#### TH Dialectic

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I would like to take you through some information on the 6th stem of the liberal arts, geometry. We will look at how it has been applied in our objective world and how it has been twisted by sophisters to support their unrealistic claims. Please understand that I am not professing to know anything other than what we are not.

Let’s start with few definitions and a certain Mathematician.

Euclid 1500 years ago, Euclid’s Elements was one of the first books to start defining first principles based on definitions and axions. So 4 axioms were created as a base. The book it self was first translated to English around 17th century (questionable) This is the mathematical bible, its the foundations of mathematics and geometry, if anything in euclidian geometry fails, it all fails! It is the main pillar in geometry.

Let the following be postulated (never deduced):

These are facts in our objective existence, non of the above postulates can be deduced when applied practically here on “Earth” so we have starting blocks. Architects and engineers have always worked from Euclidean plane geometry. Plumb and Datum lines can only work using Euclidean first principles. Our objective dualistic world is built using the aforementioned, this is the only geometry we use here on "Earth". Surveyors are never required to factor the supposed curvature of the Earth into their projects. Canals and railways, for example, train lines are always cut and laid horizontally for often over hundreds of miles without any allowance for curvature. We have fences that run for miles and miles built using plumb and datum lines.

J.C. Bourne in his book, “The History of the Great Western Railway” stated that the entire original English railroad, more than 118 miles long, that the whole line with the exception of the inclined planes, may be regarded practically as level. The British Parliament Session in 1862 that approved its construction recorded in Order No. 44 for the proposed railway,

In surveying,

Triangulation can also refer to the accurate surveying of systems of very large triangles, called triangulation networks. This followed from the work of

The knowledge of the triangle is an essential piece of this puzzle. Triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and the directing of weapons.

The use of triangles to estimate distances dates to antiquity. In the 6th century BC, about 250 years prior to the establishment of the Ptolemaic dynasty, the Greek philosopher

Imagine if I drew a triangle on a piece of paper, everyone knows that all of the interior angles equate to 180° and no matter how I orientate the paper, no matter which way you turn the paper all said interior angles remain the same.

If I sew to draw a triangle on a deflated balloon, and the proceed to blow up the balloon, the bigger the balloon becomes, the properties of the triangle will change; the bigger the balloon, the bigger the angles become.

There is no such thing in spherical geometry as congruency. Using Euclidian postulates, if I draw a small triangle and a large triangle I can scale them, all angles will remain the same. No matter how big the triangle becomes comparative to the other triangle, they are congruent. But when applied to a 3 dimensional ball the angles dramatically change!

We have to understand that objective practical mathematics is what rings true, formal mathematics is absolute nonsense. At some point maths as a useful tool was formalised to a language that only mathematicians supposed to understand. Maths was formalised to confuse, the change of mathematics to algebra changes mathematics to a formal language, there is absolutely no doubt in my mind that practicality and the application of practical mathematics would come before the formal arts of applying numbers to letters!

Let’s look at how we use our experience to come to conclusions, we take a bunch of axioms or assumptions and then deduce everything that doesn’t work with practical experimentation to come to the reality of our objective world.

Inductive reasoning is where we are today, stuck with physicists and astronomers who hold modern nihilistic educations, splurting hypothesise and more general theorems making it impossible to prove them wrong, as long as you can’t prove it wrong, its true! Madness.

To conclude, the whole world has been built using the aforementioned elements of goemetry. They are universal ideas, universal ideas are universal truths, such truths one can’t deduct from their existence. Things which are equal to the same thing are also equal to one another. If equals be added to equals, the wholes are equal. If equals be subtracted from equals, the remainders are equal. Things which coincide with one another are equal to one another.

The latter section of the above diagram (Geometry of Physical Space) constitutes to our real objective world, the former (Geometry of Visible Space) delves in to the realms of subjectivity.

