Art of the Possible by Poat

Puzzle explanation

The answers to the 12 normal clues were anagrammed to make the words entered in the grid. In the other 24 clues, a word was anagrammed and had to be resolved before solving; the initial letters of the resulting words spelt out “cubic and quartic equations”. Re-anagramming the entries in the bottom and top rows produced ARS MAGNA (an anagram of “anagrams”) and CARDANO, to be highlighted. The solutions to cubic equations and quartics were first published in 1545 by Gerolamo (or Geronimo) Cardano in his Latin treatise Ars Magna (The Great Art). He is mentioned in Chambers as the inventer of the cardan joint.

Clue explanations

Conventions: * = anagram, < = reversal

No Anagram (clue word) Answer Explanation
Across
1 cadet (acted) ARCADES CADE(t) in ARS
5 unescorted (Uncorseted) ALONE (wh)AL(eb)ONE
10 bedroom (Boredom) BREEZILY BR + homophone of EASILY
12   PIRAYA RAY in PISCINA − (SCI + N)
13 Isle (Lies) VISAGE I in (V + SAGE)
14 clary (Lycra) PASSAGE PA + S in SAGE
15 Australian (Saturnalia) ASLAN (SLANG − G) after A
16   TOTEMS TO + STEM with S moved later
20   ATRESIA (TRÈS + I) in AA
21 nastily (Saintly) WET-LOOK TOWEL * + OK
25   MANUAL MAN U + A + L
26 dragoon (gadroon) UHLAN ((Cardi)NAL HU(me)) <
28 quite (quiet) GUTSERS GUTS + ERS(t)
30   AERIAL homophone of ARIEL
31 untidy (nudity) NIELLO LIONEL *
32 American (Cinerama) ESSENCIA SCENES * + I’ + A
33 rock (Cork) TRASS TRESPASS − ESP
34   GATEMAN (NAME TAG) <
Down
1 tamboura (marabout) ALAP A + LAP
2   SCATTIER SCAT + TIGER − G
3 iron (nori) DERATION FEDERATION − FE
4 condies (secondi) SIVERS SI + VERS
6   SLAYS LAY in SS
7 exam (Amex) ORAL FOR ALL = FL around ORAL
8 quits (squit) NEGATION NEGATION − EG = NATION
9   ANTEDATE (w)ANTED A TE(sla)
11 uveal (value) EASEL EAU + SEL − U(veal)
16 abused (daubes) MOWBURNT (YET + MOWBURNT) * = MUTTONY BREW
17 telling (gillnet) OVERHEAR OVER + homophone of HERE
18   TITLINGS TITLING + (puzzle)S
19 insane (Sienna) BROMELIN (MILLER + B + ON) * − L
22 organism (Orangism) ORGASM ORGANISM − NI
23 neanic (canine) CUSEC (E + (neani)C) after CU’S
24   SWEAL SWEAR with L for R
27 stream (master) LAVA LAVATORY − TORY
29   AMOS ’S after (A + MO)
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