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Evokation
  
 
Index
  

 

26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
9
-
-
-
-
5
6
-
-
-
1
-
-
-
-
6
-
8
+
=
43
4+3
=
7
-
7
-
7
-
-
-
-
-
-
-
-
8
9
-
-
-
-
14
15
-
-
-
19
-
-
-
-
24
-
26
+
=
115
1+1+5
=
7
-
7
-
7
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
-
-
1
2
3
4
-
-
7
8
9
-
2
3
4
5
-
7
-
+
=
83
8+3
=
11
1+1
2
-
2
-
1
2
3
4
5
6
7
-
-
10
11
12
13
-
-
16
17
18
-
20
21
22
23
-
25
-
+
=
236
2+3+6
=
11
1+1
2
-
2
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
+
=
351
3+5+1
=
9
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
+
=
126
1+2+6
=
9
-
9
-
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
+
=
1
occurs
x
3
=
3
-
3
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
+
=
2
occurs
x
3
=
6
-
6
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
-
3
-
-
-
-
-
+
=
3
occurs
x
3
=
9
-
9
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
-
-
-
-
+
=
4
occurs
x
3
=
12
1+2
3
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
+
=
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
6
-
-
+
=
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
7
-
+
=
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
8
+
=
8
occurs
x
3
=
24
2+4
6
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
+
=
9
occurs
x
2
=
18
1+8
9
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
45
-
-
26
-
126
-
54
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
4+5
-
-
2+6
-
1+2+6
-
5+4
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9
-
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
-
-
-
-
-
-
-
-
-
-
26
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
-
-
9
-
-
8
-
9
-
9

 

 

ADVENT 731 ADVENT

 

THIS IS THE SCENE OF THE SCENE UNSEEN

THE UNSEEN SEEN OF THE SCENE UNSEEN THIS IS THE SCENE

 

 

NETERS TEN NET ENTERS

 

 

THE, MIND, OF, HUMAN, KIND
ONE, TWO, THREE
THIRTEEN, ONE THREE, THIRTY ONE
ONE THREE, ONE, THREE
THIRTEEN, ONE THREE
ONE THREE
THIRTEEN
PERSEID
PERSEID, THIRTEEN, PERSEUS
PERSUES, PE, R, SE, U, S
PERSEUS
VOX, POP
VOX POP
ENLIGHTENER, ENL, I, GHTEN, E, R
CHINA, CHINESE
I CHING
I CHING
CONFUCIOUS
TAO
CHINAS, TERRACOTTA, WARRIORS
FIRST, EMPEROR
FIRST, EMPERORS, CHINESE, TERRACOTTA, WARRIORS
THE, EMPERORS, TOMB
RUSSIAN, RUSSIANS
THE, CHINESE
THE, RUSSIANS
QIN SHI HUANG
QIN SHI HUANG, Q, I, N, SH, I, H, UAN, G
THE, GREAT, WALL, OF, CHINA
CHINAS GREAT WALL
GREAT WALL
CHINAS, GREAT, WALL
PERSONAL, EXPRESSION
GEOMAGNETIC, GEO, MAGNETIC, THIRTEEN
GEOMAGNETIC
GEO, CENTRIC

 

 

3
THE
33
15
6
4
MIND
40
22
4
2
OF
21
12
3
9
HUMANKIND
95
41
5
18
First Total
189
90
18
1+8
Add to Reduce
1+8+9
9+0
1+8
9
Second Total
18
9
9
-
Reduce to Deduce
1+8
-
-
9
Essence of Number
9
9
9

 

 

O
=
6
3
ONE
34
16
7
-
1
T
=
2
3
TWO
58
13
4
-
2
T
=
2
5
THREE
56
29
2
-
3
-
-
10
11
First Total
148
58
13
-
6
-
-
 1+0
1+1
Add to Reduce
1+4+8
5+8
1+3
-
-
Q
-
1
2
Second Total
13
13
4
-
6
-
-
-
-
Reduce to Deduce
1+3
1+3
-
-
-
-
-
1
2
Essence of Number
4
4
4
-
6

 

 

8
THIRTEEN
99
45
9
8
ONE THREE
81
45
9
9
THIRTY ONE
134
53
8

 

 

-
-
-
-
ONE THREE
-
-
-
-
-
O
=
6
3
ONE
34
16
7
-
1
T
=
2
5
THREE
56
29
2
-
3
-
-
8
8
THREE ONE
90
45
9
-
4
-
-
-
-
-
9+0
4+5
-
-
-
Q
-
1
2
ONE THREE
9
9
4
-
4

 

 

8
THIRTEEN
99
45
9
8
ONE THREE
81
45
9

 

 

-
8
O
N
E
-
T
H
R
E
E
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
-
-
8
-
-
-
+
=
19
1+9
=
10
1+0
1
-
1
-
-
15
14
-
-
-
8
-
-
-
+
=
37
3+7
=
10
1+0
1
-
1
-
8
O
N
E
-
T
H
R
E
E
-
-
-
-
-
-
-
-
-
-
-
-
-
-
5
-
2
-
9
5
5
+
=
26
2+6
=
8
-
8
-
8
-
-
-
-
5
-
20
-
18
5
5
+
=
53
5+3
=
8
-
8
-
8
-
8
O
N
E
-
T
H
R
E
E
-
-
-
-
-
-
-
-
-
-
-
-
15
14
5
-
20
8
18
5
5
+
=
90
9+0
=
9
-
9
-
9
-
-
6
5
5
-
2
8
9
5
5
+
=
45
4+5
=
9
-
9
-
9
-
8
O
N
E
-
T
H
R
E
E
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
3
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
5
-
-
-
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
7
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-``
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
-
9
15
8
O
N
E
-
T
H
R
E
E
-
-
30
-
-
8
-
45
-
27
1+5
-
-
-
-
-
-
-
9
-
-
-
-
3+0
-
-
-
-
4+5
-
2+7
6
8
O
N
E
-
T
H
R
E
E
-
-
3
-
-
8
-
9
-
9
-
-
6
5
5
-
2
8
9
5
5
-
-
-
-
-
-
-
-
-
-
6
8
O
N
E
-
T
H
R
E
E
-
-
3
-
-
8
-
9
-
9

 

 

-
8
O
N
E
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
-
6
5
-
-
-
8
-
-
-
+
=
19
1+9
=
10
1+0
1
-
1
-
-
15
14
-
-
-
8
-
-
-
+
=
37
3+7
=
10
1+0
1
-
1
-
8
O
N
E
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
5
-
2
-
9
5
5
+
=
26
2+6
=
8
-
8
-
8
-
-
-
-
5
-
20
-
18
5
5
+
=
53
5+3
=
8
-
8
-
8
-
8
O
N
E
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
-
15
14
5
-
20
8
18
5
5
+
=
90
9+0
=
9
-
9
-
9
-
-
6
5
5
-
2
8
9
5
5
+
=
45
4+5
=
9
-
9
-
9
-
8
O
N
E
-
T
H
R
E
E
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
5
5
-
-
-
-
5
5
-
-
5
occurs
x
4
=
20
2+0
2
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-``
-
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
-
9
15
8
O
N
E
-
T
H
R
E
E
-
-
30
-
-
8
-
45
-
27
1+5
-
-
-
-
-
-
-
9
-
-
-
-
3+0
-
-
-
-
4+5
-
2+7
6
8
O
N
E
-
T
H
R
E
E
-
-
3
-
-
8
-
9
-
9
-
-
6
5
5
-
2
8
9
5
5
-
-
-
-
-
-
-
-
-
-
6
8
O
N
E
-
T
H
R
E
E
-
-
3
-
-
8
-
9
-
9

