Cassidy points out the amazing similarity between the word slats in English, which can be used as a slang term for the ribs, and an identical word in Irish:
Slat, pl. slats, n. a rib or ribs, especially those of a person.
Slat, pl., slata,n. a rib, ribs (of the body), (Dinneen, 1052).
This is a typically stripped-down, sculpted presentation of the facts. The reason why Cassidy doesn’t quote from the major modern Irish dictionary, Ó Dónaill, is that it doesn’t give the meaning ribs for the word slat. You can find the following entry at the excellent focloir.ie:
slat1, f. (gs. -aite, npl. ~a, gpl. ~). 1. Rod. (a) Slender stick; cane, switch. ~ sailí, choill, sally-, hazel-, rod. An t~ a thabhairt do dhuine, to take the rod to s.o. Bhain sé ~ a sciúr é féin, he cut a rod for his own back. ~ bhuachailleachta, tiomána, rod used to herd, to drive, cattle. ~ iascaigh, iascaireachta, fishing-rod. ~ ribe, rod with snare attached. ~ chlaímh, sword-stick. ~ mhaoile, strickle (for levelling). (b) Wand. ~ draíochta, magic wand. ~ ríoga, sceptre. Bheith faoi shlat ag duine, to be ruled by s.o., to be under s.o.’s thumb. ~ mhaoraíochta, big stick, control, coercion. (c) Slender bar. ~ chopair, iarainn, copper, iron, rod. ~ croiche, transverse bar of pot-rack. ~ chuirtín, curtain-rod. ~ ghunna, ramrod. ~ loine, piston-rod. ~ phota, pot-hook. ~ teallaigh, fire-iron. ~ tumtha, dip-stick. El: ~ charbóin, since, carbon, zinc, rod. S.a. crios 3. (d) ~ tomhais, measuring-rod; yardstick, criterion. ~ a chur ar rud, to measure sth.; to run the rule over sth. Dá gcuirfeá ~ ar Éirinn (ní bhfaighfeá a leithéid), if you were to search the whole of Ireland (you wouldn’t find the like of it). ~ dá thomhas féin a thabhairt do dhuine, to pay s.o. in his own coin. (e) Rail. ~ staighre, stair-rail. ~ droichid, rail guarding side of bridge. (f) Nau: ~ bhéil, ~ bhoird, gunwale. Tá sí síos go ~ an bhéil, it (boat) is down to the gunwale, heavily loaded. (g) Nau: ~ seoil, sail-yard. ~ bhrataí, jack-staff. (h) ~ droma, backbone. Síneadh ar shlat a dhroma, ar shlat chúl a chinn, é, he was stretched on the broad of his back. (i) Arb: ~a dubha, mountain willow. S.a. domhnach 1. (j) Algae: ~a mara, sea-rods. S.a. ceann1 1(l). (k) Bot: ~a gorma, bitter-sweet, woody nightshade. ~a dearga, spotted knot-grass. (l) Sapling, slip, scion. ~ de bhuachaill, de chailín, slip of a boy, of a girl. (m) Astr: ~ an Rí, an Bhodaigh, an Cheannaí, belt of Orion. (n) Physiol: ~ (fhearga), penis. 2. Meas: Yard. ~ ar fad, a yard long. Rud a thomhas ina shlata, to measure sth. in yards. ~ éadaigh, yard of cloth. S.a. cóta 2. 3. (pl.) Outskirts. Ar shlata na cathrach, on the outskirts of the city. (Var: pl. ~acha)
Dinneen’s Irish dictionary does give the meaning ribs for slat, but buried among these many other meanings. It is also worth remembering that the usual word for rib in Irish is easna.
As for the English word slat, Dictionary.com says:
a long thin, narrow strip of wood, metal, etc., used as a support for a bed, as one of the horizontal laths of a Venetian blind, etc.
The same source tells us that it is sometimes used as a slang term for the ribs and that its origin is from French: 1350-1400; Middle English sclat, slatt a slate < Middle French esclat splinter, fragment …
The French language Wiktionary tells us that the ultimate root of this word is a Frankish (i.e. Germanic) word which is etymologically linked to the English word slit.
A look on eDIL shows that slat is a very ancient term for a rod or stick in Irish. It has cognates in other Celtic languages and derives, according to McBain’s Gaelic Dictionary (which contains etymological notes) from the Proto-Celtic *slattā, which means a stalk or staff.
In other words, there is absolutely no room for doubt that these two words, in spite of the fact that they sound the same and are similar in meaning (both mean a kind of rod or stick), have no etymological connection. People who are ignorant of languages will assume that the fact that they are similar in both meaning and form means they must be related. However, we have already discussed such random similarities in the context of the Irish daor, which means expensive, and the English dear, with the same meaning. These two words also have totally different etymologies and are unrelated. The fact is, when comparing thousands and thousands of words from one language with the thousands and thousands of words in another, it would be surprising if we didn’t find matches of this kind. What makes them more than random coincidence is when we find lots of them following a regular pattern, which is not the case here.