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 Infra Orbital Artery passes through a canal of the same name in the floor beneath the orbit, in company with the infra-orbital nerve beneath which it lies. In this course it sends some small branches to the inferior rectus and inferior oblique muscles of the eye. Having arrived at the anterior part of this canal, it gives off the anterior superior dental branch, which descends through the anterior wall of the antrum, to supply its mucous membrane, and the canine and incisor teeth. After giving off this branch, it leaves the infra-orbital canal, and is found on the face beneath the outer head of the levator labii superioris alaeque nasi, and lying on the levator anguli oris. In this situation it supplies the adjacent muscles, and anastomoses with the facial, dental, buccal, and nasal arteries.
The Vidian Artery, extremely small, passes backwards through the Vidian canal above the root of the internal pterygoid plate, and enters the aqueduct of Fallopius through the hiatus Fallopii. It supplies the facial nerve, Eustachian tube, and pharynx, and anastomoses with the pharyngea ascendens, and with the stylo-mastoid branch of the occipital artery. This vessel is sometimes given off by the trunk of the middle meningeal.
The Superior Palatine Artery descends obliquely forwards through the posterior palatine canal. In this situation it sends two or three small branches through the accessory palatine canals to the velum palati. The continued trunk after leaving the posterior palatine canal advances on the roof of the mouth, and is distributed to its lining membrane, and to the gums and superior maxillary bone. At the foramen incisivum it communicates with the spheno-palatine arteries, which descend from the nose through the anterior palatine canals.