CHAPTER IV¶
On Those Things Which the Reader Must Observe for the Understanding of This Treatise
Furthermore, for the avoidance of difficulty in what follows, let the reader note that whenever we cite “the first of the first” ([I.1]), “the fourth of the second” ([II.4]), “the tenth of the fifth” ([V.10]), “the twentieth of the sixth” ([VI.20]), and so on up to the fifteenth Book, the first number is always to be understood as the number of the proposition (conclusione), and the second number as the number of the Book of our philosopher Euclid, whom we follow in all things as the archimandrite [supreme leader] of these faculties. That is, to say “by the fifth of the first” ([I.5]) means “by the fifth proposition of his first Book,” and so likewise for the other particular books of his complete work on the Elements and first principles of Arithmetic and Geometry. When, however, an authority adduced by us is drawn from another work of his [such as the Optics or Catoptrics] or from another author, we shall name that work and that author explicitly.
Moreover, because of the many varied characters and abbreviations that are customarily employed in such faculties—especially by us, just as is required in every other profession: for medicine uses its own symbols for scruples, ounces, drachms, and handfuls (manipoli); silversmiths and jewelers use theirs for grains, pennyweights (denari), and carats; astrologers use theirs for Jupiter, Mercury, Saturn, the Sun, the Moon, and the rest; and merchants likewise use theirs for pounds (lire), shillings (soldi), groats (grossi), and pence (denari) for the sake of brevity, solely to avoid prolixity in writing and reading, since otherwise they would fill much paper with ink—in the same way we too, in the mathematical sciences and in algebra (that is, speculative practice, pratica speculativa), employ characters that denote the unknown (cosa, $x$), its square (censo, $x^2$), its cube (cubo, $x^3$), and the other algebraic powers, as contained in our aforesaid work [Summa de Arithmetica]. Some of these we shall also use in the present treatise, namely those which we have set forth in the Table at the beginning of the book [Folio 0011r, e.g., R. for Radice (root), p. for più (plus), m. for meno (minus)].
Likewise, let the reader observe that these terms—namely multiplication (multiplicatione), product (producto), and rectangle (rectangolo)—signify one and the same thing [for $a \cdot b$ is the area of the rectangle contained by segments $a$ and $b$]. And similarly, square of a quantity (quadrato de una quantità) and power of a quantity (potentia d’alcuna quantità, $\delta\acute{\upsilon}\nu\alpha\mu\iota\varsigma$) are one and the same thing: for the power of a line refers to its square, by the last proposition of the First Book ([I.47]), and the utmost that a line can produce in power (più che possa la linea) is its square. These equivalences must be kept in mind throughout our discourse, lest any equivocation arise in the meaning of the words.