Geometry is the science of determining the quantity of anything, not measured, by comparing it with some other quantity or quantities measured. Which science therefore whosoever shall go about to teach, must first be able to tell his disciple what measuring or dimension is; by what each several kind of quantity is measured; what quantity is, and what are the several kinds thereof. Therefore as they, who handle any one part of geometry, determine by definition the signification of every word which they make the subject or predicate of any theorem they undertake to demonstrate; so must he which intendeth to write a whole body of geometry, define and determine the meaning of whatsoever word belongeth to the whole science. The design of Euclid was to demonstrate the properties of the five regular bodies mentioned by Plato; in which demonstrations there was no need to allege for argument the definition of quantity, which it may be was the cause he hath not anywhere defined it, but done what he undertook without it. And though having perpetually occasion to speak of measure, he hath not defined measure; yet instead thereof he hath, in the beginning of his first elements, assumed an axiom which serveth his turn sufficiently as to the measure of lines, which is the eighth axiom; that those things which lie upon one another all the way (called by him ἐφαρμόζοντα) are equal. Which axiom is nothing else but a description of the art of measuring length and superficies. For this ἐφάρμοσις can have no place in solid bodies, unless two bodies could at the same time be in one place. But amongst the principles of geometry universal, the definitions are necessary, both of quantity and dimensions. Quantity is that which is signified by what we answer to him that asketh, _how much_ any thing is? and thereby determine the magnitude thereof. For magnitude being a word indefinite, if a man ask of a thing, _quantum est?_ that is, _how much_ it is, we do not satisfy him by saying it is magnitude or quantity, but by saying it is _tantum_, _so much_. And they that first called it in Greek, πηλικότης, and in Latin _quantity_, might more properly have called it in Latin _tantity_, and in Greek τηλικότης; and we, if we allowed ourselves the eloquence of the Greeks and Latins, should call it the _so-muchness_.