Page:Euclid's Elements 1714 Barrow translation.djvu/154

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142
The ſeventh Book of

X. A number oddly odd is that which an odd number meaſures by an odd number.

XI. A prime (or firſt) number is that, which is meaſured only by an unit.

XII. Numbers prime the one to the other, are ſuch as only an unit doth meaſure, being their common meaſure.

XIII. A compoſed number is that which ſome certain number meaſures.

XIV. Numbers compoſed the one to the other, are they, which ſome number, being a common meaſure to them both, does mcaſure.

In this, and the preceding definition, unity is not a number.

XV. One number is ſaid to multiply another, when the number multiplied is ſo often added to itſelf, as there are units in the number multiplying, and another number is produced.

Hence in every multiplication a unit is to the multiplier, as the multiplicand is to the product.

Obſ. That many times, when any number are to be multiplied as (A into B) the conjunction of the letters denotes the product: So AB=A×B, and CDE=C×D×E.

XVI. When two numbers multiplying themſelves produce another, the number produced is called a plain number; and the numbers which multiplied one another, are called the ſides of that number: So 2(C)×3(D)=6=CD is a plain number.

XVII. But when three numbers multiplying one another produce any number, the number produced is termed a ſolid number; and the numbers multiplying one another, are the ſides thereof: So 2(C)x3(D)x5(E)=30=CDE is a ſolid number.

XVIII. A ſquare number is that which is equally equal; or, which is contained under two equal numbers. Let A be the ſide of a ſquare; the ſquare is thus noted, AA, or Aq. or A².

XIX. A