48. Peurbach

Elementa arithmetices : algorithmvs de nvmeris integris, fractis, regulis communibus, et de proportionibus / autore Georgio Peurbachio ... ; cum praefacione Philip. Melanth. (Viterbergae : Impressum Vitebergae per Iosephum Klug, 1536)

This book is tiny––about 180mm by 100mm, and less than 5 mm thick––but leads us into a microcosm of the early 16th century. It is Monash’s oldest mathematics book, originally acquired for £45 in the eighties.

Of the preface by Philip Melanchthon, Luther's best friend, two pages have been cut out, and the third page was heavily censored, in 1642, by a Spanish lay official for the Inquisition: Don Cristoval Guillen.

The book was first published in 1497, the year of Melanchthon's birth, and long after Peuerbach’s death in 1461. This is the second edition. It gives practical rules for working with fractions and proportions: most importantly, it shows how to convert fractions to degrees, minutes and seconds––techniques that Peuerbach employed in his much more sophisticated astronomical work involving Ptolemy’s Almagest, some time before Copernicus's revolutionary treatise of 1543.

The rules are written out entirely in words––a method we still find difficult to follow––but he does give examples, and this work would have been invaluable to students.

Peuerbach's book also signals the convergence of the academic quadrivial tradition (coming from Boethius) and the practical algebra of the abacist schools. These two only came together in university curricula in the early 16th century.

So this little book leads us into questions of academic versus technical education, and of religious freedom.

Finally, it is bound in contemporary, i.e. 16th century, limp vellum with ties (now gone) and, tucked inside the binding for padding, there is a little piece of vellum manuscript, probably from the 14th century. A couple of words are legible: edificium and societat[is]: ‘building’ and ‘society’. So a manuscript was destroyed in binding this printed book.

That was not unusual: manuscripts were often used for this purpose as they became ‘superseded’ by the new, printed versions of texts.

Perhaps Peuerbach’s book has a lesson for us. When we use the web to read books, and care less about the real, physical books, we thereby miss out on all that more that a book can tell us beyond its intellectual content.