 

 

-
THIRTEEN
-
-
-
2
TH
28
10
1
1
I
9
9
9
1
R
18
9
9
4
TEEN
44
17
8
8
THIRTEEN
99
45
9
-
-
9+9
4+5
1+8
8
THIRTEEN
18
9
9
-
-
1+8
-
-
8
THIRTEEN
9
9
9

 

 

-
PERSEID
-
-
-
2
PE
21
3
3
1
R
18
9
9
2
SE
24
6
6
1
I
9
9
9
1
D
4
4
4
7
PERSEID
76
31
31
-
-
7+8
3+1
3+1
7
PERSEID
13
4
4
-
-
1+3
-
-
7
PERSEIDr
4
4
4

 

 

7
PERSEID
13
31
4
8
THIRTEEN
99
45
9
7
PERSEUS
103
31
4

 

 

The famous Perseid meteor shower has been observed for about 2000 years, ... The Perseid meteor shower peaks on the new-Moon night of Sunday–Monday, ...
en.wikipedia.org/wiki/Perseids

The Perseids (pûr'sē-ĭdz, or psijdz in IPA) are a prolific meteor shower[1] associated with the comet Swift-Tuttle. The Perseids are so called because the point they appear to come from, called the radiant, lies in the constellation Perseus. Meteor showers occur when Earth moves through a meteor stream. The stream in this case is called the Perseids cloud and it stretches along the orbit of the Comet Swift-Tuttle. The cloud consists of particles ejected by the comet as it passed by the Sun. Most of the dust in the cloud today is approximately a thousand years old. However, there is also a relatively young filament of dust in the stream that boiled off the comet in 1862. The approximate rate of meteors originating from this filament is much higher than normal.

[edit] Observation

The famous Perseid meteor shower has been observed for about 2000 years, with the first known information on these meteors coming from the Far East. In early Europe, the Perseids came to be known as the "tears of St. Lawrence."

The shower is visible from mid-July each year, with the greatest activity between August 8 and 14, peaking about August 12. During the peak, the rate of meteor reaches 60 or more per hour. They can be seen all across the sky, but because of the path of Swift-Tuttle's orbit, Perseid are mostly visible on the northern hemisphere.

To experience the shower in its full, one should observe in the dark of a clear moonless night, from a point far outside any large cities, where stars are not dimmed by light pollution. The Perseids have a broad peak, so the shower is visible for several nights. On any given night, activity starts slowly in the evening but picks up by 11 p.m., when the radiant gets reasonably high in the sky. The meteor rate increases steadily through the night as the radiant rises higher, peaking just before the sky starts to get light, roughly 1½ to 2 hours before sunrise.

The Perseid meteor shower peaks on the new-Moon night of Sunday–Monday, August 12–August 13 and can be seen from any place in the northern hemisphere. The Perseid meteors appear to stream away from their radiant near the border of Perseus and Cassiopeia.

The meteor rate, for an observer at a dark-sky site in the northern temperate latitudes, increases to roughly 30 per hour in the predawn hours on Saturday, 45 per hour on Sunday morning, and 80 per hour before the sky starts to get light on Monday morning.

 

PERSEUS PURSUES PERSEUS

IDEAS

 

Perseus, Perseos, or Perseas (Greek: Περσεύς, Περσέως, Περσέας), the legendary founder of Mycenae and of the Perseid dynasty there, was the first of the ...
en.wikipedia.org/wiki/Perseus

The oracle fulfilled

[edit] King of Mycenae

The two main sources regarding the legendary life of Perseus—for he was an authentic historical figure to the Greeks— are Pausanias and Apollodorus, but from them we obtain mainly folk-etymology concerning the founding of Mycenae. Pausanias[17] asserts that the Greeks believed Perseus founded Mycenae. He mentions the shrine to Perseus that stood on the left-hand side of the road from Mycenae to Argos, and also a sacred fountain at Mycenae called Persea. Located outside the walls, this was perhaps the spring that filled the citadel's underground cistern. He states also that Atreus stored his treasures in an underground chamber there, which is why Heinrich Schliemann named the largest tholos tomb the Treasury of Atreus.

Apart from these more historical references, we have only folk-etymology: Perseus dropped his cap or found a mushroom (both named myces) at Mycenae, or perhaps the place was named from the lady Mycene, daughter of Inachus, mentioned in a now-missing poem, the great Eoeae.

For whatever reasons, perhaps as outposts, Perseusfortified Mycenae according to Apollodorus[18] along with Midea, an action that implies that they both previously existed. It is unlikely, however, that Apollodorus knew who walled in Mycenae; he was only conjecturing. In any case, Perseus took up official residence in Mycenae with Andromeda.

[edit] The Perseids

Perseus by Salvador Dalí

Perseus and Andromeda had seven sons: Perses, Alcaeus, Heleus, Mestor, Sthenelus, Electryon and Cynurus, and two daughters, Gorgophone ("Gorgon Killer") and Autochthoe ("Born in the Land"). Perses was left in Aethiopia and became an ancestor of the emperors of Persia. The other descendants ruled Mycenae from Electryon down to Eurystheus, after whom Atreus got the kingdom. However, the Perseids included the great hero, Heracles, son of Amphitryon, son of Alcaeus. The Heraclides, or descendants of Heracles, successfully contested the rule of the Atreids.

A statement by the Athenian orator, Isocrates[19] helps to date Perseus roughly. He said that Heracles was four generations later than Perseus, which corresponds to the legendary succession: Perseus, Electryon, Alcmena, and Heracles, who was a contemporary of Eurystheus. Atreus was one generation later, a total of five generations.

[edit] Etymology

Because of the obscurity of the name Perseus and the legendary character of its bearer, most etymologists pass it by, on the presumption that it might be pre-Greek. However, the name of Perseus’ native city was Greek and so were the names of his wife and relatives. There is some prospect that it descended into Greek from the Proto-Indo-European language. In that regard Robert Graves has espoused the only Greek derivation available.

Perseus might be from the ancient Greek verb, perthein, “to waste, ravage, sack, destroy”, some form of which appears in Homeric epithets. According to Carl Darling Buck (Comparative Grammar of Greek and Latin), the –eus suffix is typically used to form an agent noun, in this case from the aorist stem, pers-. Pers-eus therefore is a sacker of cities; that is, a soldier by occupation, a fitting name for the first Mycenaean warrior.

The origin of perth- is more obscure. J. B. Hofmann[20] lists the possible root as *bher-, from which Latin ferio, "strike". This corresponds to Julius Pokorny’s *bher-(3), “scrape, cut.” Ordinarily *bh- descends to Greek as ph-. This difficulty can be overcome by presuming a dissimilation from the –th– in perthein; that is, the Greeks preferred not to say *pherthein.

