"The Human Figure in Early Greek Art," which goes on view this morning at the National Gallery of Art, opens with a creature only half a man. His right hand has six fingers, his round ears are enormous, beneath his human torso is the body of a horse.

A terra-cotta centaur unearthed in 1969, he was made in Euboea in the 10th century B.C. A gash on his foreleg suggests he may be Chiron -- who taught healing to Asclepius and courage to Achilles and then, declining immortality, went calmly to his death. Chiron of the myth is remembered for his kindliness. There is no trace of his wisdom in this antique statuette's harsh, demonic gaze.

The final object one encounters in this long-awaited loan show in the gallery's East Building is a fragmentary stone relief from the 5th century B.C. It was found in 1915 buried in the sanctuary of Athena at Sounion. It shows a smoothly muscled Attic youth, an athlete, a winner. So perfect is his marble skin you almost feel him breathe. He is autostephanoumenos, "self-crowning." His gaze is calm and modest, his head is slightly bowed. With a gesture of great gentleness, he places on his brow the victor's laurel wreath.

He ends this show in triumph. His crowning is a presage of the Golden Age.

Chiron is half-bestial. That boy is wholly human. The development that's traced between these antique objects -- from the static to the lifelike, from the Archaic to the Classical -- is one of the great victories of early Western art.

It is not easy to imagine an art historical exhibition more needed in this city. Some golden dream of Greece hovers all about us. We owe the germ of our democracy to the government of Athens. The game that will be played today, and the way it grips the populace, have roots in the Olympics. The monuments that line the Mall, those pedimented temples with their rows of fluted columns, insistently remind us of the debts we owe to Greece.

And of our own impoverishment. Fine red-figured vases and superb Attic marbles -- much like those displayed -- are on view every day in London, Paris, Rome, Berlin, Munich, and Manhattan. Washington's museums own almost nothing of Greek art.

Thosewho stand in line expecting an epiphany may be slightly disappointed. The Tut show gleamed with gold, its treasures were undamaged. Here one sees instead fragments of clay plaques, cases of once-broken pots, and marbles, almost all of which are missing hands and noses. The colors of the show, its reds and blacks and beiges, are faded and subdued.

I do not mean to sound ungrateful. While the government of Greece has been exceptionally generous -- these 67 objects all are irreplaceable -- much has been held back. It is certainly no wonder that many of the best-known objects of the period -- the "Calf Bearer" from the Acropolis, the head of the "Blond Boy," the magically complete "Kouros From Anavysos," the gravestone of Aristion, the bronze charioteer from Delphi -- have not made the trip. Those yearning for immersion in the glory that was Greece may leave this show still hungering. It offers to the viewer few blinding revelations. It does not overwhelm.

Ideally, the viewer ought to see it at least twice, for its lessons unfold slowly. Unlike Galatea, its graceful human figures take time to come to life.

Those seen in the first gallery are crude and rudimentary. The naked human figures who march and dance and fight around the oldest pots on view have heads as bland as thumb-prints and triangles for torsos. They are little more than roughly done stick-figure silhouettes. Yet something crucial stirs within them. The way they're wed to measure, to number and geometry -- and their ceaseless, restless motion -- predicts much yet to come.

One word of caution is in order before you visit the exhibit. Despite the "early" in its title, this show does not survey the beginnings of Greek art.

It is worthwhile remembering that these artists weren't the first -- they weren't even the first Greeks -- to portray the human figure. Artists of the Ice Age were carving "goddesses" of stone 20,000 years before this show commences. Ur had superb sculptors. At a time when these Greek painters were daubing their coarse figures, the Great Sphinx of Egypt had been staring across Giza for more than 1,500 years.

The exhibition catalogue is occasionally chauvinistic. The engineers and architects who built the Pyramid of Cheops knew something about squares and triangles and numbers. The sculptors who produced the statues of the pharaohs were masters at the blending of portraiture and measure. When archeologist Mary Pandou of the Greek Ministry of Culture tells us in the catalogue that "geometric art is the creation of Greek tribes on Greek soil and is a unique phenomenon in the universal history of art," she is speaking nonsense pure.

Even in Greek waters, in the Cycladic islands of the Aegean Sea, sculptors were acknowledging the magic of geometry at least 2,000 years before this show begins. You see that in the circles, the triangles and spirals inscribed on their vases, and, even more impressively, in their figurines. The "goddesses" they've left us are, in subject, not so different from those rounded, lumplike figures first carved in the Ice Age. But their forms are something new.

Half observed, and half abstracted, they show the human figure wed to mathematics. An allegiance to geometry is immediately apparent in their heads, like rounded triangles, and the clear numerical proportions governing their limbs.

Later Mycenaean art -- of stone and gold and ivory -- is comparably impressive. The heroes of Homeric myth were Mycenaean warriors. For reasons still debated their civilization ended about 1100 B.C.

To those who study early Greece, the two centuries that followed are known as the Dark Age. The objects on display might lead one to believe that the past had been forgotten, that these artists were required to start again from scratch. But I do not think that's true. That time of poverty and turmoil was just an interruption. The slow climb toward the style that we now call High Classical was already underway millennia before the present show begins.

