Etymologiae, Book III, chapters 1-4: De vocabulo arithmeticae disciplinae to Quid praestent numeri
Book III. On mathematics Mathematics is called in Latin the doctrinal science, which considers abstract quantity
For abstract quantity is that which, separating it by the intellect from matter or from other accidents, as the even and the odd, or from others of this kind, we treat in reasoning alone. Its species are four: namely Arithmetic, Music, Geometry and Astronomy.
Arithmetic is the discipline of numerable quantity in itself. Music is the discipline that speaks of numbers which are found in sounds. Geometry is the discipline of magnitude and of forms. Astronomy is the discipline that contemplates the courses of the heavenly bodies and all the figures and habits of the stars.
These disciplines we shall set forth in turn a little more widely, so that their causes may be competently shown.
Chapter I. On the name of the discipline of arithmetic Arithmetic is the discipline of numbers. For the Greeks call number arithmos. The writers of secular letters wished it to be first among the mathematical disciplines, since it needs no other discipline in order to be; whereas Music and Geometry and Astronomy, which follow, need its help in order to be and to subsist.
Chapter II. On its authors They affirm that Pythagoras was the first among the Greeks to write down the discipline of number, and that it was afterwards set out more fully by Nicomachus; among the Latins Apuleius first translated it, then Boethius.
Chapter III. What number is Number is a multitude made up of units. For one is the seed of number, not a number. The coin (nummus) gave its name to number (numerus), and from its frequency attached the word. Unus draws its name from the Greek; for the Greeks call one hena: so two and three, which they call duo and tria. Quattuor took its name from the square figure. Quinque received its word not according to nature but according to the pleasure of the will, from him who gave names to the numbers. Sex and septem come from the Greek. For in many names which in Greek have an aspiration, we put S for the aspiration. Hence for hex we have sex, and for hepta septem, as for herpyllon we have herba serpillum. Octo by transference, as they and we: so they ennea, we novem; they deka, we decem. Decem are so named from Greek etymology, because they bind and join the numbers lying below. For deagos means among them to join or to bind. Further, viginti are so called because they are ten twice begotten, U put for the letter B. Triginta, because they are begotten from the ternary of the denary: so up to ninety. Centum are called from kanthos, which is a circle; ducenti from duo centum. So also the rest up to a thousand. Mille is from multitude, whence also militia, as if multitia: hence also milia, which the Greeks, changing a letter, call myriada.
Chapter IV. What numbers offer The reckoning of numbers is not to be despised. For in many places of the Holy Scriptures it shines forth how great a mystery they hold. For it was not in vain said in the praises of God: “Thou hast ordered all things in measure, and number, and weight.” The number six, which is perfect in its parts, declares the perfection of the world by a certain signification of its number. Similarly the forty days on which Moses and Elias and the Lord himself fasted are not understood without knowledge of numbers. So also there are other numbers in the Sacred Scriptures, whose figures none but those who know this science can solve. It has been given to us also in some part to live under the discipline of numbers, when we reckon the hours by it, when we dispute of the course of the months, when we recognize the space of the returning year. For through number we are instructed lest we be confounded. Take away number from all things, and all perish. Take reckoning from the world, and blind ignorance embraces all, nor can one be distinguished from the other animals who do not know the reason of calculation.