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Henry Gray (1825–1861).  Anatomy of the Human Body.  1918.
 
and gives off in its course two or three vessels which ascend to the nose; a septal branch ramifies on the nasal septum as far as the point of the nose, and an alar branch supplies the ala of the nose.
  The Lateral Nasal branch is derived from the external maxillary as that vessel ascends along the side of the nose. It supplies the ala and dorsum of the nose, anastomosing with its fellow, with the septal and alar branches, with the dorsal nasal branch of the ophthalmic, and with the infraorbital branch of the internal maxillary.
  The Angular Artery (a. angularis) is the terminal part of the external maxillary; it ascends to the medial angle of the orbit, imbedded in the fibers of the angular head of the Quadratus labii superioris, and accompanied by the angular vein. On the cheek it distributes branches which anastomose with the infraorbital; after supplying the lacrimal sac and Orbicularis oculi, it ends by anastomosing with the dorsal nasal branch of the ophthalmic artery.
  The Muscular Branches in the neck are distributed to the Pterygoideus internus and Stylohyoideus, and on the face to the Masseter and Buccinator. The anastomoses of the external maxillary artery are very numerous, not only with the vessel of the opposite side, but, in the neck, with the sublingual branch of the lingual, with the ascending pharyngeal, and by its ascending palatine and tonsillar branches with the palatine branch of the internal maxillary; on the face, with the mental branch of the inferior alveolar as it emerges from the mental foramen, with the transverse facial branch of the superficial temporal, with the infraorbital branch of the internal maxillary, and with the dorsal nasal branch of the ophthalmic.

Peculiarities.—The external maxillary artery not infrequently arises in common with the lingual. It varies in its size and in the extent to which it supplies the face; it occasionally ends as the submental, and not infrequently extends only as high as the angle of the mouth or nose. The deficiency is then compensated for by enlargement of one of the neighboring arteries.
  4. The occipital artery (a. occipitalis) (Fig. 508) arises from the posterior part of the external carotid, opposite the external maxillary, near the lower margin of the posterior belly of the Digastricus, and ends in the posterior part of the scalp.

Course and Relations.—At its origin, it is covered by the posterior belly of the Digastricus and the Stylohyoideus, and the hypoglossal nerve winds around it from behind forward; higher up, it crosses the internal carotid artery, the internal jugular vein, and the vagus and accessory nerves. It next ascends to the interval between the transverse process of the atlas and the mastoid process of the temporal bone, and passes horizontally backward, grooving the surface of the latter bone, being covered by the Sternocleidomastoideus, Splenius capitis, Longissimus capitis, and Digastricus, and resting upon the Rectus capitis lateralis, the Obliquus superior, and Semispinalis capitis. It then changes its course and runs vertically upward, pierces the fascia connecting the cranial attachment of the Trapezius with the Sternocleidomastoideus, and ascends in a tortuous course in the superficial fascia of the scalp, where it divides into numerous branches, which reach as high as the vertex of the skull and anastomose with the posterior auricular and superficial temporal arteries. Its terminal portion is accompanied by the greater occipital nerve.

Branches.—The branches of the occipital artery are:
Muscular.
Sternocleidomastoid.
Auricular.

Meningeal.
Descending.
  The Muscular Branches (rami musculares) supply the Digastricus, Stylohyoideus, Splenius, and Longissimus capitis.
  The Sternocleidomastoid Artery (a. sternocleidomastoidea; sternomastoid artery) generally arises from the occipital close to its commencement, but sometimes springs directly from the external carotid. It passes downward and backward over the hypoglossal nerve, and enters the substance of the muscle, in company with the accessory nerve.
  The Auricular Branch (ramus auricularis) supplies the back of the concha and frequently gives off a branch, which enters the skull through the mastoid foramen

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