Four species machine

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The Hanoverian model 2005 of the Leibniz four-species calculating machine , demonstrated here by Franz Otto Kopp in 2012 at the Leibniz University of Hanover

The four-species machine is a generic name for mechanical calculating machines . Essentially, it is characterized by the fact that mathematical calculations in all four basic arithmetic operations (addition, subtraction, multiplication and division) are easily possible.

The first functioning four-species machines came from Anton Braun and Philipp Matthäus Hahn in the 18th century

Problems of concept formation

The term "four-species calculating machine" requires further explanation. In general, a four-species machine should be a calculating machine on which you can calculate at least all four basic arithmetic operations, but this also applies to some adding machines . The specialist literature does not provide a sufficiently delimiting definition of the term four-species machine (see literature list).

In today's pocket calculator , each function is represented by a key combination. This is why the “range of functions” can be determined comparatively easily just by looking at the machine. This is not the case with mechanical calculating machines. Although these also offer a certain (analyzable) mechanical basic function, the mathematical functionality only arises together with the handling by the operator. This can be found in contemporary operating instructions and in some cases enables unexpected functionality solely through manual positions or the clever use of counters. These cannot be determined by just looking at the mechanics.

The loose use of the term “four-species calculating machine” in contemporary literature is probably due to the fact that such terms were introduced at the beginning of the 20th century for advertising purposes. These were intended to distinguish own products from those of the competition and in some cases did not correspond to the facts.


4 species calculator

The term four-species calculating machine is mostly used for machines in which algorithms for the four basic arithmetic operations have been historically proven, so that addition and subtraction can be carried out directly, and on which multiplication and division , compared with addition and subtraction, must not require any fine motor skills and only little cognitive effort.

The direct route means that the operands do not have to be preprocessed and the calculation is carried out exclusively in and with the calculating machine. Little extra cognitive effort should already exclude mental arithmetic and counting and include control activities such as paying attention to the bell signal or observing whether the counter display goes into negative territory.

A disadvantage of this definition is that a calculating machine cannot be classified if the calculation rules for the machine are not known.

Alternative definitions

Definitions of four-species machines, as can be found in many works on the subject of calculating machines, often fall short:

  • “A four-species machine is a calculating machine on which one can theoretically calculate all four basic arithmetic operations.” Such a definition would apply to too many calculating machines. It was quite common to use algorithms that included mental arithmetic or written ancillary calculations. This is why you can develop a suitable algorithm for simple machines.
  • “A four-species machine is a calculating machine that was actually used for all four basic arithmetic operations.” This approach is problematic with calculating machines that were not built, whose users are unknown, or where different user groups use the machine for different purposes to have.
  • “A four-species calculating machine is a multiplication machine.” This definition probably arises from the differentiation from the adding machines typical in America. However, this designation is misleading, because firstly, on full-keyboard adding machines, it is quite easy to multiply manually. Secondly, it is implicitly meant here that as soon as the operation multiplication is available by inversion , it can also be divided, which is largely correct and is solved in the technique of the time by a sometimes tricky formation of the inverses during the calculation. The third objection to this too narrow definition is that it can lead to confusion with the high technology of the time, since there are calculating machines that were specially designed for multiplication in a mechanical operation (e.g. multiplication body calculating machines ).


  • Ernst Martin: The calculating machine and its development history - calculating machines with automatic tens transmission . 1st volume, 1st edition. 1925.
  • A. Hennemann, [di Adolf Schranz]: The technical development of the calculating machine. Peter Basten, Aachen 1952.
  • Karl Lenz: The calculating machines and machine computing. (= From nature and the spiritual world. Volume 490). BG Teubner, Leipzig / Berlin 1915.