Across
Rib principally toughens the thorax, reportedly? Enter as per fill at 1 Across, with alternate letters filling white squares (5)
Support in the library to reserve hotel in person (9)
Annoyed as new water heater, failing to start, died (7)
Dummy swallowed plant with bad smell (7)
See God's city for, unfortunately, the lowest of the low (5,2,7)
Top Cambridge mathematician abandoning arithmetic, perhaps at the first opportunity, for calculator? (7)
Starts to notice habitual halitosis, having, in elemental form, gas (7)
Container prone to leaking - ridiculously wet, total bother (3-5,6)
5d
(and 5 Down) See 5 Down (7,4)
See e.g. gents pursuing sex and the Bible in retreat (7)
Walk briskly, then run from Tea Party participant (5,4)
Island occasionally banned nature study in central location (5)
Down
Now, on date to be taken for a ride, where are you? If you have not done so already, enter as per fill at 1 Across, with alternate letters filling white squares (2,3,4)
In Japan, the only circular temple (8)
Earldoms? Do not present incorrectly as provinces (6)
I make an offer in the same place (4)
See 25 Across
One revered before the first year of Our Lord, I'm thinking, in the Colosseum? (7)
Upright judge replaced by king in purge (5)
25 Across, 5 Down turned up after following string along (4)
Original day of 1 Across to 6 Across others (5)
Broadcasting acceptable song (2-3)
Catholic state supported by us in Paris, like Notre Dame (9)
Cloth we fabricated using traditional methods (3-4)
1 Across? I don't know ... (3,1,4)
Command and control (5)
Making a face, head away for trip (6)
Smile awkwardly, maybe losing heart (4)
Mock debut of Stallone, a terrible actor (4)
See 6 Across directions (4)
Type letters or click words in the clue