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In the book "Calculus Made Easy" by Silvanus Thompson, in the Chapter 5 ("Next Stage. What To Do With Constants"), Thompson says (about the graph of an equation $ y = 7x^2 $ and the graph of $ \frac {dy}{dx} $, that:

Carefully compare the two figures, and verify by inspection that the height of the ordinate of the derived curve, Fig. 6a, is proportional to the slope of the original curve, (See here about slopes of curves.) Figure 6, at the corresponding value of x. To the left of the origin, where the original curve slopes negatively (that is, downward from left to right) the corresponding ordinates of the derived curve are negative.

What does he mean by "height of the ordinate of the derived figure"? The relevant section of the book can be found here: Calculus Made Easy: Chapter 5.

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    $\begingroup$ The abscissa and ordinate are, respectively, the $x$- and $y$-coordinates of a point. $\endgroup$ Nov 27, 2018 at 21:48
  • $\begingroup$ @WorldGov you asked a question relating to ordinate and abscissa 2 months ago? Did you forget haha math.stackexchange.com/questions/2931954/… $\endgroup$
    – user29418
    Nov 27, 2018 at 22:25
  • $\begingroup$ @user29418 I do! I was just confused because he used "height of the ordinate" instead of just saying "ordinate". For example, "height of the y-coordinate" sounds weird. $\endgroup$
    – WorldGov
    Nov 27, 2018 at 22:47

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Ordinate is an old-fashioned way of saying $y$-axis or $y$-value.

The $x$-value is called abscissa.

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    $\begingroup$ o, that's why it's called a co - ordinate $\endgroup$
    – user29418
    Nov 27, 2018 at 22:00
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    $\begingroup$ @user29418 I didn‘t make that connection, neat! Makes me wonder why it‘s not co-abscissa though. $\endgroup$
    – bsbb4
    Nov 27, 2018 at 22:20
  • $\begingroup$ I should have mentioned this in the question. I know this, but why did he say "height of the ordinate" instead of just saying "the ordinate". I mean, we don't usually talk about the "height of the y-coordinate" do we? Is there something to this? Or am I just reading too much into it? $\endgroup$
    – WorldGov
    Nov 27, 2018 at 22:48

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