Как инженеры Древнего Рима делали расчёты, если у них были только латинские (натуральные) числа?
https://www.reddit.com/r/explainlikeimfive/comments/13vcm21/eli5_how_did_romans_do_advanced_math_using_roman/They didn't do calculations using Roman numerals.
Instead, they used calculus.
No, not the Newton-Leibniz one.
A calculus is a little calx; that is, a small piece of limestone — a pebble.
Calculi, pebbles, were used on counting-boards, with techniques similar to the later abacus.
The word "calculation" comes from the calculi that were used to do it.
We still use rocks to do our arithmetic today, but these days we use silicon instead of limestone.
—
Most ancient cultures didn’t do math with their numerals. Their numeral systems were used for recording numbers, but any math they did was with devices such as the abacus or counting board.
In order to efficiently do math with numerals, your system needs a couple different attributes: first, it needs to be a ‘base’ system (like our current base 10 system). Second, you need to have symbols for each digit up to the base.
For example, the Babylonians had a base 60 system, but they only had symbols for 1 and 5. So to write 68 they would put a 1 in the sixties place and a 5 and three 1s in the ones place. If you try to do addition or multiplication using these numerals, it kind of works, but you run into issues carrying numbers. There was also the issue where they didn’t have a symbol for 0, so there was no placeholder.
The Mayans had a similar system: base 20 (mostly, though one of their places only went up by a factor of 18 instead of 20), but they only had symbols for 1 and 5.
The Egyptian hieroglyphic system was similar to Roman numerals in that there was no base, though they didn’t have the subtraction rules based on the order of the symbols that the Romans had.
None of these cultures really used their numerals for mathematics. It was the Arabs that started that using their base 10 system that eventually became the system we use today (Edit: the Hindu-Arabic numeral system actually originated in India. Thanks to Illiad7342 for the correction). This is one of the main reasons that their number system spread throughout the world.
—
They didn't. They never made it past natural and rational numbers. That's whole positive numbers and fractions without zero.
The mathematical proof that pi is not rational got buried by the Roman scholars. If you believe in hearsay, it got buried along with the body of the guy who first proved it.
The concept of zero which came to Europe from India through Arabia was rejected in Europe for millennia. It was only accepted around year 1200.
A lot of modern math is less than 500 years old. Linear algebra got invented in ~1600. Calculus just before ~1700 by Isaac Newton.