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You could just as easily rewrite it this way:

At common mathematical law, with the nomenclature known by geometrists, it was never doubted that all polygons with three equal sides and equal vertex angles are triangles. These are the regular triangles, or equilateral triangles, as distinguished from squares and pentagons. Some experts go further and include as triangles all shapes with three sides without reference to the length of their sides. As to this class there are doubts, but never to the first. For the purposes of this case, it is not necessary to solve these doubts. It is sufficient for everything we have now that all shapes composed of three equal sides with equal vertex angles are triangles."

which is the way those of us who disagree with you have been saying it should be read. The problem with yours is that you left out anything analogous to "born within the jurisdiction," a problem my "with three sides" addresses.

“All shapes” is the phrase that is analogous with “children born within the jurisdiction” ... the extra detail you came up with doesn’t change the obvious fact that equilateral triangle is only defined by the criteria in the preceding sentence.

If you concentrate and view these two sentences listed below, they will appear different in some very significant way. After consuming 8 shots of Jamesons Irish whiskey, these two sentences written in plain English will begin to appear to be virtually identical. Honest to god, you will not be able to tell the difference between the two after 20 shots. Try it! (If they are not Identical, you have not consumed enough shots. Its best to do this with a full bottle at hand, and take a shot every five minutes.) After doing this exercise, I can attest that, yes, Obama is in fact a natural born citizen, per Minor V Happersett. I saw it with my own two eyes! I have heard that you can also do this exercise with KWA, using LSD, and the word “Natural born citizen” will appear magically in place of “citizen” when describing Mr. Kim.

"Ha Ha I'm an Illogical bore", these are the two sentences. How many shots did it take to make them the same for you?.

Some authorities go further and include as citizens children born within the jurisdiction without reference to the citizenship of their parents.

Some authorities go further and include as Natural born citizens children born within the jurisdiction without reference to the citizenship of their parents.