Graves carries the meaning still further, to the perse- in Persephone, goddess of death. John Chadwick in the second edition of Documents in Mycenaean Greek speculates as follows about the goddess pe-re-*82 of Pylos tablet Tn 316, tentatively reconstructed as *Preswa:

”It is tempting to see...the classical Perse...daughter of Oceanus...; whether it may be further identified with the first element of Persephone is only speculative.”

A Greek folk etymology connected the name of the Fars people, whom they called the Persai. The native name, however has always had an -a- in Iranian. Herodotus[21]recounts this story, devising a foreign son, Perses, from whom the Persians took the name. Apparently the Persians themselves[22] knew the story, as Xerxes tried to use it to suborn the Argives during his invasion of Greece.

Cyrus Gordon, known for his daring theories, proposed[23] that Perseus is a Semitic name, from p-r-s, "to cut." Nothing in the lore or the evidence excludes the possibility of Semitic elements among the early Greeks. The Greeks thought that Perseus meant "destroyer", but p-r-s would mean that as well.

[edit] Perseus on Pegasus

The replacement of Bellerophon as the tamer and rider of Pegasus by the more familiar culture hero Perseus was not simply an error of painters and poets of the Renaissance. The transition was a development of Classical times which became the standard image during the Middle Ages and has been adopted by the European poets of the Renaissance and later: Giovanni Boccaccio's Genealogia deorum gentilium libri (10.27) identifies Pegasus as the steed of Perseus, and Pierre Corneille places Perseus upon Pegasus in Andromède.[24]

 

[edit] Modern uses of the theme

 

[edit] Notes

  1. ^ Kerenyi 1959:45; see also Danaus.
  2. ^ In post-Renaissance paintings the setting is often a locked tower.
  3. ^ Eurymedon: "far-ruling"
  4. ^ For the familiar motif of the Exposed Child in the account of Moses especially, see Brevard S. Childs, "The Birth of Moses" Journal of Biblical Literature 84.2 (June 1965), pp 109-122, and Donald B. Redford, "The Literary Motif of the Exposed Child (Cf. Ex. ii 1-10)" Numen 14.3 (November 1967), pp 209-228. Another example of this mytheme is the Indian figure of Karna.
  5. ^ Such a banquet, to which each guest brings a gift, was an eranos. The name of Polydectes, "receiver of many", characterizes his role as intended host but is also a euphemism for the Lord of the Underworld, as in the Homeric Hymn to Demeter 9, 17.
  6. ^ Kerenyi 1959:48; Pausanias (viii.25.5): "When Demeter was wandering in search of her daughter, she was followed, it is said, by Poseidon, who lusted after her. So she turned, the story runs, into a mare, and grazed with the mares of Oncius; realizing that he was outwitted, Poseidon too changed into a stallion and enjoyed Demeter."
  7. ^ The sword of Perseus is an antique weapon, a harpe with a sickle-like extension to one side of the blade, for thrust and cut. See Canova's Perseus (illustration).
  8. ^ Ordinarily the helm of invisibility belonged to Hades.
  9. ^ For the Greeks, the tamer and first rider of Pegasus was Bellerophon.
  13. ^ 12.16.1
  14. ^ 2.4.4
  15. ^ Ovid, Metamorphoses, 5.177
  16. ^ loc. cit.
  17. ^ 2.15.4, 2.16.3-6, 2.18.1
  18. ^ 2.4.4, pros-teichisas, "walling in"
  19. ^ 4.07
  20. ^ Hofmann, Etymologisches Wörterbuch des Griechischen (Munich) !950.
  21. ^ Herodotus, vii.61
  22. ^ Herodotus vii.150
  23. ^ Forgotten Scripts, Basic Books, 1982, ISBN 0-465-02484-X, Chapter 7
  24. ^ George Burke Johnston "Jonson's 'Perseus upon Pegasus'" The Review of English Studies New Series, 6.21 (Jan., 1955), pp. 65-67.

[edit] References

 

 

Perseus (IPA: /ˈpəː(r)siəs, -sjuːs/) is a northern constellation, named after the Greek hero who slew the monster Medusa with the help of some godly items. ... en.wikipedia.org/wiki/Perseus_(constellation)

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Perseus
List of stars in Perseus
Abbreviation: Per
Genitive: Persei
Symbology: Perseus
Right ascension: 3 h
Declination: +45°
Area: 615 sq. deg. (24th)
Main stars: 6, 22
Bayer/Flamsteed stars: 63
Stars with planets: 2
Bright stars: 5
Nearby stars: 2
Brightest star: α Per (Mirfak) (1.79m)
Nearest star: ι Per (34.4 ly)
Messier objects: 2
Meteor showers: Perseids
September Perseids
Bordering constellations: Cassiopeia
Andromeda
Triangulum
Aries
Taurus
Auriga
Camelopardalis
Visible at latitudes between +90° and −35°
Best visible at 21:00 (9 p.m.) during the month of December
For other meanings, see Perseus (disambiguation)

Perseus (IPA: /ˈpəː(r)siəs, -sjuːs/) is a northern constellation, named after the Greek hero who slew the monster Medusa with the help of some godly items. It is one of Ptolemy's 48 constellations and was also adopted by the International Astronomical Union as one of the 88 modern constellations. It contains the famous variable star Algol (β Per), and is also the location of the radiant of the annual Perseids meteor shower.

[edit] Notable features

  • α Per (Mirfak): The brightest star of this constellation is also called Algenib (a name which is used for other stars as well, e. g. γ Peg). Mirfak (Arabic for elbow) is a supergiant of spectral type F5 Ib with an apparent brightness of 1.79m lying at a distance of ca. 590 light-years. Its luminosity is 5,000 times and its diameter is 62 times that of our Sun.
  • Algol (β Per): This may not be the brightest star of this constellation, but it definitely is its most famous star. Algol (from Arabic al-Ghul, which means The Ghoul or The Demon Star) represents the eye of the gorgon Medusa. This star is the prototype of a whole group of eclipsing variable stars. Its apparent brightness ranges between 2.12m and 3.39m with a period of merely 2.867 days. It is of spectral type B8 V and lies at a distance of only 93 ly.
  • Nova Persei 1901 (GK Per), a bright nova discovered on February 23, 1901.

[edit] Deep sky objects

  • h + χ Per: These two open clusters (NGC 869 and NGC 884 respectively) belong to the most beautiful objects of the night sky for binoculars and small telescopes. They are sometimes called the Double Cluster. Both lie at distances of more than 7,000 ly and are separated by several hundred light-years.
  • M34: This open cluster with an apparent brightness of 5.5m lies at a distance of approximately 1,400 ly and consists of about 100 stars that are scattered over an area larger than that of the full moon. Its true diameter is about 14 ly. M 34 can be resolved even with good binoculars but is best viewed using a telescope at low magnifications.
  • M76: This planetary nebula is also called Little Dumbbell Nebula. It measures about 65 arc seconds and has an apparent brightness of 10.1m.
  • NGC 1499: Also called California Nebula this emission nebula, discovered in 1884-85 by the American astronomer Edward E. Barnard, is a great target for astrophotographers. Due to its low surface brightness it's a very difficult object when observed visually.
  • NGC 1333 is a reflection nebula and the location of star formation.
  • NGC 1260 contains the brightest known object in the universe, SN 2006gy.

