Friends, [I see the list is supposed to shut down tomorrow. Very sorry about that. It has been useful. I suppose the on-line discussion of this message will be very brief, but my email address is encoded below.]
Does anyone begin reading the Data without a feeling of utter bafflement? What the heck is this thing? Where to begin? What question to ask? When I read through the definitions and some of the propositions, I feel I am being swindled, my pocket is being picked, the words do not seem to mean what they should. Let me begin with the word "given". The definitions do not seem to conform with the ordinary meaning of the word. (This is not a matter of the translation - there is no question of the appropriate translation of "dedosthai".)
Def. 1: " Areas, lines and angles are said to be given in magnitude when we can make others equal to them."
But what line can we not make a copy of?
And then we come to:
Def. 4: Points, lines and angles are said to be given in position when they always occupy the same place.
Do WHAT? Of this Heath says, "not very illuminating". Really? Simson calls it "imperfect and useless", but his perfection of it seems to me equally useless.
I must confess, this particular definition gives me the giggles. I can't help but imagine Professor Euclid in cap and gown at a blackboard drawing lines which begin to squirm and wiggle, then, breaking loose, float about the classroom, a Roger Rabbit-like vision of multicolored triangles and gnonoms fluttering about with Professor Euclid flailing at them with a pointer, shouting "stay put! you are given in position" finally batting one down and pinning it to a cork board with a pink push-pin. His pupils, meanwhile, convulsed with laughter, hide their faces in their books.
Please forgive my irreverence.
But perhaps Professor Euclid has managed to pin down one fixed datum for me. A point has no dimensions, no size, nor shape, only position. Therefore, if "given in position" is to have any meaning whatever, it must apply to a point and if "given in magnitude" or "given in form" are to have any meaning whatever, they must not apply to points.
One fixed point, while everything else seems to squirm and wiggle.
I seem to have three problems with Data, which I will attempt to express, in however muddled fashion.
I. As mentioned, the use of the word, "given", seems a verbal swindle. So let's try another word. I have tried several, "green", "hairy" but settle on "pleasant". Thus,
Prop. 2: If a pleasant magnitude has a pleasant ratio to another magnitude, the other magnitude is pleasant.
And so, Euclid works his way from one pleasant thing to another until pretty much everything is pleasant (but not everything, as Simson points out: you cannot draw a line which trisects an angle and therefore such a line is, well, unpleasant).
II. But what does it mean? Let's return to the definitions:
"Points, lines and angles are said to be pleasant in position when they always occupy the same place."
I am no better off. So I say, let's dump all the definitions in a bucket of acetone and start over:
New Def. What is given (in the ordinary sense) is pleasant. What is constructed is pleasant. So pleasant means given or constructed from given.
This leaves undefined the distinction between types of given, magnitude, shape, position.
If one is given a magnitude, what is one actually getting besides the end points? Given a magnitude and one end point, does the other end, not being fixed, whirl about, not staying in its place, but constrained by the magnitude to stay within a circle?
III. My last point, even more muddled, is "what is it for?" Both Heath and Simson insist it is useful for "solving problems". Heath (History p. 423) goes through an elaborate proof that two lines are "given", but hardly uses the data to do that, he merely constructs the lines, points to them and says they are given.
Have a pleasant day, Bob Robert Eldon Taylor philologos at mindspring dot com