Absolute and Relative Roman Numerals

Mini-Series On Classical Mathematics:
	(10-2)*(10-2)=64 As History of Mathematics ... Sigh ... Absolute and Relative Roman Numerals Two is Still Not a Number With any Square Root
Now, for the essay:

I=1 II=2 III=3 IIII=4

VI=(5+1) VII=(5+2) VIII=(5+3) VIIII=(5+4)

IV=(5-1) IIV=(5-2) IIIV=(5-3) IIIIV=(5-4)

If you cannot have absolute numerals meaning "as many as fewer than none", you can have relative numerals not only adding but also detracting "as different as fewer than other number by itself". And the Romans had that.

I	II	III	IIII	V	*
I	II	III	IIII	V	I
II	IIII	VI	VIII	X	II
III	VI	VIIII	XII	XV	III
IIII	VIII	XII	XVI	XX	IIII
V	X	XV	XX	XXV	V

They also had a smaller multiplication table "than we do" (though a longer one than computers have). Not that we have not got their multiplication table too if we want to, but the one we learn in school is longer.

And here are the examples of how the work out together, with a V modified by relative numerals I - IIII on the right or the left:

V I * XXV V V V I I XXV V V I XXXVI

I V * I V I V XXV V I | V V ||XXV V V || XXVI

Let's skip intermediates and go directly to the last two multiplications of these simple Roman Binomials, shall we:

V IIII * XXV XX V XX XVI IIII XXV XX XX XVI L XXV VI LXXXI

IIII V * XVI XX IIII XX XXV V XVI | XX XX || XXV XX XX || XXV XVI X || V V I

Which means that in Roman Subtraction, to simplify the algorithm, something subtracted from the subtrahent is instead added to the total from which one subtracts:

IV || V
V || V I.

Which in turn works out as the "multiplication table of signs" which in turn has after Wallis and others been misunderstood as if absolutely negative numbers (there is no such thing) could by themselves make positive products.

As simple as "Romani ite domum!" (Which does not always necessarily come across as a blasphemy against Our Lord, as said in previous, unless you would say that Écône is rather telling the Vatican - in very correct Latin usually - "Romani venite domum", but that subtlety may securely have been lost on Anglican and Atheist critics of Latin Mass Society).

Hans-Georg Lundahl
BpI, G. Pompidou Library
Day of Sts Aurelius and Natalia,
Martyrs of Cordoba
27-VII-2012

For this and previous two posts, many thanks extended to the Latin and Greek Studies Seminar of Copenhagen in ... was it 1992 or something?

Now, in case anyone wonders what I think about e or π or φ or the Mandelbrot formulas, those simply are not numbers.

π is a proportion between the diameter and the perimeter (περιµετρoc=π) of a circle.

These are not numbers and do not belong to Arithmetic, they are proportions and belong to Geometry.