[edit] Graphic visualization

The stars of the constellation Perseus can be connected in an alternative way.

Perseus' body is formed by the stars β Per, κ Per, ι Per, α Per, σ Per, ν Per, and ε Per. α Per and β Per are of the second magnitude. The star ε Per is of the third magnitude.

The stars α Per, γ Per, τ Per, and ι Per form Perseus' head: gamma Persei is of the third magnitude. Stars γ Per, η Per, and τ Per form Perseus' cap.

The stars α Per, ψ Per, δ Per, 48 Per, μ Per, and λ Per form Perseus' left arm and hand: δ Per being of the third magnitude.

The stars ι Per, θ Per, and φ Per form the right arm and hand. Perseus' right hand, φ Per, is yanking at one of Andromeda's feet (51 Andromedae), intent on liberating her. (After liberating her, he marries her.)

Stars ε Per, ξ Per, ζ Per, and ο Per form Perseus' left leg and foot: ζ Per being of the third magnitude.

Finally, stars β Per, ρ Per, and π Per form Perseus' right leg and foot.

[edit] References

  • H. A. Rey, The Stars — A New Way To See Them. Enlarged World-Wide Edition. Houghton Mifflin, Boston, 1997. ISBN 0-395-24830-2.
  • Ian Ridpath and Wil Tirion (2007). Collins Stars and Planets Guide, HarperCollins, London. ISBN 978-0007251209.

 

 

-
PERSEUS
-
-
-
2
PE
21
12
3
1
R
18
9
9
2
SE
24
6
6
1
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21
3
3
1
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19
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1
7
PERSEUS
103
31
22
-
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7
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13
4
4
-
-
1+3
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7
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4
4
4

 

 

-
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38
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-
-
-
-
--
-
-
-
-
-
22
15
24
-
16
15
16
+
=
10 8
1+0+8
=
9
-
9
=
9
-
4
6
6
-
7
6
7
+
=
36
3+6
=
9
-
9
=
9
6
V
O
X
-
P
O
P
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
=
4
-
-
6
6
-
-
6
-
-
-
6
occurs
x
3
=
18
1+8
9
-
-
-
-
-
7
-
7
-
-
7
occurs
x
2
=
14
1+4
5
6
V
O
X
-
P
O
P
-
-
17
-
-
6
-
36
-
18
-
-
-``
-``
-
-
-``
-
-
-
1+7
-
-
-
-
3+6
-
1+8
6
V
O
X
-
P
O
P
-
-
8
-
-
6
-
9
-
9
-
4
6
6
-
7
6
7
-
-
-
-
-
-
-
-
-
-
6
V
O
X
-
P
O
P
-
-
8
-
-
6
-
9
-
9

 

 

- ENLIGHTENER

-

-

 -
3 E+N+L

31

13

 4
1 I

9

9

 9
5 G+H+T+E+N

54

27

 9
1 E

5

5

 5
1 R

18

9

 9
11 ENLIGHTENER

117

63

 36
1+1
 - 1+1+7 6+3 3+6
2 ENLIGHTENER

9

9

 9

 

 

5
CHINA
35
26
8
7
CHINESE
63
36
9

 

 

-
6
I
-
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
8
9
5
-
+
=
31
3+1
=
4
=
4
=
4
-
-
9
-
-
8
9
14
-
+
=
40
4+0
=
4
=
4
=
4
-
6
I
-
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
7
+
=
10
1+0
=
1
=
1
=
1
-
-
-
-
3
-
-
-
7
+
=
10
1+0
=
1
=
1
=
1
-
6
I
-
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
9
-
3
8
9
14
7
+
=
50
5+0
=
5
=
5
=
5
-
-
9
-
3
8
9
5
7
+
=
41
4+1
=
5
=
5
=
5
-
6
I
-
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
6
-
-
-
-
-
-
-
-
-
-
6
SIX
6
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
9
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
13
6
I
-
C
H
I
N
G
-
-
32
-
-
6
-
41
-
32
1+3
-
9
-
-
-
9
-
-
-
-
3+2
-
-
-
-
4+1
-
3+2
4
6
I
-
C
H
I
N
G
-
-
5
-
-
6
-
5
-
5
-
-
9
-
3
8
9
5
7
-
-
-
-
-
-
-
-
-
-
4
6
I
-
C
H
I
N
G
-
-
5
-
-
6
-
5
-
5

 

 

6
I
-
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
-
9
-
-
8
9
5
-
+
=
31
3+1
=
4
=
4
=
4
-
9
-
-
8
9
14
-
+
=
40
4+0
=
4
=
4
=
4
6
I
-
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
7
+
=
10
1+0
=
1
=
1
=
1
-
-
-
3
-
-
-
7
+
=
10
1+0
=
1
=
1
=
1
6
I
-
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
-
9
-
3
8
9
14
7
+
=
50
5+0
=
5
=
5
=
5
-
9
-
3
8
9
5
7
+
=
41
4+1
=
5
=
5
=
5
6
I
-
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
9
-
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
6
I
-
C
H
I
N
G
-
-
32
-
-
6
-
41
-
32
-
9
-
-
-
9
-
-
-
-
3+2
-
-
-
-
4+1
-
3+2
6
I
-
C
H
I
N
G
-
-
5
-
-
6
-
5
-
5
-
9
-
3
8
9
5
7
-
-
-
-
-
-
-
-
-
-
6
I
-
C
H
I
N
G
-
-
5
-
-
6
-
5
-
5

 

 

6
I
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
-
9
-
8
9
5
-
+
=
31
3+1
=
4
=
4
=
4
-
9
-
8
9
14
-
+
=
40
4+0
=
4
=
4
=
4
6
I
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
7
+
=
10
1+0
=
1
=
1
=
1
-
-
3
-
-
-
7
+
=
10
1+0
=
1
=
1
=
1
6
I
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
-
9
3
8
9
14
7
+
=
50
5+0
=
5
=
5
=
5
-
9
3
8
9
5
7
+
=
41
4+1
=
5
=
5
=
5
6
I
C
H
I
N
G
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
-
-
5
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
9
-
-
9
-
-
-
-
9
occurs
x
2
=
18
1+8
9
6
I
C
H
I
N
G
-
-
32
-
-
6
-
41
-
32
-
9
-
-
9
-
-
-
-
3+2
-
-
-
-
4+1
-
3+2
6
I
C
H
I
N
G
-
-
5
-
-
6
-
5
-
5
-
9
3
8
9
5
7
-
-
-
-
-
-
-
-
-
-
6
I
C
H
I
N
G
-
-
5
-
-
6
-
5
-
5

 

 

