This section is from the book "Anatomy Of The Arteries Of The Human Body", by John Hatch Power. Also available from Amazon: Anatomy of the Arteries of the Human Body, with the Descriptive Anatomy of the Heart.
The Inferior Dental Artery arises from the inferior surface of the internal maxillary, nearly opposite the origin of the middle meningeal, and runs obliquely downwards and forwards, between the internal lateral ligament, and the ramus of the lower jaw. In this course it sends numerous branches to the pterygoid muscles, and to the gustatory and inferior maxillary nerves. Lower down it gives off a mylo-hyoidean branch which descends in the groove leading from the dental foramen, accompanied by the mylo-hyoidean branch of the inferior dental nerve, and supplies the mylo-hyoid muscle and mucous membrane of the mouth. Immediately after giving off this last branch, the inferior dental artery enters the dental foramen, in company with the dental nerve, which is situated in front of it. It descends beneath the alveoli, till it arrives at the first molar tooth, where it divides into two branches; one of which is continued to the symphisis menti, supplying the alveoli of the canine and incisor teeth; the other escapes by the mental foramen, together with the mental branch of the inferior dental nerve, to supply the integuments, and triangularis and depressor labii inferioris muscles; it anastomoses with the adjacent branches of the facial artery. In its course through the inferior maxillary bone it sends branches into the alveoli, each of which penetrates the bottom of the tooth to be distributed on the membrane lining its cavity.
The Meningea Parva Artery is not a constant branch; when it exists it arises from the internal maxillary, close to the origin of the inferior dental. Some of its branches are distributed to the soft palate and the nasal fossae: a principal branch of the artery passes upwards through the foramen ovale and supplies the inferior maxillary nerve, Casserian ganglion, and dura mater.
The Posterior Deep Temporal Artery arises from the internal maxillary, while the latter is passing between the two pterygoid muscles; it ascends between the temporal and external pterygoid muscles, and then between the temporal muscle and the side of the cranium: to all these parts it sends numerous minute branches which ultimately terminate in anastomosing with the deep temporal branch from the superficial temporal artery.
The Masseteric Artery also arises in the triangular space between the two pterygoid muscles and ramus of the lower jaw. It passes outwards through the sigmoid notch that separates the coronoid process from the condyle of the inferior maxilla, and then descends on the outer side of its ramus, supplies the masseter muscle, and anastomoses with the transversalis faciei artery.
The Pterygoid Branches are numerous: some of them are distributed to the internal pterygoid muscle, and a still greater number to the external pterygoid.