Mathematics# Pascaline

## What is Pascaline?

## Characteristics of the pascaline

## History

## Who invented the pascaline

## How it works

**Pascaline** was the first **mechanical calculator** that worked through a series of **wheels** and **gears**. It was initially known as the ** "arithmetic machine"**, then called the

**Related topics**

Pascaline was the **first calculator** invented in the world, it worked by means of a series of **wheels** and different **gears**, which could add, subtract, divide and multiply by subtractions and additions in a repetitive way.

- It could only do addition and subtraction, with numbers entered by
**manipulating**its dials. - The Pascaline is the size of a
**shoebox**and that’s why it can be easily carried. - It has
**eight**different windows at the top. - Inside each of the windows, a small
**drum**can be seen with the**digits**of the result. - Each drum is made up of two different
**number****rows**. - In front of the windows there are eight adjustment
**mechanisms**. - Depending on the
**positional value**of the quantity to be added, the wheels will move according to the positions as they correspond to the value of the corresponding digit. - Each wheel on the top of the Pascaline has an axle that has a horizontal
**crown gear**. The gear is transmitting the wheel**rotation**to a vertical crown gear. - The subtraction could not be made by turning the machine wheel in the opposite direction but had to be made by an indirect method known as
**nines complements**, which is made by turning the wheels in the same direction. - The first Pascaline could only use 5-digit numbers, but then Pascal developed 6-digit and 8-digit versions.

**Informatics history** goes back to **ancient times**. The most remote example is the abacus, an adding instrument still used in some parts of Japan and Eastern Europe. French mathematician and philosopher **Blaise Pascal** invented the world’s first mechanical calculator in **1642** to help his father, who was the area’s tax **inspector**. The machine worked perfectly, was able to carry the numbers from the column of units to the column of tens by means of a **ratchet** mechanism and was fully functional. Blaise decided to call it Pascaline. **Gottfried Leibniz** worked on perfecting the Pascal adding machine and attempted to improve it so that it would be able to multiply and divide by achieving this goal through the placement of a mechanical device called the **Leibniz cylinder**. After having perfected this machine, Leibniz focused his efforts on creating a method that would allow the decimal system to be converted into a **binary-based system**. The first use of Pascaline was in the **French farm**, where Pascal’s father worked.

Pascaline was invented by Blaise Pascal in 1642. It was the son of a civil servant whose job was to **collect taxes**. Pascal, who occasionally helped his father to write his official reports, wondered how to help his father in the different **arithmetic** operations in which large numbers had to be added.

Pascaline had the shape of a **shoe box** and was low and somewhat elongated. On the inside, there were a series of **sprockets** that were connected to each other, thus forming a **transmission chain**, so that when a wheel turned completely on its axle, it advanced one degree to the next. These different wheels that were inside the Pascaline had as function to represent the **decimal system of numeration**. Each wheel consisted of ten steps, so it was also marked with numbers ranging from 9 to 0. In total it consisted of eight wheels, six of them were used to represent **whole numbers** and two more wheels, at the far left, to represent **decimal numbers**. With this arrangement, whole numbers between 0’01 and 999.999’99 could be handled. By means of a **crank**, the toothed wheels could turn to achieve **adding** or **subtracting** in this way. If a number needed to be subtracted, the crank had to be operated in the opposite direction.

Written by Gabriela Briceño V.

Briceño V., Gabriela. (2019). *Pascaline*. Recovered on 18 February, 2024, de Euston96: https://www.euston96.com/en/pascaline/