Across and Down

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There are 128 clues with the answer 'ARCHIMEDES'
# CLUE
1.
Scientist from Syracuse building bridges across island and sea (10)
2.
Greek agreed to take a rest mostly outside (10)
3.
Excited emir chased legendary streaker (10)
4.
Excited emir chased legendary streaker
5.
Ancient Greek scientist
6.
With 36-Across, the upward buoyant force of a body immersed in a fluid is equal to the weight of the fluid the body displaces (2 wds.)
7.
Famous mathematician rang during a short break (10)
8.
A man of principle deems chair repairable
9.
He took the plunge for a basic truth (10)
10.
"Give me a lever long enough, and a fulcrum strong enough, and single-handed I can move the world." Who said this?
11.
Old mathematician rang, interrupting warlord
12.
Hear chime described in part by Ancient mathematician (10)
13.
Inventor agreed to obstruct Olympian
14.
Me? I would search for old Greek (10)
15.
Mathematician who screwed up? (10)
16.
Ancient inventor made riches in a new way (10)
17.
'Rub-a-dub-dub' went his thoughts in the tub, till raising hell and high water with Eureka! (10)
18.
Greek maths whizz maids cheer up (10)
19.
Mathematician once corresponded in a matter of law
20.
Greek scientist associated with the cry "Eureka!"
21.
Man of principle made riches in a strange way (10)
22.
Ancient Greek, sound as a bell, died in his god's embrace
23.
Among cunning old people there's one mathematician (10)
24.
Man of principle made riches in a strange way
25.
Among cunning old people there's one mathematician
26.
"Eureka!" shouter (10)
27.
Old Greek could be forced to heed racism (10)
28.
Ancient Greek popularly remembered for saying 'Eureka' (10)
29.
Chief ordered demise of Greek mathematician (10)
30.
Old Greek building new side, including this writer (10)