Testwiki:Reference desk/Archives/Mathematics/2011 December 12

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December 12

Obsolete typography

Cossical characters

Earler version

(Copied from Miscellaneous)Template:Break I'm looking for some obsolete symbols, as illustrated in the image. The text comes from an eighteenth century printing of a seventeenth century book, but the symbols are drawn from a sixteenth century work, so may have been obsolete even then. Obviously supported Unicode would be nice, but mathml might be an alternative. Rich Farmbrough, 14:10, 12 December 2011 (UTC).

The Testwiki:Reference desk/Archives/Mathematics/Miscellaneous#Obsolete typography thread got me some answers. There are effectively four unusual symbols, two of which we have identified as ℨand (provisionally)φ. The third is somewhat like IPA ʑ which will suffice if no better character can be found, and the fourth appears to be an "ss" ligature. An earlier version is in the second illustration, and the last character has changed considerably in the intervening century and a half (it was a long s and a ℨ). Ellen of the Roads has found something similar in a magical alphabet.Rich Farmbrough, 16:57, 12 December 2011 (UTC).

After some cross-analysis of the two sources (and after recovering from sadistic laughter at zenzizenzizenzike) I would say that the earlier version uses the following, in order:

"Number": Looks like a type of ampersand & or ƪ shape ("reversed esh loop")

"Root": I'd agree with using IPA ʑ ("curly z")

"Square": ʒ or Ʒ ("ezh" by IPA or Latin ext.)

"Cube": & ampersand is almost definitely the symbol used by the printer

"Zenzizenzike": ʒʒ or ƷƷ

"Sursolide": an esszet digraph ʃʒ ("esh" + "ezh") (or ∫Ʒ math ext.) which is elided to ß in modern print, as in the second image

You'll notice a lot of variants on the "z" character. This is because there's a lot of German influence in mathematics at this time affecting notation (still through to the first half of the 20th century), and the word for "number" is "Zahlen", hence why the integers are denoted by Template:Math or Template:Math. SamuelRiv (talk) 02:55, 13 December 2011 (UTC)

Of course I came across this researching zenzizenzizenzike and zenzizenzizenzizenzike. I do agree with your esszet interpretation, the more I look at it, it is pragmatically an esszet, however it is produced in a very different way - which would be cool to reproduce. There's an interesting comment from Inductive Itinerant1 back in the other thread. Rich Farmbrough, 12:43, 13 December 2011 (UTC).

I've got it. "Number" is a zeta ζ. Makes sense with the z theme, and it's so often written that way. SamuelRiv (talk) 23:03, 15 December 2011 (UTC)

Intersection of circle and line

Starting from the form of a circle.

${(x-a)}^2+(y-b{)}^2=r^2$

Centre at (0,r) , substitue d for y.

$x^2+(d-r{)}^2-r^2=0$

$(d-r{)}^2=r^2-x^2$

$(d-r)=\sqrt{r^2-x^2}$

$(d)=r+\sqrt{r^2-x^2}$

Rearrange for d is claimed to be $d=r-\sqrt{(r^2-x^2)}$ here http://www.virtualrailroader.com/diverge-calc.html

Which step have I got wrong, or is the original explanation not clear? The formulae works either way :)

Sfan00 IMG (talk) 22:42, 12 December 2011 (UTC)

If you have an equation of the form $a^2=b^2$ then it has two solutions, a=b and a=-b. You need to figure out which makes sense in your context. In your case, both will - each gives you one half of the circle. --Tango (talk) 23:55, 12 December 2011 (UTC)