Complete Instruction in Algebra

There are, therefore, very many different kinds of quantities, which cannot easily be enumerated; and from this arise the different parts of mathematics, each of which is occupied with a particular kind of quantity, since mathematics in general is nothing other than a science of quantities, and which finds the means by which one should measure them.

However, a quantity cannot be determined or measured otherwise than by assuming a quantity of the same kind as known, and indicating the proportion in which any given quantity of the same kind stands in relation to it.

Thus, if the amount of a sum of money is to be determined, a certain piece of money, such as a Gulden guilder, a Rubel ruble, a Thaler thaler, or a Ducaten ducat and the like, is assumed to be known, and it is indicated how many such pieces are contained in the aforementioned sum of money.

Just so, if the size of a weight is to be determined, a certain weight, such as a Pfund pound, a Centner hundredweight, or a Loth half-ounce and the like, is assumed to be known, and it is indicated how many of them are contained in the former weight.

But if a length or a width is to be measured, one is accustomed to using a certain known length, which is called a Fuß foot.

In determinations or measurements of quantities of all kinds, it is therefore important that, first, a certain known quantity of the same kind be firmly