A sense of harmony is central to the spirit of Greek thought: The universe is ordered. Change is all about us, but underneath the ceaseless shiftings of the visible some ideal order rules. One sees that sense of measure in the statues of the Cyclades, as one hears it in the rhythms of Homeric verse. Pythagoras and Euclid were not the first Greek thinkers to glimpse the ageless realm of numbers. Some obedience to geometry is apparent even in the earliest objects here on view.

The second thing one sees (even older than the centaur), is a "Protogeometric Skyphos," a turned Athenian vase from the 11th century B.C. The painted lines on it do not show the human figure. Instead, for decoration, they are concentric circles -- drawn, the catalogue observes, "not by hand, but by the multiple-brush compass that is characteristic" of the time.

The lines drawn on the centaur suggest the same sense of strict order. He has straight lines on his arm, and dark right-angled triangles march along his flanks. The first painted images of humans here -- they decorate an Attic vase from 770 B.C. -- are also geometrical. Their shields, bows and warships show that they are warriors, perhaps those sung by Homer. Their chests are downward-pointing triangles, they have straight black lines for arms. But they do not merely stand there, they leap, they fall with arms outflung, they hurl their pointed spears.

The bronze statuettes nearby are similarly caught between stasis and free movement. One -- found below the foundations of the temple of Hera at Olympia -- is a standing figure of a warrior. The crest of his helmet is based upon the circle, his torso is a triangle. His body, too, is governed by numerical proportions in the ratio of 1 to 3: From the top of his head to his navel is one-third of his height; his oddly lengthened lower body, from his navel to his feet, is precisely twice as long. But like the painted soldiers, he seems to be in movement. His right hand is upraised. Once it held a spear.

The Greeks loved active play, running, leaping, dancing. The boat-borne warriors that appear on a proto-Attic plaque by the so-called Analatos painter hide their unseen bodies behind perfectly round shields. The figures on a clay cup made in Athens circa 680 B.C. have torsos that are square. A statuette from Thera, which shows a mourning woman (she grips her head in grief), has a lower body that's cylindrical. Almost all the older figures here, while rigorously geometrical, still appear to move.

We occasionally can recognize the stories they relate. A fragment of a 7th-century clay vase (found in Argos in 1952) illustrates a famous passage from the "Odyssey," the one in which the brave companions of Odysseus blind the cyclops Polyphemus: "So seizing the fire-hardened timber, we twirled it in his eye, and the blood boiled around the hot point {and} the roots of his eye crackled."

Homer's verse still startles. His words are far more lifelike than the paintings of the time. The oldest figures shown, although their bodies move, have inexpressive faces. The first fully human faces here owe less to old Greek myths than to Egyptian art.

Look, for instance, at the earliest stone figure on display. She probably was carved (circa 630 B.C.) for the acropolis at Mycenae. Her face may well be Helen's, so the catalogue suggests. It also says her face predicts the Greek Archaic smile. What it does not tell us is that Egypt is her source.

One glance makes that clear. Her smile is Egyptian, her hairdo is Egyptian, so, too, is the static symmetry of her face.

These early Greeks had trouble when they carved in three dimensions. A stone relief from Athens, a marble portrait of an athlete, makes that difficulty clear. The young man holds a discus (it frames his head like a halo). His lips and nose are lifelike, but his eye is somehow wrong. His head is shown in profile, but the eye is seen full-face.

That same misreading of physiognomy continues to be seen in many of the finest vase paintings on display. One of the most beautiful, a red-figured kylix, was found (in many pieces) discarded in a well near the Agora in Athens in 1954. It seems to have been shattered -- like so many objects here -- during Xerxes' sack of the city in 480 B.C.

A young man (drawn delightfully in black outlines on red) kneels in the circle painted on the bowl. He may well be a lover, for he wears a wreath of honeysuckle, and holds in his right hand a furry, fertile hare, a saucy symbol of the chase. His pectorals are clearly shown, so too are his ribs and the muscles of his calves. His body turns convincingly. Just his eye is wrong. That doesn't really matter. His coiled, youthful grace takes the breath away.

Active, moving bodies are seen throughout the show. But only in the last rooms do the faces of the figures assume a beauty that's as clear.

That amazing facial beauty first appears in its full glory in the stone korai from the Acropolis in Athens that seem to rule the show.

These life-size marble carvings show young maidens in the first full flowering of womanhood. They wear their hair in ringlets. Three are near-complete. They stand in modest pride. While the fabric of their dresses swings to hint at movement, its perfect, balanced folds manage to suggest -- as do the geometric figures with which the show began -- a sort of pure and measured order. These young women are not nude, but their dresses are so sheer that one can clearly see their perfect bodies underneath. The head of a fourth kore is in a case beside them. Her nose and neck are broken, but her beauty still astonishes.

The young athlete with the laurel wreath, who ends the exhibition, does as much for male grace. The path traced by this show was anything but smooth, but the end was worth the journey. A sense of quarreling opposites brought into harmony -- of stillness wed to movement, of the ideal given human form -- glows within these marbles. They are noble works of art.

"The Human Figure in Early Greek Art" was organized by the Greek Ministry of Culture. It will travel to Kansas City, Los Angeles, Chicago and Boston after closing here June 12.