I’m still reading Hollinghurst’s The Line of Beauty, and I’ve gotten to the part where the title is explained. First, on p. 176:
The ogee curve was repeated in the mirrors and pelmets and in the wardrobes, which looked like Gothic confessionals; but its grandest statement was in the canopy of the bed, made of two transecting ogees crowned by a boss like a huge wooden cabbage. It was as he lay beneath it, in uneasy post-coital vacancy, that the idea of calling Wani’s outfit Ogee had come to him: it had a rightness to it, being both English and exotic, like so many things he loved. The ogee curve was pure expression, decorative not structural; a structure could be made from it, but it supported nothing more than a boss or the cross that topped an onion dome. […] The double curve was Hogarth’s ‘line of beauty’, the snakelike flicker of an instinct, of two compusions held in one unfolding movement. He ran his hand down Wani’s back. He didn’t think Hogarth had illustrated this best example of it, the dip and swell—he had chosen harps and branches, bones rather than flesh. Really it was time for a new Analysis of Beauty.
Then, on p. 196, a fuller exposition:
“So you’ve got a name for the bloody thing.”
“Yah, we’re calling it Ogee, like the company,” Wani said, very straightforwardly.
Bertrand pursed his plump lips. “I don’t get it, what is it…? ‘Oh Gee!,'” is that it?” he said, bad-tempered but pleased to have made a joke. “You’ll have to tell me again because no one’s ever heard of this bloody ‘ogee.'”
“I thought he was saying ‘Orgy,'” said Martine.
“Orgy?!” said Bertrand.
Wani looked across the table, and since this unheard-of name had originally been his idea Nick said, “You know, it’s a double curve, such as you see in a window or a dome.” He made the shape of half an hourglass with his hands raised in the air, just as Monique, in one of her occasional collusive gestures, did the same and smiled at him as if salaaming.
“It goes first one way, and then the other,” she said.
“Exactly. It originates in… well, in the Middle East, in fact, and then you see it in English architecture from about the fourteenth century onwards. It’s like Hogarth’s line of beauty,” Nick said, with a mounting sense of fatuity, “except that there are two of them, of course… I suppose the line of beauty’s a sort of animating principle, isn’t it…” He looked around and swooped his hand suggestively in the air. It wasn’t perhaps the animating principle here.
First off, I love the writing: “a boss like a huge wooden cabbage”! It’s also interesting that Hollinghurst changes Hogarth’s phrase, which is “line of grace”; in Analysis of Beauty (1754), he writes: “that sort of proportioned, winding line, which will hereafter be called the precise serpentine line, or line of grace.”
But there’s actually an item of etymological interest, which is the word ogee itself; it may be historically identical with ogive. OED (both entries updated March 2004) for ogee:
Origin uncertain; perhaps shortened < ogive n., or perhaps < an unattested Anglo-Norman *ogé < an unattested post-classical Latin *obviatum, use as noun of neuter singular past participle of classical Latin obviāre obviate v., the sense being assumed to be ‘going against’ and hence ‘supporting’.
And for ogive:
< Old French, Middle French, French ogive diagonal arc under a vault (1260), also œgive (1325), augive (1347), orgive (1399), osive, oisive (1462–3), oysive (1472), further etymology uncertain and disputed: perhaps < Spanish aljibe cistern (1202 as algib, 1278 as algibe) < Spanish Arabic al-jubb < al the + jubb well, cistern, pit (see note below), or perhaps < an unattested derivative (see –ive suffix) of classical Latin obviāta, feminine past participle of obviāre (see obviate v.), the sense being assumed to be ‘going against’ and hence ‘supporting’. French augive is also attested in sense 2 (1606). Compare post-classical Latin ogiva (1289, 1325 in British sources).
The proposed Spanish-Arabic etymology implies that the cistern is subterranean and supported by pillars with groined vaulting; support has been drawn from the correspondence between French voute d’ogive (1676) and Spanish bóveda de aljibe, lit. ‘vault of a cistern’ (1661), but this phrase is attested much later than the French or English words. The etymology remains uncertain: see further G. B. Pellegrini Gli Arabismi nelle Lingue Neolatine (1972) 89 n. 93.
The etymological conjectures recorded by N.E.D. (1902) (connection with French auge trough; with Italian auge (1336), Spanish auge (1256–76), Portuguese auge (1460–8) ‘the highest point of any planet’ (Florio), culmination, highest point < Arabic awj; or with classical Latin augēre to increase, augment) have now been superseded.
It always gives me perverse pleasure when the OED (ex-NED) explicitly rejects its old etymologies, as in the last paragraph above. (Oh, and if you’re wondering about the pelmets in the first quote, a pelmet is “A narrow border of cloth or wood, fitted across the top of a door or window to conceal curtain fittings,” and it’s probably “a variant of palmette n. …, palmette designs having been a conventional ornament on window cornices” — OED, entry updated 2003.)