tax

The root tax comes from Latin taxāre, which carried two intertwined ideas: 'to handle / touch repeatedly' and, from that, 'to assess, appraise, evaluate.' To taxāre a thing was to feel it over, size it up, put a value on it. That single act of valuation is the seed of the whole family.

Follow the 'assess a value' thread and you arrive at the most familiar member: tax. A tax is literally a charge assessed on the value of your income, goods, or property — the government appraises what you have and demands a share. Taxation is the whole system of doing this, and to find something taxing is to feel it drain you, as if it levied a heavy charge on your energy.

Now follow the second thread — 'arrangement, ordering.' Latin taxāre sits beside Greek taxis, meaning 'an orderly arrangement, a drawing-up of ranks.' From Greek taxis + nomos ('law, ordering') we get taxonomy: the science of arranging living things into ordered ranks — kingdom, phylum, class, and so on — and a taxonomist is the person who does that sorting.

A word of caution about look-alikes. Tactic, tactical, tactician, and tactics also come from Greek taktikos, 'fit for arranging (troops),' a close cousin of taxis — so they share the 'arrange in order' idea. But the tact- in tactile / contact / tact (meaning 'touch') comes from a different Latin verb, tangere 'to touch.' Same-looking spelling, separate root. And taxi is a fun surprise: it is short for taximeter cab — a cab fitted with a taximeter, the device that taxes (charges) you by distance.

So the family splits cleanly: 'put a value on it' gives tax / taxation / taxing / taxi; 'put it in order' gives taxonomy / tactic / tactical.