ArticleslgStudy

mathematics

The Calculating Machines

The Calculating Machines is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand The Calculating Machines rather than just read about it. In short: Die Rechenmaschinen, by Ernst Martin, and its English translation, The Calculating Machines (Die Rechenmaschinen): Their History and Development, are books on mechanical desktop calculators from prior to World War II. Publication history Die Rechenmaschinen, the original book by Martin, was published in 1925, and revised in 1937.

The Calculating Machines — main illustration
The Calculating Machines — illustration

Key takeaways

  • The Calculating Machines belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect The Calculating Machines to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of The Calculating Machines from memory before moving on to harder problems.

Reference excerpt

Die Rechenmaschinen, by Ernst Martin, and its English translation, The Calculating Machines (Die Rechenmaschinen): Their History and Development, are books on mechanical desktop calculators from prior to World War II.

Publication history Die Rechenmaschinen, the original book by Martin, was published in 1925, and revised in 1937. Both editions are very rare. Little is known about Martin beyond these books. The 1925 edition was edited and translated into English by Peggy A. Kidwell and Michael R. Williams, and published in 1992 by the MIT Press as the final 16th volume of its The Charles Babbage Institute Reprint Series for the History of Computing (ISBN 0-262-13278-8). Kidwell and Williams chose this edition, rather than the revised edition, because of "the rarity of the books and the poor condition of the illustrations in extant copies". Indeed, they were only able to locate three copies of Martin's book. The book and its translation includes many illustrations, and the translation preserves some idiosyncrasies of the original work, including a set of advertisements for calculating machines at the end of the book.

Topics After an introduction grouping calculating machines into seven types, the book describes over 200 machines, comprising "almost every desk-top calculator available before World War II", ordered chronologically. It also contains biographical information about some of the people who contributed to the design of these machines, including Blaise Pascal, Gottfried Wilhelm Leibniz, and Giovanni Poleni.

Audience and reception At the time Martin wrote the book, "mechanical calculating machines were a symbol of high-tech sophistication in the workplace"; reviewer Jonathan Samuel Golan suggests that it was aimed at collectors rather than historians, while the editors of the Bulletin of Science, Technology & Society suggest that instead its purpose was to inform the public. Nowadays, reviewer A. D. Booth suggests that readers of the book are likely to be people who once used these machines, looking back at them with nostalgia, while the Bulletin editors point to new use by collectors, and Golan instead suggests that it can be used to study the history of a bygone technology. In terms of its content, Booth complains that the contributions of Samuel Morland are overlooked, and that Morland's calculator was at least the equal of Pascal's in priority and quality. Similarly, Doron Swade notes the omission of the work of Wilhelm Schickard, earlier than that of both Morland and Pascal, but excuses this lapse by noting that Schickard's work was forgotten and only rediscovered after Martin's book was published. Golan writes that the descriptions of older calculating machines are "cursory" and secondhand, while the later ones seem to be copied from advertisements. Booth praises the quality of the translation, and calls the newly reprinted edition "an invaluable window on the past". Similarly, Golan calls it "a valuable document, providing a fascinating portrait of the state of the art". Swade is more cautious, pointing to the book's clear biases, but still noting its value as "reference material for collectors and curators as well as historians".

References

External links The Calculating Machines on the Internet Archive The Calculating Machines, online PDF edition with permission of the MIT Press

Illustrations

The Calculating Machines illustration

Worked examples

Example 1 — a first encounter with The Calculating Machines

Start with the simplest possible case. Write down what The Calculating Machines claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to The Calculating Machines before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about The Calculating Machines ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of The Calculating Machines

In research
The Calculating Machines appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses The Calculating Machines in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
The Calculating Machines is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1925 non-fiction books, 1937 non-fiction books, 1992 non-fiction books, so understanding it makes those chapters shorter.
In everyday life
Look for The Calculating Machines outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “The Calculating Machines” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study The Calculating Machines in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what The Calculating Machines means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain The Calculating Machines out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is The Calculating Machines in simple terms?

Die Rechenmaschinen, by Ernst Martin, and its English translation, The Calculating Machines (Die Rechenmaschinen): Their History and Development, are books on mechanical desktop calculators from prior to World War II. Publication history Die Rechenmaschinen, the original book by Martin, was publish…

Why does The Calculating Machines matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study The Calculating Machines?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on The Calculating Machines.

Tags

  • 1925 non-fiction books
  • 1937 non-fiction books
  • 1992 non-fiction books
  • Mathematics books
  • Mechanical calculators

Keep exploring