Hold one picture: a band going all the way around a middle and meeting itself. On a horse it is a real leather strap under the belly, pulled tight so the saddle cannot slide. Take the strap off, lay it flat and measure it, and you have the other meaning - how far it is around a tree, a pipe or a waist. Even the maths use counts the smallest way around a loop.
From the word’s history
The packet's source traces girth to Middle English girth, from Old Norse gjord, from a Proto-Indo-European root meaning to encircle, enclose, belt. It names gird and German Gurt as relatives. So the encircling band is the oldest recorded idea in the word.
這份資料的來源說，girth 來自中古英語 girth，再往前是古諾斯語 gjǫrð，最早的字根意思是圍起來、圈住、束帶。來源還列出 gird 和德語 Gurt 這些同源字。所以繞一圈的帶子這個概念，在這個字裡是有紀錄的最早一層。
Wiktionary 'girth' etymology as supplied in this packet (source_ref kaikki:3f6f69a190036ae4:524088070, 524112045)
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