Geometrical Constructions with a Ruler, Given a Fixed Circle with its Center. Translated from the First German Edition (1833) [Number 4 of the Script Mathematica Studies]

As with any profession or field of study, the branch of mathematics known as geometry has always had different schools of thought and specialties. And, as with most of those professions and fields of study, members of geometry's specialties and adherents of its different schools of thought could sometimes become rivals, convinced that their way was the best way of doing things, or even the only way. In the nineteenth century, geometry was basically divided between two camps: analytic geometry and what became known as synthetic geometry. (That sentence is a gross simplification, but we've only got a paragraph to work with here, so bear with us.) Analytic geometry was inspired by the work of 17th-century mathematician René Descartes and approached geometry through the use of coordinates, representing geometric shapes through the use of numbers and mathematical, particularly algebraic, formulas. Synthetic geometry, on the other hand, was particularly inspired by the great Greek geometer, Euclid, and used axioms to prove its results. It didn't get its name until 19th-century mathematicians needed to come up with a term for the type of geometry that was NOT analytic as analytic geometry became more popular and, by the end of the century, also the dominant method of teaching geometry and solving advanced geometric problems in fields such as engineering and physics. Before that, synthetic geometry was just plain old.geometry. Swiss mathematician Jakob Steiner was one of synthetic geometry's best defenders, and in his day he was considered to be the greatest geometer since Apollonius of Perga of Hellenistic Greece. He despised analytic geometry--he was known to say that relying on calculation hampered thinking, while pure geometry such as what he practiced stimulated creativity. Steiner wrote "Geometrical Constructions with a Ruler Given a Fixed Circle with Its Center" in 1833 to prove the point that, once one used a compass to draw an initial circle, a geometer could discard even that basic tool to solve advanced problems without resorting to mathematical equations. It's as if he's throwing down a gauntlet to his analytic competitors, daring them to approach problems as simply as he did. This volume, part four of The Scripta Mathematica Studies, is the first translation of "Geometrical Constructions with a Ruler" into English. A review when it was published said it should be of particular interest not only to those interested in the history of mathematics but also to teachers. Mathematicians began rethinking geometric axioms around the turn of the twentieth century, well after Steiner's death, and the two schools are taught as one except at the most elementary level. In other words, as fierce as the rivalry once was, it has now completely withered away. Our copy is "fine." The gold stamped lettering on the black cloth binding is exceptionally bright and clear. There is light bumping on the ends of the spine and the corners, and a minor dent at the top of the rear cover, but neither the bumping nor the dent harms the binding cloth.The text block is tight and square and there are no marks anywhere in the interior. The pages show age tanning but otherwise are in fine condition, including the two plates of portraits of Steiner at different stages in life, one serving as a frontis. Photos are forthcoming or available upon request. …