Subject: [HM] Old text books
From: Don Cook (tdctdc@surfsouth.com)
Date: Wed Jan 26 2000 - 01:45:43 EST
Dear All,
Karen Dee Michalowicz wrote:
> It is also interesting to see when coordinate graphing appears in
> U.S. texts. One would assume that they would appear in algebra high
> school texts. Yes, they do, but not until the 1910's in high
> school algebra books. Coordinate graphing does appear in the middle
> l800's in college analytical geometry texts. But, the coordinates
> are not at right angles.
Coordinate graphing is earlier than that:
Day's book is my favorite because he discusses philosophy instead of
merely a statement of rules. He does right angle coordinate graphing,
except he doesn't have numbers on the axis. I have limitations of email,
but let's try to derive the equation of a circle. Draw the circle FGMN
with the diameters GN (vertical) and FM (horizontal) perpendicular to
each other. Let A be the center and D a point on the arc GF.
Now quoting:
"From any point in the curve, draw the ordinate DB perpendicular to AF;
and AB will be the corresponding abscissa. Let the radius AD = r, AB = x,
BD = y. Then by Euc.47.1 (Legendre, 186), (BD)^2 =(AD)^2 - (AB)^2 [note:
a vinculum is used in the text rather than ()]
That is y^2 = r^2 - x^2
And by evolution y = +- Sqr(r^2 - x^2)
In the same manner x = +- Sqr(r^2 - y^2)
...
If the radius of the circle be taken for a unit, its square will also be
1, and the last two equations will become
y = +- Sqr(1 - x^2) and x = +- Sqr(1 - y^2)
...
To understand the applications to the other quarters of the circle ...
The values of x and y may be either positive or negative. ... In the
first quarter GF, the co-ordinates are supposed to be both positive.
In the second, GM, the ordinates are still positive, but the abscissa
becomes negative."
The book has a copyright "BE IT REMEMBERED, That on the Thirteenth day
of March, in the fifty-first year of Indepeneence of the United States
of America..."
Peace,
Don Cook
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