1 (number)

“Things consisting of fewer Principles are more accurate, than those understood by Addition [of more principles], as Arithmetic is more accurate than Geometry. ...That Science is more accurate which consists of fewer Principles, than what is only to be understood by Addition, as Arithmetic is more accurate than Geometry. I say by Addition, as Unity is a Being understood without Position, but a Point is to be understood only by Position.”

“Every quantity is recognized as quantity through the one, and that by which quantities are primarily known is the one itself; therefore the one is the source of number as number.”

“More knowable than the number is the unit; for it is prior and the source of every number.”

“Let us take as the basis of our consideration first of all a thought-thing 1 (one).”

“Number is limited multitude or a combination of units or a flow of quantity made up of units; and the first division of number is even and odd.”

“Arithmetic is indeed more accurate than Geometry, for its Principles respect Simplicity. Unity implies no Position, a Point does, and a Point requiring Position is the Principle of Geometry, Unity of Arithmetic.”

“Since each number is with respect to its own kind one and without parts but with respect to its own material, as it were, divisible into parts, though not with respect to all of the material either; but rather what is ultimate [in it, i.e., the unit] is without parts even in the material, and in this ultimate thing [counting or calculation and, above all, partitioning] comes to a stop.”

“I cannot satisfy myself that, when one is added to one, the one to which the addition is made becomes two, or that the two units added together make two by reason of the addition. I cannot understand how, when separated from the other, each of them was one and not two, and now, when they are brought together the mere juxtaposition or meeting of them should be the cause of their becoming two...”