One of the greatest inventions of the 17th century was the creation by the German mathematician Gottfried Wilhelm Leibniz of an arithmometer (photo is given in the article), capable of performing all four basic mathematical operations in the decimal system. It is this computing device that can be fully called the prototype of a modern calculator.
Young genius
The future inventor was born on July 1, 1646 in Leipzig and at the age of 14 he entered the university of his native city, where he studied the humanities - history, philosophy and jurisprudence. Recalling this period of his life, the scientist always emphasized that acquaintance with the works of prominent thinkers of the past developed in him the ability to be creative in solving purely technical problems, while avoiding repeating the paths previously made by other researchers.
Leibniz seriously engaged in mathematics only two years later, having left Leipzig and becoming a student at the University of Jena. Attending the lectures of his distinguished contemporary, the German mathematician Erhard Weigel, he nevertheless continued his studies in law and at the age of 17 published several hand-written treatises.
On the way to invention
The impetus for the creation of the arithmometer by Gottfried Leibniz was his meeting with the Dutch astronomer Christian Huygens, who, by the nature of his studies, constantly had to perform cumbersome and very complicated mathematical calculations. Wanting to help his new acquaintance, the ingenious German set out to invent a certain mechanical device capable of taking on this routine work.
When creating a mechanical arithmometer, Leibniz was able to draw on the experience of his predecessor, the French scientist Blaise Pascal, who by that time had already invented a very primitive calculating machine and even tried, albeit unsuccessfully, to establish its commercial production. We note in passing that the Frenchman was motivated by the desire to help his father, who was collecting taxes and constantly burdened with a lot of calculations.
Presentation of a new arithmometer
Having largely reworked and improved Pascal's counting apparatus, the German mathematician in 1673 presented to the German public a completely new model of the arithmetic device, stating that he intends to continue working on it further. Unlike his French counterpart, when designing an arithmometer, Leibniz used a special stepped wheel in it, which makes it possible to simplify and in many ways speed up multiple additions of numbers necessary for performing operations related to multiplication and division. There were also some other improvements that allowed to automatically complete this process.
In the subsequent period, the inventor worked hard to modernize his brainchild, after which he organized his presentation to members of the Royal Royal Scientific Society. It took place in March 1676. The creation of the Leibniz arithmometer - an advanced one that made it easy to perform complex mathematical calculations - was an event, interest in which was already shown in many European countries.
Completion of the invention
Not stopping there and continuing to improve his arithmometer, Gottfried Leibniz in the mid-90s presented his updated model to the public, which became a classic model, which later became part of all the world's directories and received the name of its creator.
It is curious that one of the calculating machines he created was later brought to Russia and came to Peter I, who, as you know, was a great lover and connoisseur of various wonders. However, on the banks of the Neva, it did not linger for a long time and was donated by the sovereign to the Chinese emperor as evidence of the extraordinary technical progress made by Europe.
The scientist conducted further work to improve his invention until 1710, after which he was forced to interrupt them due to extremely high overhead costs. Suffice it to say that in those days when Leibniz invented the arithmometer, the annual salary of the minister did not exceed 2 thousand thalers, while the mathematician invested 12 times more in his brainchild. The final model was created by him in two copies, of which so far only one has been preserved, presented in the exhibition of the Munich National Museum.
Features of the new design
As mentioned above, the cardinal difference between the arithmometer created by Leibniz and the developments made by Pascal is the presence of a stepped shaft in it - a special cylinder equipped with teeth of various sizes on the sides. This device eliminated the need for multiplication to repeatedly dial a multiplicative number. To get an answer, it was enough to just turn the handle, which sets the cylinder in motion, the required number of times. Even if it was necessary to multiply large numbers and the operation performed took a lot of time, then in this case the advantage over Pascal's arithmometer was not in doubt. Other elements were also introduced into the design that made it possible to simplify and speed up the computational process.
Stages of scientific activity
Talking about the Leibniz arithmometer, one cannot but mention the other merits of this ingenious scientist who made a powerful breakthrough in various fields of mathematics at the turn of the 17th and 18th centuries. So, starting service in the court of the Mainz elector in 1667, he devoted much time to creating the foundations of mathematical analysis, which he carried out on principles other than those formulated by Newton. Then Leibniz wrote a major scientific work in which he outlined the principles of differential calculus developed by him.
The real revolution in mathematics was the classification of real numbers introduced by Leibniz in the mid-80s, in which they were divided into transcendental and algebraic. He also managed to do the same when studying curved lines. In addition, one of the most significant achievements of the scientist was his introduction to mathematics of such a concept as the integral, by which he designated the operation opposite to differentiation.
In parallel with the development of an arithmometer, Leibniz also dealt with issues within the circle of linear algebra. However, the results of his work were appreciated only after half a century. Studying linear systems, he introduced into science the concept of “determinant”, unknown until then, which then went unnoticed in scientific circles, but over time increased its fame. Surprising as it may seem, Gottfried Leibniz also contributed to the creation of modern computer technology. It was he who, using the values of zero and one, developed the binary system of calculus that is widely used today.
The role of Leibniz in the history of Germany
The achievements of the scientist who passed away in 1716 helped Germany not only to make a significant step in its technical development, but also to overcome the economic and political decline in which it was after the defeat in the Thirty Years' War, which swept Europe in the period 1618-1648 years