What is a 'part' and why is the definition for point

because euclid's elements is shit

>>8660432
No it isn't.

t.Someone reading ancient geometrical works

>>8660375
Point is that which has no part.

To begin with, Euclid needed a fundamental unit of the plane: the point. And a fundamental unit has to have no part, because otherwise wouldn't be a fundamental unit but a derived / composed one.

>>8661724
So what do you believe 'part' to be technically defined as? Anything taking up any space?

Also, a point isn't defined as lying on the plane. It isn't until definitions 7 and 8 are reached that planes are even mentioned.

>>8661736
>What is a "part"?

A division of somehting. If something has no part, it is then undivisible.

>>8661756
But that's what Euclid defines a unit to be sometime in the fourth book or so. In Euclidean geometry, every length is composed of a number of units.

Why would a part mean the same thing? I think a part comprises everything of less length than a unit, and more than the most units. A part is anything at all, indivisibility has nothing to do with it.

>>8661761
>In Euclidean geometry, every length is composed of a number of units.

Of points.*

>length than a unit

If a length less than a unit exists, then that unit is not fundamental for length.

But by definition, the point is the fundamental unit of length. Therefore, there is no such thing as a part of a point.

>A part is anything at all

Wrong. Something is a part of a thing if and only if it constitutes a section or division of that thing.

Consider the set of all things. Clearly, it isn't the part of any thing.

>>8661783
Where does it say in Euclid that something is composed of points, not units. Please show me.
>. Something is a part of a thing if and only if it constitutes a section or division of that thing.
Again, what you're referring to is a unit, not a part.

>>8661788
Definition 3, book 1.

Now, tell me: where does it say in Euclid that something is composed of units, not points? Please show me.

>>8661794
Definition three just says the 'ends of a line are points'. Quite frankly if you wanted to say Euclid is defining points as comprising something you've hurt your overall case big time... because it looks like Euclid is denying points are even within the line itself.

>Now, tell me: where does it say in Euclid that something is composed of units, not points? Please show me
Now, it doesn't deny a claim it never makes, but Euclid asserts that the basic fundamental measure of a line is a unit through Definition one of Book VII, where he asserts that all numbers, which can essentially be viewed as lines which are multiples of units in Euclidean geometry, are composed of units.

In fact, the way that the term 'part' is used is doubly confusing because it's reiterated again in definition 1 of Book V, as a completely different definition. As a mathematician or a philosopher, this is quite an error in my opinion.

>>8661808
Lines contain points. At least two, at its ends.

>Euclid is defining points as comprising something

Wrong, Euclid defined 'point' in Definition 1.

>Euclid is denying points are even within the line itself.

False. He stated the opposite of that. The ends of a line are points.

Again wrong. Definition 1, book VII:

"A unit is that by virtue of which each of the things that exist is called one."

Don't make things up, lad.

By the way, the meaning of 'part' is the same on both definitions.

>>8661849
Alright so we are dealing with three counterclaims here

1. By defining a line to start and end with a point, you are stipulating all lines are comprised of infinite points.

2. A slight mistake on my part admittedly in not defining the scope of my inquiry on defining units to not only consist in the first definition of Book VII but also the second.

3. A part is the same in the First and Fifth book.

Now first up is one. I certainly don't think this was Euclid's aim nor intention in stating things this way. I think the infinitesimal nature of points certainly exists, but since it is a non-issue in Euclidean geometry why even bring it up? It's something you may infer if you want to, but if Euclid's intention was to say a line is composed of points, he should have done so.

Two. I am at fault for the misnomer of the definition used, but the point I made is clear, and it's what you wanted: that all lines in Euclid's framework are composed of units.

Three. You are asserting that a part in the fifth book is same as the definition of a part in the first book. I will concede this point to you, I believe it makes sense.

>>8661866
>1. By defining a line to start and end with a point, you are stipulating all lines are comprised of infinite points.

Not me, but rather, Euclid.

>if Euclid's intention was to say a line is composed of points, he should have done so.

He didn't need to. That is implied from the definitions he gave (at least for the case of straight lines, and once division of lines in N-line segments is defined and introduced).