For centuries, the mental midgets who came before me could not understand the purpose of constructions as used by Euclid. These constructions are merely a means of communicating the perfect ideas in geometry. Proposition 1 states: Given any SHORTEST distance between two points A and B, it is possible to DERIVE a geometric object (known commonly as a triangle) with an extra point C, such that the distance between point A and C is the SAME as the distance between C and B which is the same as the distance between A and B. Can you see now why it is useful to talk about these perfect ideas with diagrams? We would become very verbose and have to imagine these things in our mind without the diagrams or constructions. My free eBook which is the most important mathematics book ever written explains all these things and much more. You will be dazzled! Download it now! https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view ... https://www.youtube.com/watch?v=Q__2I3d6KM0

The mainstream academic understanding of number is based mostly on the flawed concept of distance to number correspondence. It is delusional to think that assigning a symbol such as π to a calibrated marker means the same as a valid name for the measure of the distance. There is no formula or series that ever produces anything but a "rational number" approximation for π. In reality, there is no such thing as a "real number line" because there is no such thing as a "real number". In order to be a number, the measure must be rational because there is no "irrational measure". Chuckle. ALL numbers come from ratios. There is no number which is not a rational number. To be a number the initial ratio must be rational. Duh! A number is a NAME given to a MEASURE that describes a MAGNITUDE or SIZE (such as distance, mass, area, density, etc). Link to applet used in video: https://drive.google.com/file/d/19VuxeI2JNx1w96rSV6KCpYTb-tZkaQGG Link to article used in video: https://drive.google.com/drive/folders/0B-mOEooW03iLcmRkcUwweXRUckE ... https://www.youtube.com/watch?v=zeqk1KdCVzI

Synopsis: I discuss the proof of proposition 1 which Archimedes assumed. The actual proof was part of a book on conics which predated Euclid and was lost in the great fire of the library in Alexandria, Egypt along with so many other texts. I provide a geometric proof because none of the theorems of calculus were known to Archimedes over 2000 years ago. Download the most important mathematics book ever written here. It's free! https://drive.google.com/file/d/1CIul68phzuOe6JZwsCuBuXUR8X-AkgEO/view ... https://www.youtube.com/watch?v=AyZVb-n4yO8

Book 2, Proposition 12 would also be unremarkable if it did not give rise to more circular geometry known as trigonometry. In particular, well known formulas such as sine and cosine. The proposition is a variation on Pythagoras and many will say that Pythagoras is just a special case of the proposition which is true, however, the latter would not have been realised without the discovery of the Pythagorean theorem first. Link to applet used in video: https://drive.google.com/file/d/1ZmIK7LTBBUufeVvyb6QGIABjEwnGEMYJ A 12-minute introduction to trigonometry: https://youtu.be/0ue6x3Tzz10 Articles: https://drive.google.com/drive/folders/0B-mOEooW03iLUUlFR0ZwMjNNVjg Applets: https://drive.google.com/drive/folders/0B-mOEooW03iLd1Z2cVRtOElpYms LinkedIn articles: https://drive.google.com/drive/folders/0B-mOEooW03iLcmRkcUwweXRUckE My Historic Geometric theorem - A general derivative formula for all smooth functions: https://drive.google.com/file/d/1RDulODvgncItTe7qNI1d8KTN5bl0aTXj Explaining the historic identity: https://drive.google.com/file/d/1sjs3eZJZnwI6caaUA1MtC7FhNYSLfICZ Applet: Derivative through geometry: https://drive.google.com/file/d/1ON1GQ7b6UNpZSEEsbG14eAFCPv8p03pv Greek Language Applet: https://drive.google.com/file/d/120g3VfFFqAzyZWHzHljXZYuWYpl5kUDB Fixing the broken maimstream formulation of calculus: https://drive.google.com/file/d/1uIBgJ1ObroIbkt0V2YFQEpPdd8l-xK6y Applet: Integral through geometry: https://drive.google.com/file/d/1JYRxjGb3MxlYWp_2KqVXwXNr5XUvUNz7 Greek Language Applet: https://drive.google.com/file/d/1iG5Oc7pV3x3AIVcz6Cpd4x5UavYMwhhp There are no axioms or postulates in Greek mathematics: https://drive.google.com/file/d/1vlU-PJeIk672bFwZyULD1ASTRFF3jXg8 Greek Language - What they couldn't tell you because they did not know: https://drive.google.com/file/d/1p8wSD7qu5fgHG7vAYTuRdUWt5JAMN1Qg ... https://www.youtube.com/watch?v=B1jNkN3Y7gI