Arithmetic is the science of numbers. The name comes from the Greek word 'arithmos' that means 'number'. In India, Arithmetic was called Rasi-Vidya, Samkyaana or Ganana.
Here and for now, I will say a few things about the Rule of Three. The Hindu name for the Rule of Three was trairasika and the method was known in India 2000 years ago. It occurs first in Bakshali Manuscript (beginning of Christian Era) and subsequently in the writings of Aryabhatta I (499 CE), Brahmagupta(628CE), Sridhara (c.750), Mahavira (850 CE), Aryabhatta II (950 CE), Bhaskara II (1150 CE).
Rule of Three is a method for solving, mechanically, arithmetic problems (in proportion) without knowledge of the general theory of proportion. What the rule says is this: Knowing three quantities A, B, C, we can determine the fourth unknown quantity directly without resorting to proportion or the use of the variable x. Write A, B, C in a line (row) or linear sequence. Multiply the last term C with the middle term B and divide the product by the first term A to straightaway arrive at the answer. Example: if 4 (A) metres of cloth cost 100 (B) Rupees, how much 10 metres (C) of cloth will cost? We instantly write the answer as 10x100/4 = 250 Rupees. Hindu mathematicians called A Pramana, B Phala and C Iccha.
The rule was perfected among Hindus during the early centuries of the Christian era. It then travelled to the Arabs, in all probability, in the 8th century CE, and from them to Europe where it came to be known as the "Golden Rule." Both the Arabs and the Europeans adopted the Hindu name 'Rule of Three' . They also adopted the practice of placing the terms in a line and kept the first and the last similar. But the names of the three terms were altered.