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I'm sure his has a general form and welcome a link to a duplicate, but as I don't quite know what to search for, here goes.

Whilst answering a question on the Mathematics Stack Exchange, I found myself needing to say the mid point of one diagonal of a rectangle is coincidental with the mid point of the other and that that point is the centre of the rectangle. So I said:

"The key is to prove that for all rectangles, the mid points of the diagonals are coincidental at the centre of the rectangle ..."

It suddenly struck me that the correct form might have been:

"The key is to prove that for all rectangles, the mid point of the diagonals are coincidental at the centre of the rectangle ..."

I suspect this is related to "everyone took off his hat".

Could someone explain the reasoning behind the correct form.

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FWIW, I would write midpoint, not mid point, and I would say that the points coincide instead of saying that they are coincidental.

And I would definitely write midpoints of the diagonals, even if midpoint of the diagonals can be tolerated.

Why? Because the latter can be read as asserting that there is a single midpoint for both diagonals, IOW, asserting just the claim to be proved. That is not how you want it to be read, but it is possible to read it that way. Eliminate this ambiguity.

IOW, the context is Math, not just English. That the midpoints of two different line segments are in fact the same point is not obvious a priori. And it is precisely what is to be proved.

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  • Another case of wording around the ambiguity, indeed. – stevemarvell Aug 1 '14 at 18:15
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From the context I would say that the first would be acceptable in the given situation.

"The key is to prove that for all rectangles, the mid points of the diagonals are coincidental at the center of the rectangle ..."

is appropriate use for your situation as you are referring to the individual midpoints of each diagonal. And in the second use

"The key is to prove that for all rectangles, the mid point of the diagonals are coincidental at the center of the rectangle ..."

is not appropriate use as you would not be saying the collective midpoint of the two diagonals (which happens to also be true)

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  • 2
    So, the collective midpoint are plural? I don't think I can agree. – RegDwigнt Aug 1 '14 at 14:58
  • Wouldn't the latter make "the mid point of the diagonals IS"? And in fact, how can a singular be coincidental? – stevemarvell Aug 1 '14 at 15:01
  • @RegDwight I have been wrong before... And reading through it I think I see what you mean. But I interpreted it as, given two diagonals in a rectangle, the intercept point is at the center. But that is not what the sentence is saying at all. It should be that you are testing the individual midpoints of each diagonal being at the center of the rectangle and the intercept point is irrelevant? – MegaMark Aug 1 '14 at 15:03
  • To explain further ... if you find the mid point of one diagonal of a rectangle and the mid point of the other diagonal of a rectangle, there exists a mathematical exercise which you need to perform in order to prove that they are in the same place. – stevemarvell Aug 1 '14 at 15:05
  • Then I retract the latter statement. It would have to read something more along the lines of "...the mid point of each diagonal..." – MegaMark Aug 1 '14 at 15:08

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