15 May 2012

Arithmetica Universalis

Staffan Rodhe's office door was open today, I was passing by, so I dropped in. I was admiring the collection of ancient mathematical texts on his shelves. I first picked up a book by Lagrange, then one by Euler, and then the Arithmetica Universalis by Newton. I opened it somewhere in the middle and found a square piece of paper  (size around 10 cm) with some equations on one side and a couple of geometric drawings on the other. Clearly, it belonged to an careful reader of some past century. Most likely, Staffan explained, it was written some time in the 18th c. I took a couple of photos of both sides, as well as a copy of the title page of the book because they are, in my opinion, like pieces of art. It also makes me wonder how people thought back then, how similar to us they were, etc.
Note that this edition of Arithmetica Universalis was published in 1732 in Lugdunum Batavorum, i.e., Leiden. There is a free version on the internet from a 1752 copy from Amstelodamum (Amsterdam). The original edition dates from 1707.

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What measure theory is about

It's about counting, but when things get too large.
Put otherwise, it's about addition of positive numbers, but when these numbers are far too many.

The principle of dynamic programming

max_{x,y} [f(x) + g(x,y)] = max_x [f(x) + max_y g(x,y)]

The bottom line

Nuestras horas son minutos cuando esperamos saber y siglos cuando sabemos lo que se puede aprender.
(Our hours are minutes when we wait to learn and centuries when we know what is to be learnt.) --António Machado

Αγεωμέτρητος μηδείς εισίτω.
(Those who do not know geometry may not enter.) --Plato

Sapere Aude! Habe Muth, dich deines eigenen Verstandes zu bedienen!
(Dare to know! Have courage to use your own reason!) --Kant