Understanding measurement in light of its origins

During the course of history, the natural sciences have seen the development of increasingly convenient short-hand symbolic devices for denoting physical quantities. These devices ultimately took the form of physical algebra. However, the convenience of algebra arguably came at a cost - a loss of the clarity of direct insights by Euclid, Galileo, and Newton into natural quantitative relations. Physical algebra is frequently interpreted as ordinary algebra; i.e., it is interpreted as though symbols denote (a) numbers and operations on numbers, as opposed to (b) physical quantities and quantitative relations. The paper revisits the way in which Newton understood and expressed physical definitions and laws. Accordingly, it reviews a compact form of notation that has been used to denote both: (a) ratios of physical quantities; and (b) compound ratios, involving two or more kinds of quantity. The purpose is to show that it is consistent with historical developments to regard physical algebra as a device for denoting relations among ratios. Understood in the historical context, the objective of measurement is to establish that a physical quantity stands in a specific ratio to another quantity of the same kind. To clarify the meaning of measurement in terms of the historical origins of physics carries basic implications for the way in which measurement is understood and approached. Possible implications for the social sciences are considered.