TH

**Geometry is all about measurement.**

*“Latin geometria, from Greek geometria "measurement of earth or land; geometry," from combining form of gē "earth, land" (see Gaia) + -metria "a measuring of" (see -metry). Old English used eorðcræft "earth-craft" as a loan-translation of Latin geometria”.*Let’s start with few definitions and a certain Mathematician.

*Euclid**-**Euclid - Wikipedia*Euclid 1500 years ago, Euclid’s Elements was one of the first books to start defining first principles based on definitions and axions. So 4 axioms were created as a base. The book it self was first translated to English around 17th century (questionable) This is the mathematical bible, its the foundations of mathematics and geometry, if anything in euclidian geometry fails, it all fails! It is the main pillar in geometry.

Let the following be postulated (never deduced):

*1. To draw a straight line from any point to any point.***2. To produce [extend] a finite straight line continuously in a straight line.****3. To describe a circle with any centre and distance [radius].***4. That all right angles are equal to one another.*

*5. [The parallel postulate]: That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which the angles are less than two right angles.***Number 5**has been manipulated over the years, it is how things have been twisted with hypotheses, people have changed the meaning of a straight line, fabricating things like the bending of space time, hyperbolic geometry etc. If you can change the definition of a straight line you can hypothesise anything. So let's stick with the first 4 and use them as undeniable proofs.These are facts in our objective existence, non of the above postulates can be deduced when applied practically here on “Earth” so we have starting blocks. Architects and engineers have always worked from Euclidean plane geometry. Plumb and Datum lines can only work using Euclidean first principles. Our objective dualistic world is built using the aforementioned, this is the only geometry we use here on "Earth". Surveyors are never required to factor the supposed curvature of the Earth into their projects. Canals and railways, for example, train lines are always cut and laid horizontally for often over hundreds of miles without any allowance for curvature. We have fences that run for miles and miles built using plumb and datum lines.

J.C. Bourne in his book, “The History of the Great Western Railway” stated that the entire original English railroad, more than 118 miles long, that the whole line with the exception of the inclined planes, may be regarded practically as level. The British Parliament Session in 1862 that approved its construction recorded in Order No. 44 for the proposed railway,

*“That the section be drawn to the same HORIZONTAL scale as the plan, and to a vertical scale of not less than one inch to every one hundred feet, and shall show the surface of the ground marked on the plan, the intended level of the proposed work, the height of every embankment, and the depth of every cutting, and a DATUM HORIZONTAL LINE which shall be the same throughout the whole length of the work.”***Let us move on to some more objective proofs, using Euclidian postulates.**In surveying,

**triangulation**is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly as in trilateration. The point can then be fixed as the third point of a triangle with one known side and two known angles.Triangulation can also refer to the accurate surveying of systems of very large triangles, called triangulation networks. This followed from the work of

**Willebrord Snell**in 1615–17, who showed how a point could be located from the angles subtended from three known points, but measured at the new unknown point rather than the previously fixed points, a problem called resectioning. Surveying error is minimised if a mesh of triangles at the largest appropriate scale is established first. Points inside the triangles can all then be accurately located with reference to it. Such triangulation methods were used for accurate large-scale land surveying until the rise of global navigation satellite systems in the 1980s.The knowledge of the triangle is an essential piece of this puzzle. Triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and the directing of weapons.

The use of triangles to estimate distances dates to antiquity. In the 6th century BC, about 250 years prior to the establishment of the Ptolemaic dynasty, the Greek philosopher

**Thales**is recorded as using similar triangles to estimate the height of the pyramids of ancient Egypt. He measured the length of the pyramids' shadows and that of his own at the same moment, and compared the ratios to his height (intercept theorem).**Thales**also estimated the distances to ships at sea as seen from a clifftop by measuring the horizontal distance traversed by the line-of-sight for a known fall, and scaling up to the height of the whole cliff. Such techniques would have been familiar to the ancient Egyptians. Problem 57 of the Rhind papyrus, a thousand years earlier, defines the seqt or seked as the ratio of the run to the rise of a slope, i.e. the reciprocal of gradients as measured today. The slopes and angles were measured using a sighting rod that the Greeks called a dioptra, the forerunner of the Arabic alidade. A detailed contemporary collection of constructions for the determination of lengths from a distance using this instrument is known, the Dioptra of Hero of Alexandria (c. 10–70 AD), which survived in Arabic translation; but the knowledge became lost in Europe. In China, Pei Xiu (224–271) identified "measuring right angles and acute angles" as the fifth of his six principles for accurate map-making, necessary to accurately establish distances; while Liu Hui (c. 263) gives a version of the calculation above, for measuring perpendicular distances to inaccessible places.**Here is why triangulation doesn’t work on their fantasy sphere …**

