It is difficult to read or understand Euclid without letting our current knowledge get in the way. For example, we started talking about points and planes and lines, and just as easily the conversation turned over to third dimensions and second dimensions etc (I don't even know if Euclid knew about dimensions). I think that to truly understand Euclid we have to think as if we are someone who has no past knowledge of mathematics, geometry, algebra and all of the other kinds of math, someone who lived in the time when Euclid lived. Maybe then we will be able to comprehend it without our knowledge getting in the way. (isn't it ironic how we have to let go of our knowledge to comprehend something?)
I also find Euclid difficult to comprehend, maybe because of the same reasons I mentioned before, because I also find Euclid to be vague about some ideas. Like his definition of a point, in which he says that a point is that which has no part. What is he talking about there? It has no part… It isn't until you read more ahead that you understand that the point is the extremity of a line, and that a line can't exist without points at its extremities. But is this actually saying that a line can't exist without the point or that the point can't exist without the line?
So you have to go back to the first definition of a point, it has no part.. still, I don't understand. some people were saying that it meant that the point was the origin of something (a line), but it doesn't quite convince me.
Reading the rest of Euclid's definitions, it became a little less confusing. I can grasp the idea of what a line is, of what a surface is and of what a circle is. I also understand each of these in their different types, like a straight line or just a regular line. But I always keep going back to what a point is. Can all of these mentioned before exist without a point? Well, I don't think so. Then again, What is a point? Im starting to think this is just one of those really abstract questions that can't be truly answered and that everyone has their own idea based on their perspective.
I am just hoping that the rest of Euclid's Elements is not as complicated as these definitions. Thank you Euclid!
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