Geometry Described in Euclid’s Elements. /1

Construction of an equilateral triangle on a given finite straight-line, reconstruction of a given finite straight-line at a given point.

Foreword.

Some books speak for themselves. Without further ado, readers know what they are about. Definitely, Euclid’s Elements, which until the XX century backed down primacy only to Holly Bible, belongs to them. The book was the most used textbook to study mathematics for over 2000 years. It tells a lot.

Galileo Galilei had used stored-in knowledge across all his works.

Abraham Lincoln kept a copy on his bookshelf. For every trip, he packed it in his saddlebag to study it at nights within lamplight.

Albert Einstein had said that along with his compass, it was the best gift he got as a child.

And, no surprise. After all, Euclid’s Elements treats mostly of geometry, which reminds Lego just of self-made interlocking bricks. Who does not like to build out of imagination? With geometry, the limit is your mind.

Let’s go and have some fun building these bricks!

I. Construction of an equilateral triangle on a given finite straight-line.

Draw a finite straight-line AB.

Construct a circle BCD of radius AB and center at point A.

Construct a circle ACE of radius BA and center at point B.

Recombine both circles together. A notion, C must be the intersection point of the circles.

Draw straight-lines from C to A and B.