Algebra I, Article 79. How to Divide One Polynomial by Another

In article 79, we are learning how to divide one polynomial by another.   To master this lesson, you must read SLOWLY and make sure you understand every step in the lesson. First, the teacher shows how two polynomials are multiplied so that we can see how the product is formed.  The product of multiplication becomes the dividend in division, so in division, we are seeking to move backwards to find that polynomial which, when multiplied by the divisor produced the dividend. Second, the teacher explains to us that before we can divide, we must make sure that the leading letter … Continue

Understanding Chapter 11 of Porphyry’s Introduction

Students often have a difficult time understanding chapter 11 in Porphyry’s Introduction, but this is actually very simple. In the Introduction, Porphyry is explaining the five kinds of things that can be predicated of subjects, known as the five predicables: Genus, Difference, Species, Peculiarity and Accident. In chapter 11, Porphyry writes: “It would seem that all the differences produced are twenty”. What in the world is he talking about? Porphyry is comparing and contrasting the five predicables. So, each of the five will need to be compared with the four others. Therefore, we should expect 20 comparisons–4 comparisons for each … Continue

Intro to Classical Arithmetic, Lesson 08.   Expressing Quantities:  Number

To complete the objectives of this lesson, complete the following tasks: Study your Lesson. Complete your Memory Work. Complete your Lesson Exercises. Complete the Lesson Examination. Lesson Thus far in Arithmetic, we have learned the different branches of Mathematics: Arithmetic, Geometry, Music and Astronomy. We have learn about Unity and units. We have learned about Comparison: equalities, inequalities, majority and minority, and in the last lesson we learned the first axioms of Arithmetic and how Proofs work. If you are uncomfortable with these subjects, you should go back and review. In this lesson, we will move on to study how … Continue

Why Do Signs Change in Algebra? (Article 58)

In article 58 of Algebra I, we read the following rule: Write the quantity to be subtracted under that from which it is to be taken, placing similar terms under each other. Conceive the signs of all the terms of the subtrahend to be changed, and then reduce by the rule for Addition. Step 2 of this rule leads to some confusion. Why should we “conceive the signs of all the terms of the subtrahend to be changed”? The reason is because operations are being performed within the subtrahend before it is subtracted from the minuend in the problem. These … Continue

Latin Grammar I, Article 32. Pronomina Composita ex Provocabulo QUIS, cum Sequitur

In lesson 30, we studied the declension of the Latin pronouns. In lessons 31-34, we will study a number of different composite pronouns, built from the simple pronouns studied in lesson 30, whose meaning and declension are important to know for Latin reading and translation. To complete the objectives of this lesson, complete the following tasks: Read through the lesson from beginning to end. Study the lesson for mastery, taking notes. Complete the lesson assessment. Lesson In lesson 31, we studied the first of several classes of composite pronouns, that is, pronouns composed of simple pronouns, which begin with the … Continue