This section is from the book "Applied Anatomy: The Construction Of The Human Body", by Gwilym G. Davis. Also available from Amazon: Applied anatomy: The construction of the human body.
For the removal of a part of a rib a more formal operation is necessary. The incision is made directly on the rib down to the bone and five or more centimetres in length. The skin being retracted, the periosteum is incised and detached from the rib with a periosteal elevator which is passed down its posterior surface, pushing the pleura away from the rib. When the elevator reaches the lower border of the rib an incision is made down on it through the intercostal muscles, keeping as close to the rib as possible to avoid wounding the intercostal artery, which lies close to its lower edge. The rib is then divided either with a cutting forceps like Estlander's, or a Gigli saw. The rib, having been divided at one end of the incision, is then lifted up, the pleura stripped off, and divided at the opposite end.
Should the intercostal artery bleed, and it is often sufficiently large to spurt quite actively, it can be caught with a haemostatic forceps and secured with a ligature if necessary. This is safer than to trust to packing, on account of the lack of support due to the removal of the rib. After the incision is completed, the pleura is incised and the tube introduced. In ligating the intercostal artery, care should be taken not to include the nerve which lies close to but below it; that is, farther away from the rib.