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The Apus constellation has 10 stars with Greek letters, none of them very bright and none of them with proper names:

 
Agena 14h 03m 49.44s 14h 03.824m 213.1
θ 14h 05m 20.10s 14h 05.335m 213.5
η 14h 18m 13.97s 14h 18.233m 216.8
ε 14h 22m 23.20s 14h 22.387m 217.8
α 14h 47m 51.73s 14h 47.862m 224.3
κ¹ 15h 31m 30.82s 15h 31.514m 235.3
δ 16h 20m 20.84s 16h 20.347m 247.7
γ 16h 33m 27.46s 16h 33.458m 251.1
β 16h 43m 05.42s 16h 43.090m 253.5
ζ 17h 21m 59.53s 17h 21.992m 263.4
ι 17h 22m 05.88s 17h 22.098m 263.4
θ Apodis 5.69 76° 48′ S 14h 02m 213.5
η Apodis 4.89 81° 00′ S 14h 15m 216.8
ε Apodis 5.06 80° 06′ S 14h 19m 217.8
α Apodis 3.83 79° 02′ S 14h 44m 224.3
κ¹ Apodis 5.52 73° 23′ S 15h 28m 235.3
δ Apodis 4.68 78° 42′ S 16h 17m 247.7
γ Apodis 3.86 78° 54′ S 16h 30m 251.1
β Apodis 4.23 77° 31′ S 16h 39m 253.5
ζ Apodis 4.76 67° 46′ S 17h 18m 263.4
ι Apodis 5.39 70° 07′ S 17h 18m 263.4

In the current investigation only the last pair of stars in Apus are of possible interest:

Rohini 9 (50) 10
Pleione 6 (20) 7
June 5 6 (157)
Cb3-1 Cb3-2 (443)
E vae ra - ka oho - ki te henua - kua huki ku kikiu - te henua
5h (76.1) λ Eridani (76.7)
Haedus II (75.9), ε Leporis (76.0), Cursa (76.4)
December 6 (340) 7
Az Zubana 8 9 (205)
Sabik (259.7), η Scorpii (259.9), Nodus I (260.0) π Herculis (260.7), Ras Algethi (260.8), Sarin (261.0), ο Ophiuchi (261.4)
Rohini 11 12 13 (54) 14
Pleione 8 9 10 (24) 11
June 7 8 9 (160) 10
Cb3-3 Cb3-4 Cb3-5 Cb3-6
ko te henua - te rima e kava i haga rave ika ki kikiu - te henua
μ Leporis (77.6), ĸ Leporis (78.0), Rigel (78.1), Capella (78.4) no star listed λ Leporis (79.6) Bellatrix, Saif al Jabbar (80.7), Elnath (80.9)
December 8 9 (343) 10 11
Az Zubana 10 11 12 (208) 13
ξ Ophiuchi (262.2), θ Ophiuchi, ν Serpentis, ζ, ι Apodis (262.4) ι Arae (262.8), ρ Herculis (262.9), β, γ Arae (263.3), κ Arae (263.5) σ Ophiuchi (263.6) Lesath, δ Arae (264.7), Alwaid, Maasym (265.1), Shaula (265.3)

We can see that the beautiful bird of Paradise with no feet cannot be touched by the flames from the Altar - the constellation is ending just before the Altar is beginning.

Instead, the brighter stars above Ara belong in the Southern Triangle, another fairly modern conception:

"Triangulum Australe is a small constellation in the far southern celestial hemisphere. Its name is Latin for 'the southern triangle', which distinguishes it from Triangulum in the northern sky and is derived from the almost equilateral pattern of its three brightest stars.

It was first depicted on a celestial globe as Triangulus Antarcticus by Petrus Plancius in 1589, and later with more accuracy and its current name by Johann Bayer in his 1603 Uranometria. The French explorer and astronomer Nicolas Louis de Lacaille charted and gave the brighter stars their Bayer designations in 1756." (Wikipedia)

The form of the triangle obviously could have described the flames of fire on the Altar and it is strange that these stars do not belong in Ara.

"Its varied classical names show disagreement as to its form, yet great familiarity with its stars, on the part of early observers, with whom it was of importance as portending changes in the winds and weather; Aratos devoting twenty-eight lines - a large proportionate space - of the Phainomena to this character of Ara." (Allen)

I guess 28 lines was a Sign of Aratos. 28 * 13 = 364.

Anyhow, I ought to list also the stars of Triangulum Australe. Also they are 10 in number:

Toliman 14h 39m 40.90s 14h 39.682m 222.2
γ 15h 18m 54.69s 15h 18.912m 232.3
ε 15h 36m 43.19s 15h 36.720m 236.7
β 15h 55m 08.81s 15h 55.147m 241.3
κ 15h 55m 29.61s 15h 55.494m 241.4
δ 16h 15m 26.27s 16h 15.438m 246.5
ι 16h 27m 57.27s 16h 27.955m 249.7
ζ 16h 28m 27.80s 16h 28.463m 249.8
θ 16h 35m 44.77s 16h 35.746m 251.6
η 16h 41m 23.13s 16h 41.386m 253.1
α 16h 48m 39.87s 16h 48.665m 254.9
γ Tr. Austr. 2.87 68° 41′ S 15h 16m 232.3
ε Tr. Austr. 4.11 66° 19′ S 15h 33m 236.7
β Tr. Austr. 2.83 63° 26′ S 15h 51m 241.3
κ Tr. Austr. 5.11 68° 36′ S 15h 52m 241.4
δ Tr. Austr. 3.86 63° 41′ S 16h 12m 246.5
ι Tr. Austr. 5.28 64° 03′ S 16h 24m 249.7
ζ Tr. Austr. 4.90 70° 05′ S 16h 25m 249.8
θ Tr. Austr. 5.50 65° 30′ S 16h 32m 251.6
η Tr. Austr. 5.89 68° 18′ S 16h 38m 253.1
α Tr. Austr. 1.91 69° 02′ S 16h 45m 254.9

Only α has a proper name, viz. Atria. (The name of α Trianguli is Metallah.)

Atria, the last star in the constellation, was close to the Full Moon in May 30 (150):

  4. Rohini  
Sheratan 11 12 13 14
May 27 28 29 30 (150)
Cb2-17 Cb2-18 Cb2-19 Cb2-20
manu rere - toga manu toga ka tuu te toga o te manu
no star listed Aldebaran (68.2), Theemin (68.5) no stars listed
November 27 28 (332) 29 30
Syrma 12 13 (196) Az Zubana 1 2
τ Scorpii (250.7), Han (251.0) ζ Herculis (252.1), η Herculis, β Apodis (252.5) no star listed Atria (253.9), Wei, η Arae (254.3)