the Galilean principle that light or any object travels at its speed plus the speed of the frame in which it is emitted!

The question is can we observe anything moving faster than light? Clearly not, but what we can observe are the Doppler shift effects due to portions of a light beam ( or a sound wave) crowding in to tHe medium of transmission!

What if the medium of transmission moves independently of the carriage? Then we would expect some Doppler like variations in the light signal. At sea level Michelson and Moreley found no variation. However at higher altitudes scientists have found perceptible variations! At those heights and densities the relative motion of all mediums is not sufficiently coupled to the earth to fulfill Galileos principle.

The speed of light is not an immutable constant, but it is limited as a bulk property of any medium. Thus Lorentz contractions or Doppler shift effects do have to be accounted for in measurements using light or radiation, not because nothing can travel faster than the speed of light but because we cannot observe anything travelling faster than light speed.

Suppose now we make a measurement and by calculation it comes out faster than light speed, the question is how have we “observed” that? If we have not accounted for light speed limits in a material correctly we will make an error. For example if I measure light through different media I get different speeds . How is that constant? The assumption of a constant or maximum speed comes from a bulk property analysis. It is assumed to be maximum in a vacuum. However what if it is a maximum not in a vacuum but in some other material? How will we know?

Finally what if some other phenomena is actually faster than light, but can be detected by instruments that do not rely on light or electromagnetic radiation? Neutrinos are posited as neutral electromagnetically. If they travel faster than light and we use a statistical average detection method rather than direct observation we may very well ” detect” faster than light statistical averages!

Some investigation is in order rather than dogmatism.

Trisecting an Acute Arc

Draw a circle radius r and extend its radius to 3r, by marking off r 3 times. This creates a ruler
Bisect the ruler to find the centre for a semi circle radius 1.5 r.
Draw an acute arc on the small circle and extend the side containing the arc to cut the semi circle.
Create a right triangle by these means in the semi circle. Draw parallel lines to trisect the sine length of the right triangle and extend these to the semi circular perimeter. Connect these points on the semi circle to the centre of the small circle. Where they cross the petimeter of the small circle is a good approximation to a third of the given arc.

This uses the angle subtended by an arc at the centre of the semicircle is twice that subtended at the petimeter

This approximation is less accurate the nearer the arc gets to a quarter arc, and better the nearer the arc reduces to nil turn. It is good below a 1/6th turn.

The method can be improved by using more sections, and indeed the method allows us to section an accute arc as many times as we like with increasing accuracy.

The behaviour as the arc approaches a quarter turn and as the sectioning becomes very large is interesting. There is no angle that is small enough to exist between a tangent and its intersection point on a circle! This is a proposition in the Stoikeia book 3. Thus we can not find a section that at the same time as it approaches the orthogonal radius extends outside of the circle without cutting it in 2 places.

The circle thus bounds an infinitely divisible process . The accuracy cannot be expressed in a finite ratio. When a finite ratio is found it is a special quanta and we define it as uniform, but it actually is beyond our ability to empirically determine.

Pi is transcendental precisely because it is beyond our ability to resolve it.

Pi, I and the ratio of the perimeter of a semi circle to its diameter represent the concept of a transcendental ratio, a ratio we can state but not commensurate.

Drawing a arbitrary angle and then trisecting it’s ray segments allows a triangular arallel grid to be drawn. The grid has interesting roper ties. First it houses an arc that has a ratio to a larger arc 1:3 . But the larger arc is 3 times the rotational displacement of the smaller. Thus 3 of the smaller arcs can be topologically transformed to the larger arc.
Finally three of these small arcs nestle in a close region near the large arc within an array of rhomboid forms. These forms are transacted by the large arc. This indicates that by moving the next part of the trisection to this area may give a highly accurat pair of intersection points for trisecting the larger arc. These drawn back to the angle vertex may give a good approximation to trisecting an angle.

The fascination of attempting to proportion an arc by the radial proportions and parallel lines and circle theorems , albeit approximately has led me to attempt a kissing circles design! Using the arc subtending an angle at the permeter theorem I attempt to section an arc into 6 pieces, roughly equal, by by using a kissing circle of r and 3r , and positioning the angle to be trisected at the kissing point. Sectioning g the diameter of the 3r circle into six I use parallel lines to the angle at each segment to section the arc of the 3 r circle. Using the last 2 I subtended an angle at the kissing point of approximately a third of the given angle.