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In Classical Geometry, students must learn how to study Propositions.  To do this, they must understand the parts of propositions and how propositions work.  THE ELEMENTS OF GEOMETRY We see that the title of the classic text on the art of Geometry is Euclid’s “Elements”.  When we begin this study, we find three sets of information provided by Euclid: Definitions Postulates Common Notions, or “Axioms” These are the “elements” from which the art of Geometry is constructed.  Every point we learn about the science of “magnitudes at rest”, will be proven from these definitions, postulates and axioms.  It is recommended … Continue

Ray’s Arithmetic in the Classical Liberal Arts Academy

In the Classical Liberal Arts Academy, we provide students with the opportunity to study the excellent Ray’s Arithmetic series, which was arranged and publish by Dr. Joseph Ray in the 1800s. Our online courses make the content of this series available for free to students, and offer online quizzes, graded assignments and support as well. I. Primary Arithmetic The first study in the series is Primary Arithmetic, which covers the basics of counting and arithmetic facts. This text is intended for students getting started in Arithmetic, ages 5 and above. This study is available in the Academy’s Modern Arithmetic I … Continue

Nicomachus, Arithmetic. Lesson 01.

In this lesson, we begin Classical Arithmetic, studying the ancient work of Nicomachus. To complete the objectives of this lesson, complete the following tasks: Study the lesson for mastery. Complete the lesson assessment. Lesson The ancients, who under the leadership of Pythagoras first made science systematic, defined philosophy as the love of wisdom. Indeed the name itself means this, and before Pythagoras all who had knowledge were called “wise” indiscriminately- a carpenter, for example, a cobbler, a helmsman, and in a word anyone who was versed in any art or handicraft. Pythagoras, however, restricting the title so as to apply … Continue

Euclid, Geometry. Book I, Proposition 1

In this lesson, we study the demonstration of the first proposition in Euclid’s Geometry (Proposition 1.1). The analysis of the proposition is provided below. To complete the objectives of this lesson, complete the following tasks: Review the memorization of the elements of Book I. Study the proposition for mastery. Identify the parts of the proposition. Complete the lesson assessment. Lesson Identify the Proposition studied in this lesson.In this proposition, we are studying Proposition 1 of Book I, i.e., Proposition 1.1. Summarize what has been studied in recent/previous propositions to prepare for this proposition.This is the first proposition. State the proposition. … Continue

Modern Arithmetic III (88). How to Find Common Prime Factors

In this lesson, we will learn how to find the prime factors common to two or more numbers. To complete the objectives of this lesson, complete the following tasks: Study the lesson for mastery. Memorize the rule given in the lesson. Complete all lesson exercises. Complete the lesson assessment. Lesson To learn how to find the prime factors common to two or more numbers, let us begin with an example problem by which the rule may be understood. 1. What prime factors are common to 30 and 42? Step 1. Write the numbers in line. 30 42 Step 2. From … Continue

Classical Geometry Text Now Available in Print

The text of Euclid’s Elements used in the Classical Liberal Arts Academy’s Classical Geometry course is now available in a large study edition (8.5″ x 11″) for students. Copies can be purchased from Lulu directly. The text is centered on the pages with 2″ of space on all sides for student notes. The cover is a nice, matte paperback that can endure some wear and tear. This is the first of three volumes that will be published, providing everything students need to master Euclid’s famous work. Normally, however, school-age students get through only Books I and II, which are both … Continue

Monteverdi and Goals in Catholic Homeschooling

The selection above is a musical setting by Claudio Monteverdi for evening prayers (vespers) on the eve of Marian feast days. Monteverdi lived from 1567 to 1643, and composed this work 1610 and dedicated it to Pope Paul V. Monteverdi is important for us as we consider the restoration of classical Catholic education and the real-life challenges we face a parents and students. The patron saint of students is St. Aloysius Gonzaga, who lived from 1568-1591, dying at age 23. Catholic parents often speak of “raising saints” as if this is a matter of choosing. The truth, however, is that … Continue

The Order of the Classical Quadrivium

The following is taken from Thomas Taylor’s “Theoretic Arithmetic” (1818) Arithmetic is to be learned the first of the mathematical sciences, because it has the relation of a principle and mother to all the rest. For it is prior to all of them, not only because the fabricator of the universe employed this as the first paradigm of his distributed intellection, and constituted all things according to number. But the priority of Arithmetic is also evinced by this, that whenever that which is prior by nature is subverted, that which is posterior is at the same time subverted; but when … Continue

A Modern Mathematician with a Classical Education: Interview with Dr. Jonathan Kenigson

This past year, I have been blessed to make the acquaintance of Dr. Jonathan Kenigson. Dr. Kenigson contacted me after discovering the Classical Liberal Arts Academy website, and we’ve corresponded a bit about the study of mathematics and classical education in general. He wrote at the time: “I am quite convinced that what you have assembled rivals (or in fact exceeds) the standards of the finest universities of modern Europe.”–which I took as a great compliment, since he was one to know. What intrigued me more than Dr. Kenigson’s mathematical interests and expertise, was bits and pieces I gathered concerning … Continue

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