This classic text explores the properties of the quartic curve and its inscribed configurations, providing a comprehensive overview of the subject that will appeal to students and experts alike. With clear exposition and numerous examples, Harry Bateman introduces readers to the geometry of the quartic curve and its associated invariants, covering topics such as singular points, bitangents, inflectional tangents, and more. Whether you are a student of mathematics or a practicing mathematician, this book is an essential resource for understanding one of the most important curves in algebraic geometry. This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.