6
I CHING
50
41
5
-
-
-
-
-
-
-
-
-
-
9
I CHANGING
-
-
-
1
I
9
9
9
2
C
3
3
3
-
H+A
9
9
9
1
N+G
21
12
3
2
I
9
9
9
-
N+G
21
12
3
9
I CHANGING
72
54
36
-
-
7+2
5+4
3+6
9
I CHANGING
9
9
9

 

 

-
CONFUCIUS
-
-
-
1
C
3
3
3
1
O
15
6
6
1
N
14
5
5
1
F
6
6
6
1
U
21
3
3
1
C
3
3
3
1
I
9
9
9
1
U
21
3
3
1
S
19
10
1
9
CONFUCIUS
111
48
39
-
-
1+1+1
4+8
3+9
9
CONFUCIUS
3
12
12
-
-
1+2
1+2
1+2
9
CONFUCIUS
3
3
3

 

 

-
CONFUCIUS
-
-
-
1
C
3
3
3
3
ONF
35
17
8
1
U
21
3
3
1
C
3
3
3
1
I
9
9
9
1
U
21
3
3
1
S
19
10
1
9
CONFUCIUS
111
48
39
-
-
1+1+1
4+8
3+9
9
CONFUCIUS
3
12
12
-
-
-
1+2
1+2
9
CONFUCIUS
3
3
3

 

CONFUCIUS CONFUSES CONFUSES CONFUCIUS

 

-
CONFUCIUS
-
-
-
1
CONFUC
3
3
3
1
I
9
9
9
1
US
21
3
3
9
CONFUCIUS
111
48
39
-
-
1+1+1
4+8
3+9
9
CONFUCIUS
3
12
12
-
-
-
1+2
1+2
9
CONFUCIUS
3
3
3

 

 

-
9
C
O
N
F
U
C
I
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
-
-
9
-
1
+
=
21
2+1
=
3
=
3
=
3
-
-
-
15
14
-
-
-
9
-
19
+
=
57
5+7
=
12
1+2
3
=
3
-
9
C
O
N
F
U
C
I
U
S
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
6
3
3
-
3
-
+
=
18
1+8
=
9
=
9
=
9
-
-
3
-
-
6
21
3
-
21
-
+
=
54
5+4
=
9
=
9
=
9
-
9
C
O
N
F
U
C
I
U
S
-
-
-
-
-
-
-
-
-
-
-
-
3
15
14
6
21
3
9
21
19
+
=
111
1+1+1
=
3
=
3
=
3
-
-
3
6
5
6
3
3
9
3
1
+
=
39
3+9
=
12
1+2
3
=
3
-
9
C
O
N
F
U
C
I
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
2
-
-
-
-
-
-
-
-
-
-
-
-
2
TWO
2
-
-
-
-
-
-
-
3
-
-
-
3
3
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
4
-
-
-
-
-
-
-
-
-
-
-
-
4
FOUR
4
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
7
-
-
-
-
-
-
-
-
-
-
-
-
7
SEVEN
8
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
8
EIGHT
8
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
21
9
C
O
N
F
U
C
I
U
S
-
-
24
-
-
9
-
39
-
21
2+1
-
-
-
-
-
-
-
9
-
-
-
-
2+4
-
-
-
-
3+9
-
2+1
3
9
C
O
N
F
U
C
I
U
S
-
-
6
-
-
9
-
12
-
3
-
-
3
6
5
6
3
3
9
3
1
-
-
-
-
-
-
-
1+2
-
-
3
9
C
O
N
F
U
C
I
U
S
-
-
6
-
-
9
-
3
-
3

 

 

9
C
O
N
F
U
C
I
U
S
-
-
-
-
-
-
-
-
-
-
-
-
6
5
-
-
-
9
-
1
+
=
21
2+1
=
3
=
3
=
3
-
-
15
14
-
-
-
9
-
19
+
=
57
5+7
=
12
1+2
3
=
3
9
C
O
N
F
U
C
I
U
S
-
-
-
-
-
-
-
-
-
-
-
3
-
-
6
3
3
-
3
-
+
=
18
1+8
=
9
=
9
=
9
-
3
-
-
6
21
3
-
21
-
+
=
54
5+4
=
9
=
9
=
9
9
C
O
N
F
U
C
I
U
S
-
-
-
-
-
-
-
-
-
-
-
3
15
14
6
21
3
9
21
19
+
=
111
1+1+1
=
3
=
3
=
3
-
3
6
5
6
3
3
9
3
1
+
=
39
3+9
=
12
1+2
3
=
3
9
C
O
N
F
U
C
I
U
S
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
occurs
x
1
=
1
=
1
-
3
-
-
-
3
3
-
3
-
-
-
3
occurs
x
4
=
12
1+2
3
-
-
-
5
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
6
-
6
-
-
-
-
-
-
-
6
occurs
x
2
=
12
1+2
3
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
9
C
O
N
F
U
C
I
U
S
-
-
24
-
-
9
-
39
-
21
-
-
-
-
-
-
-
9
-
-
-
-
2+4
-
-
-
-
3+9
-
2+1
9
C
O
N
F
U
C
I
U
S
-
-
6
-
-
9
-
12
-
3
-
3
6
5
6
3
3
9
3
1
-
-
-
-
-
-
-
1+2
-
-
9
C
O
N
F
U
C
I
U
S
-
-
6
-
-
9
-
3
-
3

 

 

-
3
T
A
O
-
-
-
-
-
--
-
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
-
15
+
=
15
1+5
=
6
=
6
-
3
T
A
O
-
-
-
-
-
-
-
-
-
-
2
1
-
+
=
3
-
=
3
=
3
-
-
20
1
-
+
=
21
2+1
=
3
=
3
-
3
T
A
O
-
-
-
--
-
-
-
-
-
-
20
1
15
+
=
36
3+6
=
9
=
9
-
-
2
1
6
+
=
9
-
=
9
=
9
-
3
T
A
O
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
-
-
2
-
-
-
-
2
occurs
x
1
=
2
3
-
-
-
-
-
-
3
THREE
3
-
-
-
4
-
-
-
-
-
-
4
FOUR
4
-
-
-
5
-
-
-
-
-
-
5
FIVE
5
-
-
-
-
-
-
-
6
-
-
6
occurs
x
1
=
6
7
-
-
-
-
-
-
7
SEVEN
7
-
-
-
8
-
-
-
-
-
-
8
EIGHT
8
-
-
-
9
-
-
-
-
-
-
9
NINE
9
-
-
-
36
3
T
A
O
-
-
9
-
-
3
-
9
3+6
-
2
1
6
-
-
-
-
-
-
-
-
9
3
T
A
O
-
-
9
-
-
3
-
9
2+0
-
20
1
15
-
-
-
--
-
-
-
-
9
8
T
A
O
-
-
7
-
-
8
-
9

 

 

