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 Buccal Artery runs tortuously, downwards, forwards, and outwards, between the two pterygoid muscles, and in company with the buccal nerve. Having arrived at the anterior margin of the ramus of the inferior maxillary bone, it penetrates the cheek and divides into a number of branches, which are distributed to the platysma myoides, buccinator and zygomatic muscles, and also to the integuments of the cheek, and to its mucous membrane and follicles. It anastomoses with the facial, infra-orbital, and transversalis faciei arteries: in some cases it is deficient, and in others it arises from some other branch of the internal maxillary.
The Anterior Deep Temporal Artery usually comes off from the internal maxillary, as this artery lies between the external pterygoid and temporal muscles; it ascends in the anterior part of the temporal fossa to supply the temporal muscle, and to anastomose with the other temporal arteries. Some of its branches penetrate the malar bone to reach the lachrymal gland and communicate with the lachrymal artery.
The Posterior Superior Dental Artery descends tortuously on the back of the antrum. Some of its branches pierce the superior maxillary bone, and supply the molar teeth and mucous membrane of the antrum, while others are distributed to the teeth, gums, and buccinator muscle: they anastomose with the labial, buccal, and infra-orbital arteries.