In his hand he bore a trident, wherewith :lie lashed the sea into fury, split the rocks, and caused horses mid XXII.
Thirdly, the three intersections by the line infinity may be coincident and real; or say we have a threefold point: this may be an inflection, a crunode or a cusp, that is, the line infinity may be a tangent at an inflection, and we have the divergent parabolas; a tangent at a crunode to one branch, and we have the trident curve; or lastly, a tangent at a cusp, and we have the cubical parabola.
Nereus is represented with the sceptre and trident; the Nereids are depicted as graceful maidens, lightly clad or naked, riding on tritons and dolphins.
The horse was especially associated with his worship; he was said to have produced the first horse by striking the ground in Thessaly with his trident (Virgil, Georgics, i.
He decided in favour of the goddess, who planted the first olive tree, which he adjudged to be more useful than the horse (or water) which Poseidon caused to spring forth from the Acropolis rock with a blow of his trident (Herodotus viii.
Monte Santo), the most eastern of the three peninsular promontories which extend, like the prongs of a trident, southwards from the coast of Macedonia (European Turkey) into the Aegean Sea.
The cartesian parabola is a cubic curve which is also known as the trident of Newton on account of its three-pronged form.
Poseidon was also the god of springs, which he produced by striking the rock with his trident, as he did on the acropolis of Athens when disputing with Athena for the sovereignty of Athens (Herodotus viii.
His attributes are the trident and the dolphin (sometimes the tunny fish.) As represented in art Poseidon resembles Zeus, but possesses less of his majestic calm, his muscles are more emphasized, and his hair is thicker and somewhat dishevelled.
He is generally naked; his right leg rests on a rock or the prow of a ship; he carries a trident in his hand, and is gazing in front of him, apparently out to sea; sometimes he is standing on the water, swinging his trident, or riding in his chariot over the waves, accompanied by his wife Amphitrite, the Nereids and other inhabitants of the sea.
In the dolphins the teeth form simple cones, but in the seals they are often trident-like; while in the otters the dentition differs but little from the ordinary carnivorous type.
Athena also gave the Athenians the olive-tree, which was supposed to have sprung from the bare soil of the Acropolis, when smitten by her spear, close to the horse (or spring of water) produced by the trident of Poseidon, to which he appealed in support of his claim to the lordship of Athens.
It may be due partly to the natural conformation of the rock and the differences of level, partly to the necessity of enclosing within a single building several objects of ancient sanctity, such as the mark of Poseidon's trident and the spring that arose from it, the sacred olive tree of Athena, and the tomb of Cecrops.
The sacredness of the horse to Poseidon, the epithets Hippios and Equester applied to Poseidon and Neptune, the Greek fable of the origin of the first horse (produced by Poseidon striking the ground with his trident), and the custom in Argolis of sacrificing horses to Poseidon by drowning them in a well.
About the foundation of Halicarnassus various traditions were current; but they agree in the main point as to its being a Dorian colony, and the figures on its coins, such as the head of Medusa, Athena and Poseidon, or the trident, support the statement that the mother cities were Troezen and Argos.
Wilfred Tomkinson (" Phoebe," North Star," Trident," Mansfield," Whirlwind," Myngs," Velox," Morris Moorsom Melpomene, "Tempest" and "Tetrarch" to escort the force and cover it to seaward; "Termagant," "Truculent" and "Manly" to screen the Zeebrugge monitors).
So great was the esteem in which it was held, that in the early legend of the struggle between the gods of sea and land, Poseidon and Athena, for the patronage of the country, the sea-god is represented as having to retire vanquished before the giver of the olive; and at a later period the evidences of this contention were found in an ancient olive tree in the Acropolis, together with three holes in the rock, said to have been made by the trident of Poseidon, and to be connected with a salt well hard by.
In the north portico a square hole in the floor, with a corresponding hole in the roof above it, must have given access to another sacred object, the mark of Poseidon's trident in the rock.
It is to be remarked that the classification mixes together non-singular and singular curves, in fact, the five kinds presently referred to: thus the hyperbolas and the divergent parabolas include curves of every kind, the separation being made in the species; the hyperbolisms of the hyperbola and ellipse, and the trident curve, are nodal; the hyperbolisms of the parabola, and the cubical parabola, are cuspidal.