Arithmetic by Magnitsky

In the year when the Moscow Univer­sity was founded, Mikhail Vasilievich Lomonosov wrote of Peter the Great: “To his great inten­tions the wise monarch provided for a neces­sary cause, to dissem­i­nate all kinds of knowl­edge in the father­land and people skilled in the high sciences…”.

The 250th anniver­sary of the foun­da­tion of the Univer­sity was widely cele­brated in January 2005. Pres­i­dent of Russia V. Putin arrived at the opening of the new Library building. In the hall with flags of Russia, Moscow and Moscow Univer­sity there was also a display showing the video reel presented to your atten­tion. It was worth remem­bering what educa­tion meant to Peter the Great.

With Peter’s tremen­dous involve­ment the first Russian math­e­matics text­book was published in Russia. The year is 1703. Leonty Magnitsky publishes “Arith­metic”.

“Arith­metic, that is the science of numbering. Trans­lated from different languages into Russian, put together and divided into two parts”.

The work of Magnitsky was not a trans­la­tion, and no similar text­books existed at that time. This was a unique book.

“Arith­metic, or numeracy, is the art of honest, unbi­ased…”.

The research of the “Arith­metic” text­book itself and the life of its author is given in the 1914 book by Dmitrii Galanin “Leonty Filip­povich Magnitsky and his Arith­metic”.

We shall only give a few high­lights, however.

The text­book contains more than 600 pages and includes both the basics — the table of addi­tion and multi­pli­ca­tion of decimal numbers, and the appli­ca­tions of math­e­matics to the science of navi­ga­tion.

Magnitsky teaches Russia about decimal calculus. What is inter­esting, he gives the addi­tion and multi­pli­ca­tion table not in the form, which is now usually published on the last page of a 12-sheet note­book, but only half of it. In other words, the commu­ta­tivity of these oper­a­tions was given from the start.

The text­book covers geom­etry as well. For example, the Pythagorean theorem is explained via the problem of a tower of some height and a ladder of some length. How far should the bottom end of the ladder be moved away so that its top coin­cides with the top of the tower? Geom­etry of circles, inscribed poly­gons etc are studied as well.

All the prob­lems used in the book are real­istic. And “Arith­metic” ends, obvi­ously, with appli­ca­tions of the studied mate­rial to real life. For example, the appli­ca­tion of loga­rithmic tables in navi­ga­tion.

Several copies of “Arith­metic” are care­fully preserved in the Rare Books and Manu­scripts Depart­ment of the Moscow Univer­sity Library.

The second Russian text­book on math­e­matics was a book trans­lated from German by J. Bryus, “Geom­etry in Slovenian Measure­ment”. Geom­etry was based on an Austrian edition of the “Cir­cular and Ruler Methods”. The Northern War was underway and Peter the Great was person­ally editing the text­book during the rests between battles. The hand­written copy which was sent to Bruce was covered with correc­tions, notes, inser­tions and addi­tions. And the tsar gave the text­book a new title.

In this edition Peter puts into prac­tice his require­ment to Russian text­books and trans­la­tions from other languages. He consid­ered it neces­sary not to transmit a literal accu­racy of the text of the orig­inal, but " after under­standing the text, […] to write in own language as clearly as possible […] and not with high Slovene words, but in simple Russian.“

In the second edition of this book, published under the title “The Methods of Compass and Ruler”, the third part contained texts by Russian authors, and the chapter on the construc­tion of the sunglasses was written by Peter the Great.

The text­book spreads presented in the video, as well as the situ­a­tion in Russia, are wonder­fully matching the well-known quotes that the Russian Pres­i­dent would like to be reminded of:

  • “Math­e­matics is the queen of sciences, arith­metic is the queen of math­e­matics”. C. Gauss.
  • “To aim artillery preci­cely, … consid­er­able knowl­edge of geom­etry, mechanics and chem­istry is required…”. M. Lomonosov.
  • “America, […] has already lost [to Russians] the cold war of science”. J. Kennedy.

Other etudes in “Historic”