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Quantities like '10 degrees celcius', '5 feet long' and '15 miles per hour' apply to subjects but I can't figure out what the connection is.

For example, we say things like 'that cars speed is 15 miles per hour', and I can see that '15 miles per hour' is a quantity, and that 'the car' is a substance. But where does the 'speed' bit come from? and why do we say that the car 'has' a speed?

Another example, we say things like 'that table is five foot long', here 'that table' is a substance, 'five foot' is a quantity, but how does that relate to 'Length'?

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    Aristotle's treatment of quantity is generally unsatisfactory, see SEP, Aristotle’s Categories. In particular, his list of the species of quantity is too short and he often conflates them with quantified substances. But, presumably, speed and temperature are species of continuous quantity that are being predicated, and the numbers are quantities within those species. Alternatively, they could be his "relatives" that relate substances to quantities (numbers).
    – Conifold
    Commented Jan 30 at 19:51

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Categories are properties of a substance, and also the substance itself is considered one of 10 categories. The remaining 9 categories are properties of the substance. Quantity is one of the remaining 9 categories.

A car (substance) that speeds 15 miles per hour has several properties, one property is “speeding 15 miles per hours.” When the car stops, then the car (substance) remains invariant, but its speed (one of its properties) has changed.

You find the concepts of substance and its properties in Aristotle’s work “Categories”, see also Categories.

In order to apply the scheme to speed I would choose Aristotle’s category “quantity”, and consider speed as the quotient speed = space/time.

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