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Category Archives: Elucidating Euclid

Elucidating Euclid 33

Fitz Common Notions 5. And the whole is greater than the part. Scope A point is that which has no parts.  Yeah, we got that.  Okay, well, a whole is greater than the part.  Ha! Do you see it?  Book ends!  I missed it myself at first.  I’ll share the analytical path I first completed […]

Elucidating Euclid 32

Fitz Common Notions 4. And things coinciding with one another are equal to one another. Scope Every parts-free point in the world is precisely equal to, and absolutely coincides with every other parts-free point.  If you superimpose one on top of another, you will see only one point afterwards due to the fact of their […]

Elucidating Euclid 31

Fitz Common Notions 3. And if equal things are subtracted from equal things then the remainders are equal. Scope In studying for today’s essay, I was able to find the mathematician’s reason as to why the Taylor/Proclus list of axioms has 10 elements, whereas our Fitz translation offers only 5.  The mathematical reason is that […]

Elucidating Euclid 30

Fitz Common Notions 2. And if equal things are added to equal things then the wholes are equal. Scope Step by tiny step.  Equal things.  I’m thinking line segments for this one.  We have two equal line segments to begin. Are added…we get that, right? To equal things.  A second set of line segments, equal […]

Interlude: points, lines, parallels and music…

My laptop computer – it was ancient – died this morning.  I’m composing this little essay on my tablet, which, while I wait for my new laptop, I’ll likely get to know a good deal better. Fortunately, my son Nico backs up all the stuff I do, so that as soon as my new snazzy, […]

Elucidating Euclid 29

Fitz Common Notions 1. Things equal to the same thing are also equal to one another. Scope First here’s what we’re not going to do.  We’re not going to use algebra, or algebraic notation to explain this.  Consider, Euclid has by now lain down 23 definitions and 5 postulates charging us to construct things under […]

Elucidating Euclid 28

Fitz – Nope, Scope is rewriting this one completely… Postulates 5. And I’ll use letters for the parts: A. We begin with a straight line. B. It crosses over – that is, it intersects – two other two straight lines, all three lines laying on a single plane surface. C. In doing so, the internal […]

Elucidating Euclid 27

Fitz Postulates 4. And that all right-angles are equal to one another. Scope We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. It’s possible, if you’re not an American, […]

Elucidating Euclid 26

Fitz Postulates 3. And to draw a circle with any center and radius. Scope Freedom.  Think about it.  Any center, any radius.  Hey wait, what’s a radius? Aha!  Either our translator, the translating tradition, or our master himself has slipped in a new term without a definition.  Wow; that’s huge! Okay, I need to get […]

Elucidating Euclid 25

Fitz Postulates 2. And to produce a finite straight-line continuously in a straight-line. Scope So here we go with a preposition.  In.  We’re commanded to produce a finite straight line continuously IN a straight line.  What in tarnation is that supposed to mean? In my daily research, I think I found the answer.  It begins […]