The Pascaline machine, the first mechanical calculator, was invented by Blaise Pascal in the 17th century. It was a remarkable device for its time and laid the foundation for the development of more advanced calculating machines. Here's a brief explanation of how the Pascaline machine worked:

1. Numerals and Wheels: The Pascaline machine consisted of a series of numbered wheels, each representing a decimal place (units, tens, hundreds, etc.).

2. Adding: To add numbers, the user rotated the appropriate wheels. Each wheel had 10 teeth, and rotating it one full revolution advanced the next higher wheel by one tooth. This carried over the tens and hundreds places.

3. Subtracting: Subtraction was performed by rotating the wheels in the opposite direction.

4. Multiplication: Multiplication involved a more complex process called "repeated addition." The user rotated the wheels to set the multiplicand, and then repeatedly added the multiplicand to itself the number of times specified by the multiplier.

5. Division: Division required a combination of subtraction and repeated addition. The user would repeatedly subtract the divisor from the dividend and keep track of the number of times it could be subtracted. This essentially produced the quotient.

6. Carrying Over: The machine featured a mechanism known as the "carryover." When a wheel completed a full rotation, it automatically advanced the neighboring wheel by one tooth.

7. Output: The Pascaline machine produced results by displaying the calculated numbers directly on its wheels.

The Pascaline machine was considered an impressive invention during its time, and it demonstrated the practicality of using mechanical devices for mathematical computations. It marked an early step in the history of computing technology, eventually leading to the development of more sophisticated mechanical and electronic calculators and computers.