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Classical Arithmetic, Lesson 04. Book I, Chapter 4

The following tasks are required to complete this lesson:

  1. Study the Lesson carefully
  2. Watch the lesson video, if available.
  3. Complete Comprehension Questions


In this lesson, a proof is offered to demonstrate that the monad is the first of all natural numbers, and the source of all multitude.

Every number is the half of the sum of the two numbers placed about it, in a natural series.  It is likewise the half of the sum of the numbers situated above these two; and also of the sum of the numbers situated above these last two, and so on till the progression is stopped by the monad or unity.

Thus about the number 5, the numbers 6 and 4 are immediately placed, the former above, and the latter below it. These therefore, if they are added together make 10, of which 5 is the half.  But the numbers which are next situated about 6 and 4, are 7 and 3.  And of these also when added together, make 10, of which 5 is the half. Again, the sum of the numbers placed about 7 and 3 is likewise the double of 5; for these are 8 and 2. And the like will take place in all the numbers in a natural series, till we arrive at the boundary of the monad. For the monad alone has not two terms situated on either side of it, and on this account it is the half of the number alone which is placed next to it.

Hence, it is evident that the monad is the first of all the numbers that are in a natural series, and also that it is deservedly acknowledged to be the source of all multitude, however extended it may be.


After studying this lesson, answer the following questions in complete sentences, proving your answers from the lesson. Enrolled students can simply copy and paste the questions and write their answers in the Submit Assignment for Review form.

  1. Identify the lesson being studied.
  2. Summarize your recent/previous readings in the course to prepare the context for this chapter.
  3. What is the topic of this lesson?
  4. As you read, list any terms or phrases encountered in this reading that you are unfamiliar with.  Look up their definitions in the Oxford English Dictionary and enter the best definition here.
  5. Summarize the content of this chapter, proving your careful reading and study.
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