@geeoddmike sounds like you are thinking of "assumed north". There are an infinite number of ways of assigning coordinates to a point. US Surveyors often use State Plane, others use equivalent systems, or UTM derived systems which are related to the elipsoid, but surveors were using coordinates long before these were invented.
All that is required is to pick an origin and chose how to define north and you have a coordinate system.
I beg to differ. The Cartesian coordinate system was first presented by Rene Descartes in 1637. In the coordinate pair (x, y), the value of y is the ordinate and the value of x is the abscissa. Descartes' terms in French were applicata and ordonnees which translate to abscissa and ordinate in English.
In a typical geodetic plane coordinate system, North is the y-axis and East is the x-axis. Thus a coordinate pair is (E, N), E is the abscissa and N is the ordinate. (We really should say Eastings and Northings instead of the other way round.)
In early NGS papers, and in some surveying software today, x and y were and are used instead of E and N.
Now whether Decartes stole the Cartesian coordinate system from surveyors or whether surveyors adopted the system from Decartes may be open to investigation.
The abscissa is a specific type of ordinate, the same as a height.
I'm just repeating what the man who invented the system said.
But to get really fundamental, a plane cartesian system is created by the intersection of two number lines in a right angle. Every point on any number line is a coordinate. For example:
|---------|---------|---------|----->
0 1 2 3
the points on the number line are coordinates. Thus, 1 is a coordinate, 2 is a coordinate, and 3 is a coordinate. All of the points both between and beyond the marked ones, both rational and irrational, are coordinates as well.
Note that there's only one number associated with each coordinate.
When a vertical number is added to create the Cartesian plane, the points on the vertical line are also coordinates, but now coordinates on both lines contain two numbers. The coordinate 2 on the horizontal line is now (2, 0), but it's still a coordinate.
Adding a third number line perpendicular to each of the first two creates a 3-dimensional system, but the points on that third line are also coordinates. In that system, the coordinate of the 2 on the horizontal line is (2, 0, 0).
So, just as it is correct to say the x-coordinate, which is just the distance from the vertical number line to the point, it is also correct to say the Northing-coordinate.
5000,5000,100
Yea, that backsight looks to be about N45°W !
The Cartesian coordinate system was first presented by Rene Descartes in 1637.
You've piqued my interest. Was Descartes development his alone, or is it like much of the Renaissance period before Descartes, a rediscovery of Greek math principals?
I haven't had time to research it so I figured you can be Wikipedia for me.
The pre-Descartes history is sketchy but there were apparently forerunners, or at least giants on whose shoulders Decartes could have stood.
The old story is that Decartes was lying in bed watching a fly crawl on the wall when he thought of a way to represent the fly's position on the wall using the four corners of the room for reference.
An old British encyclopedia of mathematics that I have says that Decartes' original system did not employ two axes and that the system was actually refined into usability by Gauss and others.
I also looked at archaelogical grid history and found that their first documented use was in the 1920s. That's interesting since it roughly corresponds to the map projections that later became state plane systems.
I'm fascinated by how different professions modify the same concept for use in their work. Surveyors calculate angles (azimuths) from the y-axis while mathematicians calculate angles (slopes) from the x-axis. Surveyors find it useful to confine their coordinate systems to Quadrant I while mathematicians find value in using all 4 Quadrants.
But the theoretical foundations of the concepts remain the same.
@mathteacher Your first example is of a single line. The other 'ordinate' is the value of the baseline, presumably zero.
The concept of ordinates (and the term) date to at least the late 14th century. I suspect the concept was understood long before that, but Descartes was a latecomer discoverer. He absolutely was the earliest widely know publisher, but the concept was there and in use long before he came along.
My apologies for the THRAC, I recognize I occasionally get hung up on things like this. I'd like to say that will change, but it's unlikely..
I certainly won't argue the history; that's for academicians. Undoubtedly there were earlier forms and the coordinate plane was not complete until Gaus and Fermat added their contributions.
But let me ask you this: Ia (10000, 10000) the coordinates of a point or the coordinate of a point? If you answer the fromer, why is the word plural?
@mathteacher In practical terms, I would disect it. Ordinates (plural), Co (together).
That logic certainly butchers some language rule, somewhere. That's one reason I prefer elementary math. Basic truths don't change every other day...
Nothing about the coordinate plane has changed in a long, long time.
(10000, 10000) are the coordinates of the point. They are an ordered pair always presented in the same order, with the x-coordinate appearing first and the y-coordinate appearing second. The x-coordinate is also known as the abscissa and the y-coordinate is also known as the ordinate.
My example above included only one line in order to emphasize that each point on a number line has a coordinate ... one number, one coordinate.
But don't take my word for it. Google the term "coordinate pair".
Then look at the first few pages of Chapter 2 here:
Then look at Page 47 here:
It's also interesting to research what a data collector does when asked to establish a (5000, 5000) coordinate system based on a GNSS point.
Enjoying this one. Appreciating the mutually respectful dialog (dialogue).
@field-dog I have seen some instances where people have used negative coordinates.
