The art of raising equations.
The language of algebra is the equation. "To solve a problem concerning numbers or abstract relationships of quantities, the problem simply translate from English or another language to algebraic language," wrote the great Newton in his manual titled Arithmetic Universal algebra. Isaac Newton showed by example how the translation was made. Here's one:
In the vernacular In the language of algebra
A trader had a certain amount of money
X
The first year was spent 100 pounds X - 100
increased the rest with a third of it (X - 100) +1 / 3 (X-100) = 1 / 3 (4x-400)
The following year he returned to spend 100 pounds 1 / 3 (4x-400) -100 = 1 / 3 (4x-700)
and increased the amount remaining in a third of it 1 / 3 (4x - 700) +1 / 9 (4X-700) = 1 / 9 (16X-2800)
The third year it spent 100 pounds again 1 / 9 (16X-2800) -100 = 1 / 9 (16X-3700)
After he had added his third 1 / 9 (16X-3700) +1 / 27 (16X-3700) = 1 / 27 (64X-14800)
part
the capital was twice the initial 1 / 27 (64X-14800) = 2X
To determine the initial capital of the trader is not only solve the latter equation.
The solution of an equation is often easy task, however, raise the equation based on data from a problem is often more difficult. We have seen that raising the art of equations is indeed translating "the vernacular language of algebra." But the language of algebra is laconic in the extreme, so not all the turns of language are easily translated. The translations can be very different by the level of difficulty, as can convince the reader to view examples of first-degree equation set.
