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Logic within Geometry
Have You Realised Euclid Yet?
Realising Euclid is the realisation that our reality is entirely Euclidean, we all live in a 3D space - that isn't as complicated as some might try to make it. With simple to understand terms and bringing an introduction to logical processes, let logic and geometry guide you in the lost ways of learning that have helped so many of us to realise Euclid as the missing link between logic, reality and understanding.
Realising Euclid
The blue marble induced Horizontal Paradox
Obviously horizontal planes exist in reality.
So why do some people get so upset at hearing that level is a straight line on a horizontal plane?
Finding these people is what led us to realise that simplifying everything down to it's most basic form and building up from there, is what was needed to fully understand.
Taking the first principles approach to even the most simple task is what we call ADVANCED SIMPLICITY and it's how we assure ourselves that WE fully understand what it is that we are speaking of.
The Horizontal Paradox is an ideal introduction to Advanced Simplicity and it goes like this;
A plane is a geometric concept that is 2D, that means it has only 2 dimensions, length and breadth, it has no edges and therefore is infinite.
A plane is well defined and understood as the base for understanding geometry within the foundations our learning process, but have we ever really considered such simple things at the basis of our own thought processes?
There are proofs within geometry that can give you an understanding of these basics, but what's important is that you know they are there for you to find. The picture to the right is A page from a book called 'The Elements' it is a series of proofs and theorems that guide to find truth.
This one proposition (along with all the others preceding it) lets us know that all perpendiculars to a plane will be parallel, knowing this may cause cognitive pain at some point if a contradiction is pointed out.
Here's the contradiction; for some people, placing this plane in the horizontal position becomes a problem for the reason stated above - horizontals being parallel is a big problem.
The Horizontal paradox is only a paradox when a model is introduced, and once introduced how do you resolve the contradiction? How would you resolve a contradiction? How can you resolve the contradiction?
Welcome to Advanced Simplicity and On The Level Thinking.
Euclids Elements Book 11 Proposition 6
Get Real
Advanced Simplicity and Realising Euclid
In order to explain anything it's always good to know everyone understands the terms (words and their meanings) we will be using.
Obviously being a perfect axiomatic system everything within the Elements applies always but I've picked out a few of the basics that we will be using to help us #RealiseEuclid
Book 1
Definition 5. - A superficies is that which has only length and breadth.
6. The extremities of a superficies are lines.
7. A plane superficies is that in which any 2 points being taken, the straight line between them lies wholly in that superficies.
8. A plane angle is the inclination of 2 lines to one another in a plane, which meet together, but are not in the same direction.
9. A plane rectilinear angle is the inclination of 2 straight lines to one another , but are not in the same straight line.
10. When a straight line standing upon another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called perpendicular to it.
35. Parallel lines are such as are in the same plane and which being produced ever so far both ways, do not meet.
Postulates
1. That a straight line may be drawn from 1 point to another.
2. That a terminated straight line may be produced to any length in a straight line.3. And that a circle may be described from any centre, at any distance from that centre.
Propositions
I'll list them here and they will be viewable in the picture library below:
Book 1
11. (for corollary), 12, 13, 14,15, (27, 28, 29) 30.
Book 11
Definition 3. A straight line is perpendicular, or at right angles to a plane when it makes right angles with every straight line meeting it in that plane.
4. A plane is perpendicular to a plane, when the straight lines drawn in one of the planes perpendicular to the common section of the two planes, are perpendicular to the other plane.
8, Parallel planes are such as do not meet though produced.
Propositions
Can be seen below but listed here for reference;
1, 2, 3, 4, 5, (6, 7, 8,) - 9, 14.
