Algebra I

Return to MAT-351 Algebra I MAT-351 Lesson 004 – The Unit of Measure In the last lesson we learned that a quantity can be measured only by a quantity of its own kind, and that to measure is to find how many times one quantity is contained in another. We spoke there of the known quantity we lay beside the unknown one, but we did not name it. It has a name, and we shall learn it now. Ray gives the definition: one of the single parts of which a quantity of multitude is composed is called the unit of … Continue

Return to MAT-351 Algebra I MAT-351 Lesson 003 – Quantity Is Measured Only by Quantity of Its Own Kind We have learned what quantity is, and we have learned that quantity is considered either as magnitude or as multitude. We come now to the first rule of measuring, and Euler states it plainly: we cannot measure or determine any quantity except by considering some other quantity of the same kind as known, and pointing out their mutual relation. Let us take his examples one at a time, for the rule is easier to see in a particular case than in … Continue

Return to MAT-351 Algebra I MAT-351 Lesson 002 – Magnitude and Multitude In the last lesson we learned that quantity is anything capable of increase or decrease. That definition covers a great many different things — water and money, rope and time — and we shall now see that all of them fall into two sorts, according to the way the quantity is considered. Ray gives us the two names. Quantity is called magnitude when it is considered in an undivided form. His example is a quantity of water. When we speak of the water in a cistern, we do … Continue

Return to MAT-351 Algebra I MAT-351 Lesson 001 – What Quantity Is Before we can study algebra, we must settle what algebra is about. Every science has its own subject. The physician studies the body, the grammarian studies speech, and the mathematician studies quantity. So we begin by asking what quantity is, and we shall find that the answer, once we have it, governs everything that follows. Euler opens his Elements of Algebra with this definition: whatever is capable of increase or diminution is called magnitude, or quantity. Ray gives the same definition in his own words: quantity is anything … Continue