To complete this lesson, complete the following tasks:

1. Study the lesson for mastery.

2. Complete the memory work.

3. Complete the lesson exam.

## Lesson

In this first lesson of Arithmetic, we will learn what Arithmetic is and how it differs from the other Mathematical arts and sciences. Arithmetic is a very ancient study and we should never think that Mathematics are something new. Calculators and computers may be new, but Math itself is very old. Ancient Egyptians and Babylonians were famous for their understanding of numbers and much of what we know today was discovered thousands in ancient times. For example, the size of the earth was calculated by a Greek mathematician over 2,000 years ago!

Philosophers discovered that there are four basic branches of Mathematics–each with a different focus. Arithmetic is the study of multitudes by themselves. Music is the study of multitudes in relation to other multitudes. Geometry is study of magnitude in objects at rest. Astronomy is the study of magnitude in objects in motion. This may be confusing now, but in due time it will be very clear.

Arithmetic is the first of these arts to be studied because all of the others depend on our knowledge of numbers. We cannot speak of a “quarter-note” in Music unless we have first learned Arithmetic. We cannot define a triangle or an octagon in Geometry without first learning of numbers in Arithmetic. We cannot study Astronomy without the knowledge of Geometry and both depend on our knowledge of numbers. Thus we do not merely study Arithmetic for the sake of numbers, but also for the ability we gain to study other branches of mathematics and natural science.

The most important thing about Mathematics is that these studies are good for our souls. Mathematics help us to understand many things that we would not be able to understand by our senses alone. It is the gift of Reason that allows us to pursue knowledge that our eyes, ears, nose, mouth and hands could never help us with. For example, when we close one eye and hold our finger up in front of a distant tree, our sight tells us that the finger is larger than the tree. Our ears can’t help us with this problem, nor can any of our other senses. It is our Reason that comes to our aid and helps us to understand why a finger appears larger than a tree. Mathematics will help us with many such problems and allow us to study things we cannot sense–even things that belong to eternity.

## Memory Work

1. What is Mathematics?

**Mathematics is the study of Quantity.**

2. What is a Quantity?

**Quantity is any thing that may be increased or diminished.**

3. What are the two kinds of Quantity?

**The two kinds of Quantity are Multitudes and Magnitudes.**

4. What is a Multitude?

**A Multitude is a quantity consisting of disconnected parts, as three stones or seven coins. It may be also called a “Discontinued Quantity”.**

5. What are the two kinds of Multitude?

**The two kinds of Multitude are Absolute and Relative.**

6. What is Absolute Multitude?

**Absolute multitude is multitude viewed by itself, with no relation to anything else, as even, odd, perfect, and so on.**

7. What is Relative Multitude?

**Relative multitude is multitude viewed in relation to something else, as greater, smaller, half, double, and so on.**

8. By what method do we study Absolute Multitude?

**We study Absolute multitude in Arithmetic.**

9. By what method do we study Relative Multitude?

**We study Relative multitude in Music.**

10. What is a Magnitude?

**A Magnitude is a quantity that is whole and continuous, as a field, a circle, the universe, and so on. It is also called a “Continued Quantity”.**

11. What are the two kinds of Magnitude?

**The two kinds of Magnitude are Magnitude at Rest and Magnitude in Motion.**

12. By what method do we study Magnitude at Rest?

**We study Magnitude at Rest in Geometry.**

13. By what method do we study Magnitude in Motion?

**We study Magnitude in Motion in Astronomy.**

14. What then are the four Mathematical Arts?

**The four Mathematical arts are: Arithmetic, Music, Geometry and Astronomy.**