@lewm Yes, the Quad 57 (your nomenclature) is indeed curved in the vertical dimension, which effectively focusses the sound on a horizontal line behind the speaker. Most other speakers claiming 'line source' have a virtual line which is vertical!
We now recognise the 57 as having three panels in a d'Appolito configuration, though unusually this is horizontal with a central treble flanked by two bass panels. Get off-center, and the bass panels start to differ in path-length, meaning there is a very small sweet-spot.
When the Quad 57 was re\eased in 1957 it was just the ESL. Sound Labs "The Complete White Paper" states "The electrostatic speaker art was in its infancy when Sound Lab started business back in 1978" which is a bit rich considering Quad sold 54,000 pairs of the original 57, starting 21 years earlier. I have many other quibbles with the white paper, especially when it groups dynamic speakers as point sources, which most certainly aren't.
Only the ESL-63 and later had the radiation pattern of a point source. Whereas the 57 has a very small sweet-spot (sideways!) speakers that emulate a point source have a very large listening area. The ESL 63 is often reported as the world's most accurate speaker, since it has a very light diaphragm, effectively no cabinet coloration, no crossover colouration, and a coherent radiation pattern with no cancellation / reinforcement interference patterns if reflections are ignored.. The 2905 has amplifier-like distortion measurements. And if it doesn;t play loud enough for you, you can just sit closer!
Note that I am not claiming it is the world's best speaker, just very accurate. Peter Walker's perfect amplifier is "a straight wire with gain". The 63 and later aim for the same neutrality "If you don't like what comes out, pay more attention to what goes in" he said.