3
T
A
O
-
-
-
-
-
--
-
-
-
-
-
6
+
=
6
-
=
6
=
6
-
-
-
15
+
=
15
1+5
=
6
=
6
3
T
A
O
-
-
-
-
-
-
-
-
-
2
1
-
+
=
3
-
=
3
=
3
-
20
1
-
+
=
21
2+1
=
3
=
3
3
T
A
O
-
-
-
--
-
-
-
-
-
20
1
15
+
=
36
3+6
=
9
=
9
-
2
1
6
+
=
9
-
=
9
=
9
3
T
A
O
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
occurs
x
1
=
1
-
2
-
-
-
-
2
occurs
x
1
=
2
-
-
-
6
-
-
6
occurs
x
1
=
6
3
T
A
O
-
-
9
-
-
3
-
9
-
2
1
6
-
-
-
-
-
-
-
-
3
T
A
O
-
-
9
-
-
3
-
9
-
20
1
15
-
-
-
--
-
-
-
-
8
T
A
O
-
-
7
-
-
8
-
9

 

 

6
CHINAS
54
27
9
10
TERRACOTTA
121
40
4
8
WARRIORS
121
49
4
24
First Total
296
116
17
2+4
Add to Reduce
2+9+6
1+1+6
1+7
6
Second Total
17
8
8
-
Reduce to Deduce
1+7
-
-
6
Essence of Number
8
8
8

 

 

5
FIRST
72
27
9
7
EMPEROR
90
45
9

 

 

5
FIRST
72
27
9
8
EMPERORS
109
46
1
7
CHINESE
63
36
9
10
TERRACOTTA
121
40
4
8
WARRIORS
121
49
4

 

 

3
THE
33
15
6
8
EMPERORS
109
46
1
4
TOMB
50
14
5
15
First Total
192
75
12
1+5
Add to Reduce
1+9+2
7+5
1+2
6
Second Total
12
12
3
-
Reduce to Deduce
1+2
1+2
-
6
Essence of Number
3
3
3

 

 

7
RUSSIAN
101
29
2
8
RUSSIANS
120
30
3

 

 

3
THE
33
15
6
7
CHINESE
63
36
9
10
First Total
96
51
15
1+0
Add to Reduce
9+6
5+1
1+5
1
Second Total
15
6
6
-
Reduce to Deduce
1+5
-
-
1
Essence of Number
6
6
6

 

 

3
THE
33
15
6
8
RUSSIANS
120
30
3
11
Add to Reduce
153
45
9
1+1
Reduce to Deduce
1+5+3
4+5
-
2
Essence of Number
9
9
9

 

 

-
11
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
--
-
-
-
-
-
-
-
-
-
-
9
5
-
1
8
9
-
8
-
-
5
-
+
=
45
4+5
=
9
=
9
=
9
-
-
-
9
14
-
19
8
9
-
8
-
-
14
-
+
=
81
8+1
=
9
-
9
=
9
-
11
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
--
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
3
1
-
7
+
=
19
1+9
=
10
1+0
1
=
1
-
-
17
-
-
-
-
-
-
-
-
21
1
-
7
+
=
46
4+6
=
10
1+0
1
=
1
-
11
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
--
-
-
-
-
-
-
-
-
-
17
9
14
-
19
8
9
-
8
21
1
14
7
+
=
127
1+2+7
=
10
1+0
1
=
1
-
-
8
9
5
-
1
8
9
-
8
3
1
5
7
+
=
64
6+4
=
10
1+0
1
=
1
-
11
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
8
-
-
8
-
-
-
-
-
-
8
occurs
x
3
=
24
2+4
6
-
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
-
9
12
11
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
33
-
-
11
-
64
-
28
1+2
1+1
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
3+3
-
-
1+1
-
6+4
-
2+8
3
2
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
6
-
-
2
-
10
-
10
-
-
-
9
5
-
-
-
9
-
-
3
-
5
-
-
-
-
-
-
-
-
1+0
-
1+0
3
2
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
6
-
-
2
-
1
-
1

 

 

11
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
--
-
-
-
-
-
-
-
-
-
9
5
-
1
8
9
-
8
-
-
5
-
+
=
45
4+5
=
9
=
9
=
9
-
-
9
14
-
19
8
9
-
8
-
-
14
-
+
=
81
8+1
=
9
-
9
=
9
11
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
--
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
3
1
-
7
+
=
19
1+9
=
10
1+0
1
=
1
-
17
-
-
-
-
-
-
-
-
21
1
-
7
+
=
46
4+6
=
10
1+0
1
=
1
11
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
--
-
-
-
-
-
-
-
-
17
9
14
-
19
8
9
-
8
21
1
14
7
+
=
127
1+2+7
=
10
1+0
1
=
1
-
8
9
5
-
1
8
9
-
8
3
1
5
7
+
=
64
6+4
=
10
1+0
1
=
1
11
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
-
-
3
occurs
x
1
=
3
=
3
-
-
-
5
-
-
-
-
-
-
-
-
5
-
-
-
5
occurs
x
2
=
10
1+0
1
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
7
occurs
x
1
=
7
=
7
-
8
-
-
-
-
8
-
-
8
-
-
-
-
-
-
8
occurs
x
3
=
24
2+4
6
-
-
9
-
-
-
-
9
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
-
9
11
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
33
-
-
11
-
64
-
28
1+1
 -
9
-
-
-
-
9
-
-
-
-
-
-
-
-
3+3
-
-
1+1
-
6+4
-
2+8
2
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
6
-
-
2
-
10
-
10
-
 -
9
5
-
-
-
9
-
-
3
-
5
-
-
-
-
-
-
-
-
1+0
-
1+0
2
Q
I
N
-
S
H
I
-
H
U
A
N
G
-
-
6
-
-
2
-
1
-
1

 

 

-
QIN SHI HUANG
-
-
-
1
Q
17
8
8
1
I
9
9
9
1
N
14
5
5
1
S+H
27
18
9
1
I
9
9
9
1
H
8
8
8
3
U+A+N
36
9
9
1
G
7
7
7
11
QIN SHI HUANG
127
73
64
1+1
-
1+2+7
7+3
6+4
2
QIN SHI HUANG
10
10
10
-
-
1+0
1+0
1+0
2
QIN SHI HUANG
1
1
1

 

 

3
THE
33
15
6
5
GREAT
51
24
6
4
WALL
48
12
3
2
OF
21
12
3
5
CHINA
35
26
8

 

 

-
15
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
--
-
-
-
-
-
-
-
-
-
-
8
9
5
-
1
-
-
-
-
-
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
-
8
9
14
-
19
-
-
-
-
-
-
-
-
-
-
-
+
=
50
5+0
=
5
-
5
=
5
-
15
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
--
-
-
-
-
-
-
-
-
-
3
-
-
-
1
-
-
7
9
5
1
2
-
5
1
3
3
+
=
40
4+0
=
4
-
4
=
4
-
-
3
-
-
-
1
-
-
7
18
5
1
20
-
23
1
12
12
+
=
103
1+0+3
=
4
-
4
=
4
-
15
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
--
-
-
-
-
-
-
-
-
-
3
8
9
14
1
19
-
7
18
5
1
20
-
23
1
12
12
+
=
153
1+5+3
=
9
-
9
=
9
-
-
3
8
9
5
1
1
-
7
9
5
1
2
-
5
1
3
3
+
=
63
6+3
=
9
=
9
=
9
-
15
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
1
-
-
-
1
-
-
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
3
occurs
x
3
=
9
=
9
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
-
9
10
15
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
35
-
-
15
-
63
-
45
1+0
1+5
-
 -
9
-
-
-
-
 -
9
-
-
-
-
-
-
-
-
-
-
3+5
-
-
1+5
-
6+3
-
4+5
1
6
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
8
-
-
6
-
9
-
9
-
-
3
8
9
5
1
1
-
7
9
5
1
2
-
5
1
3
3
-
-
-
-
-
-
-
-
-
-
1
6
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
8
-
-
6
-
9
-
9

