<dt>Simplicius </dt> 
    <dd>According to the straight line AF,
	and not according to the curve, such being already excluded
	for such a use.</dd>

	<dt>Sagredo </dt> 
    <dd>But I should take neither of them,
	seeing that the straight line AF runs obliquely. I should
	draw a line perpendicular to CD, for this would seem to me
	to be the shortest, as well as being unique among the
	infinite number of longer and unequal ones which may be
	drawn from the point A to every other point of the opposite
	line CD. </dd>

	<dt>Salviati </dt> 
    <dd><p> Your choice and the reason you
	adduce for it seem to me most excellent. So now we have it
	that the first dimension is determined by a straight line;
	the second (namely, breadth) by another straight line, and
	not only straight, but at right angles to that which
	determines the length. Thus we have defined the two
	dimensions of a surface; that is, length and breadth. </p>

	<p> But suppose you had to determine a height -- for
	example, how high this platform is from the pavement down
	below there. Seeing that from any point in the platform we
	may draw infinite lines, curved or straight, and all of
	different lengths, to the infinite points of the pavement
	below, which of all these lines would you make use of? </p>

	<dt>Sagredo </dt> 
    <dd>I would fasten a string to the
	platform and, by hanging a plummet from it, would let it
	freely stretch till it reached very near to the pavement;
	the length of such a string being the straightest and
	shortest of all the lines that could possibly be drawn from
	the same point to the pavement, I should say that it was the
	true height in this case.</dd>

    <dd>Very good. And if, from the point on
	the pavement indicated by this hanging string (taking the
	pavement to be level and not inclined), you should produce
	two other straight lines, one for the length and the other
	for the breadth of the surface of the pavement, what angles
	would they make with the thread?</dd>

	<dt>Sagredo </dt> 
    <dd>They would surely meet at right
	angles, since the string faIls perpendicularly and the
	pavement is quite flat and level.</dd>

Previous | Next | Top | Cafe con Leche

Copyright 2007 Elliotte Rusty Harold
Last Modified March 5, 2007