If I sew to draw a triangle on a deflated balloon, and the proceed to blow up the balloon, the bigger the balloon becomes, the properties of the triangle will change; the bigger the balloon, the bigger the angles become.

There is no such thing in spherical geometry as congruency. Using Euclidian postulates, if I draw a small triangle and a large triangle I can scale them, all angles will remain the same. No matter how big the triangle becomes comparative to the other triangle, they are congruent. But when applied to a 3 dimensional ball the angles dramatically change!

**TRIANGULATION DOESN’T WORK ON A SPHERE**

****

__Deduction vs Induction__Inductive reasoning is where we are today, stuck with physicists and astronomers who hold modern nihilistic educations, splurting hypothesise and more general theorems making it impossible to prove them wrong, as long as you can’t prove it wrong, its true! Madness.

**Deduction from axioms or known facts is what the world is built on, not inductive ideas that we cant prove or disprove.***"Despite the man’s awkward gestures, unkempt hair, and ill-fitting suit, it was one of the most extraordinary speeches that Reverend John Gulliver had ever heard. It was March 1860, and the venue was Norwich, Connecticut. The following morning Gulliver struck up conversation with the speaker, a politician by the name of Abraham Lincoln, as he caught a train down to Bridgeport.**As the pair took their seats in the carriage, Gulliver asked Lincoln about his remarkable oratory skill: “I want very much to know how you got this unusual power of ‘putting things.’ ” According to Gulliver, Lincoln said it wasn’t a matter of formal education. “I never went to school more than six months in my life.” But he did find training elsewhere. “In the course of my law-reading I constantly came upon the word demonstrate,” Lincoln said. “I thought, at first, that I understood its meaning, but soon became satisfied that I did not.” Resolving to understand it better, he went to his father’s house and “staid there till I could give any propositions in the six books of Euclid at sight.”**He was referring to the first six of books of Euclid’s Elements, an Ancient Greek mathematical text. On the face of it, Euclid’s Elements was nothing but a dry textbook: There were no illustrative examples, no mention of people, and no motivation for the analyses it presented. But it was also a landmark, a way of constructing universal truths, a wonder that would outlast even the great lighthouse in Euclid’s home city of Alexandria.*

**Elements proposed that definitions were at the foundation of knowledge, and led to self-evident axioms that needed no proof. From these definitions and axioms, Euclid showed how to prove dozens of mathematical propositions, producing knowledge that was objective and undeniable. A person of reason would have to accept a proven fact, no matter what their personal beliefs or convictions were.**

**Elements would become a best-selling work, second only to the bible in printed editions,**and used**as the standard text for mathematics classes. It profoundly influenced Western thought, and shaped Western science and art. What’s less recognised is its role in the creation of modern politics: The distance from proofs about equilateral triangles to the foundations of democracy in Europe and the United States turned out to be just about two millennia."**__until recently__**- Carpenter, F.B.***The Inner Life of Abraham Lincoln: Six Months at the White House*Hurd & Houghton, New York, NY (1874).To conclude, the whole world has been built using the aforementioned elements of goemetry. They are universal ideas, universal ideas are universal truths, such truths one can’t deduct from their existence. Things which are equal to the same thing are also equal to one another. If equals be added to equals, the wholes are equal. If equals be subtracted from equals, the remainders are equal. Things which coincide with one another are equal to one another.

TH

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