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Gauss wrote in his Ph.D. dissertation:

Si quis e. g. in art. 3, aliaque incognitarum tamquam cognita spectata, reliquas per hanc et coefficientes datos rationaliter exprimere tentat, facile inueniet, hoc esse impossibile, nullamque quantitatum incognitarum aliter quam per aequationem m-1ti gradus determinari posse.

What does the ti mean?

I suppose the obvious answer is that it's an exponent consisting of two variables, t and i, multipled together. But that doesn't look right. It's strange to raise 1 to an exponent, though with complex numbers that could produce a result other than 1. But, at least on a cursory look, I don't see variables t and i defined nearby. And I see ti used unitalicized and unsuperscripted, apparently as a suffix, here:

Facile vero perspicitur m′ fore numerum formae 2n-1i′, designante i′ numerum imparem. Iam nisi m′ est impar, supponatur iterum, uu+uu′+M′ esse diuisorem ipsius U, patetque per similia ratiocinia u′ determinari per aequationem U′=0, vbi U′ sit functio (m′ . m′-1) / (1 . 2)ti gradus ipsius u′.

Is it an ordinal suffix, enabling the mathematical expression to modify gradus? Or maybe a cardinal case suffix? If so, what else in Latin is it modeled after? All I can think of is big cardinal numbers like ducenti, trecenti, etc. (and viginti).


Huic incidi nexum sequens in hoc responso Ionæ Ilmavirta.

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    Latine scribens potes forma Latina et declinabili nominis mei uti: "Ionas Ilmavirta". Necesse autem haud est; forma solita enim semper adhiberi potest.
    – Joonas Ilmavirta
    Apr 22 '17 at 8:41
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Judging by context, it must be an ordinal number in genitive. It seems that Gauss would translate "nth" from English to Latin as "ntus". This makes sense, given how many ordinals look: quartus, quintus, sextus, septimus. The genitive of -tus is -ti. (Alternatively, it could be -tius and -ti as a short form of -tii. But this is ruled out by the other two endings.)

The superindex -ti appears before the word gradus. Gauss' "nti gradus" means "of nth degree". The word "gradus" is fourth declension, so recognizing the genitive is trickier. There are also several similar phrases with concrete numbers. Search the document for "secundi gradus", "quinti superiorisue gradus", or "primi secundiue gradus".

There are also two examples of a similar superscript in the text in other forms (thanks for noticing, cnread!):

  • "Manifestum est, in serie aequationum U=0, U′=0, U′′=0 etc. ntam fore gradus imparis adeoque radicem realem habere." — It is clear that in the series of equations U=0, U′=0, U′′=0 and so on the nth one will be of odd degree and therefore have a real root. — There is an implicit "aequationem" for the ntam.
  • "Ceterum palam est, axem ipsum semper duos ramos infinitos lineae primae constituere, puta primum et m+1tum." — It is clear that the axis itself constitutes two infinite branches of the first curve; consider the first and the (m+1)st one. — There is an implicit "ramum" for the m+1tum.
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