 

 

15
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
--
-
-
-
-
-
-
-
-
-
8
9
5
-
1
-
-
-
-
-
-
-
-
-
-
-
+
=
23
2+3
=
5
=
5
=
5
-
-
8
9
14
-
19
-
-
-
-
-
-
-
-
-
-
-
+
=
50
5+0
=
5
-
5
=
5
15
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
--
-
-
-
-
-
-
-
-
3
-
-
-
1
-
-
7
9
5
1
2
-
5
1
3
3
+
=
40
4+0
=
4
-
4
=
4
-
3
-
-
-
1
-
-
7
18
5
1
20
-
23
1
12
12
+
=
103
1+0+3
=
4
-
4
=
4
15
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
--
-
-
-
-
-
-
-
-
3
8
9
14
1
19
-
7
18
5
1
20
-
23
1
12
12
+
=
153
1+5+3
=
9
-
9
=
9
-
3
8
9
5
1
1
-
7
9
5
1
2
-
5
1
3
3
+
=
63
6+3
=
9
=
9
=
9
15
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
1
1
-
-
-
-
1
-
-
-
1
-
-
-
-
1
occurs
x
4
=
4
=
4
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
3
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
3
-
-
3
occurs
x
3
=
9
=
9
-
-
-
-
5
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
occurs
x
1
=
8
-
8
-
-
-
9
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
2
=
18
-
9
15
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
35
-
-
15
-
63
-
45
1+5
-
 -
9
-
-
-
-
 -
9
-
-
-
-
-
-
-
-
-
-
3+5
-
-
1+5
-
6+3
-
4+5
6
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
8
-
-
6
-
9
-
9
-
3
8
9
5
1
1
-
7
9
5
1
2
-
5
1
3
3
-
-
-
-
-
-
-
-
-
-
6
C
H
I
N
A
S
-
G
R
E
A
T
-
W
A
L
L
-
-
8
-
-
6
-
9
-
9

 

 

-
9
G
R
E
A
T
-
W
A
L
L
-
-
--
-
-
-
-
-
-
-
-
-
7
18
5
1
20
-
23
1
12
12
+
=
99
9+9
=
18
1+8
9
=
9
-
-
7
9
5
1
2
-
5
1
3
3
+
=
36
3+6
=
9
=
9
=
9
-
9
G
R
E
A
T
-
W
A
L
L
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
1
-
-
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
2
-
-
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
3
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
-
5
-
-
-
5
-
-
-
-
-
5
occurs
x
2
=
10
1+0
1
6
-
-
-
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
-
-
-
-
-
-
9
occurs
x
1
=
9
-
9
18
9
G
R
E
A
T
-
W
A
L
L
-
-
27
-
-
9
-
36
-
27
1+8
-
-
9
-
-
-
-
-
-
-
-
-
-
2+7
-
-
-
-
3+6
-
2+7
9
9
G
R
E
A
T
-
W
A
L
L
-
-
9
-
-
9
-
9
-
9
-
-
7
9
5
1
2
-
5
1
3
3
-
-
-
-
-
-
-
-
-
-
9
9
G
R
E
A
T
-
W
A
L
L
-
-
9
-
-
9
-
9
-
9

 

 

6
CHINAS
54
27
9
5
GREAT
51
24
6
4
WALL
48
12
3
15
Add to Reduce
153
63
18
1+5
Reduce to Deduce
1+5+3
6+3
1+8
6
Essence of Number
9
9
9

 

 

8
PERSONAL
100
37
1
10
EXPRESSION
144
54
9

 

 

-
GEO MAGNETIC
-
-
-
3
GEO
27
18
9
8
MAGNETIC
72
36
9
11
GEO MAGNETIC
99
54
9
1+1
-
-
5+4
9
2
GEO MAGNETIC
99
54
9
8
THIRTEEN
99
45
9

 

 

-
11
G
E
O
M
A
G
N
E
T
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
-
5
-
-
9
-
+
=
20
2+0
=
2
-
2
-
2
-
-
-
-
15
-
-
-
14
-
-
9
-
+
=
38
3+8
=
11
1+1
2
-
2
-
11
G
E
O
M
A
G
N
E
T
I
C
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
4
1
7
-
5
2
-
3
+
=
34
3+4
=
7
-
7
-
7
-
-
7
5
-
13
1
7
-
5
20
-
3
+
=
61
6+1
=
7
-
7
-
7
-
11
G
E
O
M
A
G
N
E
T
I
C
-
-
-
-
-
--
-
-
-
-
-
-
7
5
15
13
1
7
14
5
20
9
3
+
=
99
9+9
=
18
1+8
9
-
9
-
-
7
5
6
4
1
7
5
5
2
9
3
+
=
54
5+4
=
9
-
9
-
9
-
11
G
E
O
M
A
G
N
E
T
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
1
occurs
x
1
=
1
-
1
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
2
occurs
x
1
=
2
-
2
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
3
occurs
x
1
=
3
-
3
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
4
occurs
x
1
=
4
-
4
-
-
-
5
-
-
-
-
5
5
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
-
6
-
-
7
-
-
-
-
7
-
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
-
-
-
9
occurs
x
1
=
9
-
9
8
11
G
E
O
M
A
G
N
E
T
I
C
-
-
37
-
-
11
-
54
-
36
-
1+1
-
-
-
-
-
-
-
-
-
9
-
-
-
3+7
-
-
1+1
-
5+4
-
3+6
8
2
G
E
O
M
A
G
N
E
T
I
C
-
-
10
-
-
2
-
9
-
9
-
-
7
5
6
4
1
7
5
5
2
9
3
-
-
1+0
-
-
-
-
-
-
-
8
2
G
E
O
M
A
G
N
E
T
I
C
-
-
1
-
-
2
-
9
-
9

 

 

-
GEO MAGNETIC
-
-
-
3
GEO
27
18
9
8
MAGNETIC
72
36
9
11
GEO MAGNETIC
99
54
9
1+1
-
-
5+4
9
2
GEO MAGNETIC
99
54
9
-
-
-
-
-
8
THIRTEEN
99
45
9

 

 

-
-
-
-
-
GEO MAGNETIC FIELD
-
-
-
G
=
7
-
3
GEO
27
18
9
M
=
4
-
8
MAGNETIC
72
36
9
F
=
6
-
5
FIELD
36
27
9
-
-
17
-
16
GEO MAGNETIC FIELD
135
81
27
-
-
1+7
-
1+6
-
1+3+5
8+1
2+7
-
-
8
-
7
GEO MAGNETIC FIELD
9
9
9

 

 

