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 Or Aortic Intercostals are usually from nine to ten in number on each side, according as the superior intercostal gives off three or two branches: they all arise from the posterior and lateral part of the thoracic aorta. The superior run obliquely upwards and outwards, the middle less obliquely outwards, and the inferior almost transversely: those of the right side, having to cross the spine, are necessarily longer than those on the left, and have additional relations: from their origins to the angles of the ribs, they rest on the spine posteriorly, and are covered in front by the cesophagus, thoracic duct, vena azygos, sympathetic nerve, and the right pleura. Those of the left side, traced as far as the heads of the ribs, rest on a very small portion of the spine, and are only covered by the sympathetic nerve and left pleura.
In the remainder of their course, being exactly alike on right and left, the same description will serve for the intercostal arteries of both sides. There are some differences, however, between the relations of those above and those below: thus, the superior aortic intercostal communicates with the lowest intercostal branch from the subclavian, while each of the others communicates with the aortic intercostal above and below it: again, those low down cross behind the splanchnic nerves on both sides, and behind the demi-azygos vein on the left side; and the eleventh and twelfth intercostals on either side pass behind the corresponding pillar of the diaphragm.
Having arrived in the intercostal space, each of the intercostal arteries divides into an anterior and posterior branch: the anterior branch, larger than the posterior, proceeds outwards towards the angle of the rib, having in front of it the pleura, and behind it the anterior, or inferior costo-transverse ligament, and the external layer of intercostal muscles; having arrived near the angle of the rib, it divides into a superior and inferior branch, both of which sink between the two layers of intercostal muscles: the inferior, much the smaller, runs for a short distance along the superior margin of the rib below, and is then lost in the periosteum on its external surface ; while the superior, which is really the continued anterior intercostal, runs forwards between the two layers of intercostal muscles, lodged in the groove in the inferior margin of the rib above, till it reaches the anterior part of the thorax, its corresponding vein lying above it and its nerve beneath it; here it descends in the intercostal space, and its mode of termination depends on its situation: those corresponding to the true ribs anastomose with the internal mammary artery; those corresponding to the false ribs sink into the abdominal muscles, and, having supplied them, anastomose with the mammary, epigastric, and circumflexae ilii arteries. The twelfth anterior intercostal differs somewhat from the preceding: it runs downwards and outwards between the corresponding crus of the diaphragm and the body of the last dorsal vertebra; then along the inferior margin of the twelfth rib, opposite to the middle of which it divides into transverse and descending branches; these are lost in the broad muscles of the abdomen, and in communication with the lumbar and circumflexae ilii vessels. The posterior branch of each intercostal artery passes backwards, between the body of the corresponding vertebra on the inside, and the inferior costotransverse ligament on the outside: in this situation it sends a small branch through the lateral foramen of the spine to the tunics of the spinal marrow, and then continues its course backwards to be lost in the spino-transverse, longissimus dorsi, and sacro-lumbalis muscle; some of its branches extend to the latissimus dorsi and trapezius muscles, and are lost in the integuments.