-
GEOCENTRIC

-

-
-
3
GEO

27

18
9
7
CENTRIC

72

36
9
10
GEOCENTRIC

99

54
18
1+0
-
9+9
5+4
1+8
1
GEOCENTRIC

18

9
9
-
-
1+8
-
-
1
GEOCENTRIC

9

9
9

 

 

-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
5
-
-
9
-
+
=
20
2+0
=
2
=
2
=
2
-
-
-
-
15
-
-
14
-
-
9
-
+
=
38
3+8
=
11
1+1
2
=
2
-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
3
5
-
2
9
-
3
+
=
34
3+4
=
7
=
7
=
7
-
-
7
5
-
3
5
-
20
18
-
3
+
=
61
6+1
=
7
=
7
=
7
-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
-
-
7
5
15
3
5
14
20
18
9
3
+
=
99
9+9
=
18
1+8
9
=
9
-
-
7
5
6
3
5
5
2
9
9
3
+
=
54
5+4
=
9
=
9
=
9
-
10
G
E
O
C
E
N
T
R
I
C
-
-
-
-
-
--
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
2
occurs
x
1
=
2
=
2
-
-
-
-
-
3
-
-
-
-
-
3
-
-
3
occurs
x
2
=
6
=
6
4
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
-
-
-
5
-
-
5
5
-
-
-
-
-
-
5
occurs
x
3
=
15
1+5
6
-
-
-
-
6
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
-
-
-
-
-
-
-
-
7
occurs
x
1
=
7
=
7
8
-
-
-
-
-
-
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
9
9
-
-
-
9
occurs
x
2
=
18
1+8
9
13
10
G
E
O
C
E
N
T
R
I
C
-
-
32
-
-
10
-
54
-
36
1+3
1+0
-
-
-
-
-
-
-
9
9
-
-
-
3+2
-
-
1+0
-
5+4
-
3+6
4
1
G
E
O
C
E
N
T
R
I
C
-
-
5
-
-
1
-
9
-
9

 

 

- GEOPHYSICS

-

-

 -
3 GEO

27

18

 9
7 PHYSICS

99

36

 9
10 GEOPHYSICS

126

54

 18
1+0
 - 1+2+6 5+4 1+8
1 GEOPHYSICS

9

9

 9

 

 

-
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
6
-
-
8
-
1
9
-
1
+
=
25
2+5
=
7
=
7
=
7
-
-
-
-
15
-
-
8
-
19
9
-
19
+
=
70
7+0
=
7
=
7
=
7
-
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
7
5
-
-
7
-
7
-
-
3
-
+
=
29
2+9
=
11
1+1
2
=
2
-
-
7
5
-
-
16
-
25
-
-
3
-
+
=
56
5+6
=
11
1+1
2
=
2
-
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
7
5
15
-
16
8
25
19
9
3
19
+
=
126
1+2+6
=
9
=
9
=
9
-
-
7
5
6
-
7
8
7
1
9
3
1
+
=
54
5+4
=
9
=
9
=
9
-
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
2
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
-
-
-
-
4
-
-
--
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
-
7
-
-
-
7
-
7
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
6
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
37
-
-
10
-
54
-
36
-
1+0
-
-
-
-
-
-
-
-
9
-
-
-
-
3+7
-
-
1+0
-
5+4
-
3+6
6
1
G
E
O
-
P
H
Y
S
I
C
S
-
-
10
-
-
1
-
9
-
9
-
-
7
5
6
-
7
8
7
1
9
3
1
-
-
1+0
-
-
-
-
-
-
-
6
1
G
E
O
-
P
H
Y
S
I
C
S
-
-
1
-
-
1
-
9
-
9

 

 

10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
6
-
-
8
-
1
9
-
1
+
=
25
2+5
=
7
=
7
=
7
-
-
-
15
-
-
8
-
19
9
-
19
+
=
70
7+0
=
7
=
7
=
7
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
7
5
-
-
7
-
7
-
-
3
-
+
=
29
2+9
=
11
1+1
2
=
2
-
7
5
-
-
16
-
25
-
-
3
-
+
=
56
5+6
=
11
1+1
2
=
2
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
7
5
15
-
16
8
25
19
9
3
19
+
=
126
1+2+6
=
9
=
9
=
9
-
7
5
6
-
7
8
7
1
9
3
1
+
=
54
5+4
=
9
=
9
=
9
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
-
-
5
-
-
-
-
-
-
-
-
-
-
-
5
occurs
x
1
=
5
=
5
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
occurs
x
1
=
6
=
6
-
7
-
-
-
7
-
7
-
-
-
-
-
-
7
occurs
x
3
=
21
2+1
3
-
-
-
-
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
10
G
E
O
-
P
H
Y
S
I
C
S
-
-
37
-
-
10
-
54
-
36
1+0
-
-
-
-
-
-
-
-
9
-
-
-
-
3+7
-
-
1+0
-
5+4
-
3+6
1
G
E
O
-
P
H
Y
S
I
C
S
-
-
10
-
-
1
-
9
-
9
-
7
5
6
-
7
8
7
1
9
3
1
-
-
1+0
-
-
-
-
-
-
-
1
G
E
O
-
P
H
Y
S
I
C
S
-
-
1
-
-
1
-
9
-
9

 

 

-
7
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
8
-
1
9
-
1
+
=
19
1+9
=
10
1+0
1
=
1
-
-
-
8
-
19
9
-
19
+
=
55
5+5
=
10
1+0
1
=
1
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
7
-
7
-
-
3
-
+
=
17
1+7
=
8
=
8
=
8
-
-
16
-
25
-
-
3
-
+
=
44
4+4
=
8
=
8
=
8
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
16
8
25
19
9
3
19
+
=
99
9+9
=
18
1+8
9
=
9
-
-
7
8
7
1
9
3
1
+
=
36
3+6
=
9
=
9
=
9
-
7
P
H
Y
S
I
C
S
-
-
-
-
-
--
-
-
-
-
-
-
-
-
-
1
-
-
1
-
-
1
occurs
x
2
=
2
=
2
2
-
-
-
-
-
-
-
-
-
-
2
-
-
-
-
-
-
-
-
-
-
-
-
-
-
3
-
-
-
3
occurs
x
1
=
3
=
3
4
-
-
-
-
-
-
-
-
-
-
4
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
-
-
-
5
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
-
6
-
-
-
-
-
-
-
-
-
7
-
7
-
-
-
-
-
-
7
occurs
x
2
=
14
1+4
5
-``
-
-
8
-
-
-
-
-
-
-
8
occurs
x
1
=
8
=
8
-
-
-
-
-
-
9
-
-
-
-
9
occurs
x
1
=
9
=
9
17
7
P
H
Y
S
I
C
S
-
-
28
-
-
7
-
36
-
27
1+7
-
-
-
-
-
9
-
-
-
-
2+8
-
-
-
-
3+6
-
2+7
8
7
P
H
Y
S
I
C
S
-
-
10
-
-
7
-
9
-
9
-
-
7
8
7
1
9
3
1
-
-
1+0
-
-
-
-
-
-
-
8
7
P
H
Y
S
I
C
S
-
-
1
-
-
7
-
9
-
9

 
 
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