Background Information
• St John’s College University of Cambridge: Euclid, Elementa geometriae (Venice: Erhard Ratdolt, 1482). | St John’s College, University of Cambridge
Euclid, Elementa geometriae (Venice: Erhard Ratdolt, 1482).
Erhard Ratdolt was apparently the first publisher of scientific and mathematical material, and this first edition of Euclid bears the first printed mathematical diagrams. These were crafted by Ratdolt himself, who was also famous for his initials and borders. It is still unclear what method he used to get these figures into the text, although he describes the pains he went to in the dedication, but there are over four hundred throughout the volume. In spite of Ratdolt’s diligence in producing the diagrams the text is not authoritative, as it relies heavily on the 13th-century Latin of Campanus, itself based on Arabic translations of the original Greek. Many classical works came to Renaissance Europe from the Middle East where they had been preserved and studied following the fall of the Roman Empire, but this did mean that there was plenty of scope for errors to enter texts, an example here being the fact that Ratdolt refers to Euclid as ‘Euclid of Megara’. In fact this attribution belonged to another ancient Greek philosopher with a similar name.
• Mathematical Association of America: Mathematical Treasure: Euclid’s Elementa Geometriae Printed by Ratdolt (maa.org)
Erhardus Ratdolt (1442–1528) was a German printer working in Venice during the years 1476 to 1486. In May of 1482, he published the first printed edition of Euclid’s Elements, Euclid Liber elementorum in artem geometrie. Its contents were based on the medieval translation of the work from Greek to Latin by Campanus (circa 1220-1296). In the process of producing this book, Ratdolt solved the problem of printing geometric diagrams. He is considered the first printer of scientific works and was known for his innovative typography. This edition of Euclid’s Elements remains today a masterpiece of mathematical printing.
Christie’s https://www.christies.com/en/lot/lot-6332167
“For twenty-three centuries the Elements of Geometry has been changing the world. A compendium of facts about space and its properties—lines and shapes, numbers and ratios—it has drawn countless readers into its limitless world of abstract beauties and pure ideas” (Wardhaugh). The Elements organizes all geometric knowledge from the time of Pythagoras “into a consistent system so that each theorem follows logically from its predecessor; and in this simplicity lies the secret of its success” (PMM). Read, reprinted and translated continuously, it has been a model for mathematical exposition up to the present day, training over two millennia of mathematicians from Archimedes to Anne Lister (and beyond). Originally composed in Greek at the court of Ptolemy in Alexandria, the present text is a Latin translation from an Arabic recension, likely that of Al-?ajjaj ibn Yusuf ibn Ma?ar (which itself does not survive complete today). Produced as part of the Latin scientific translation movement of the 12th century, the translation is the work of Adelard of Bath and Robert of Chester, which was then edited and augmented in the 1250s by Campanus of Novara to become the definitive Latin version for the next several hundred years.
Ratdolt’s first edition of the Elements is not only “one of the great classics in the history of science [but also] a masterpiece of early typographical ability and ingenuity” (Bühler). “Ratdolt created geometric diagrams which are so finely wrought that the method of manufacture still baffles historians of printing. The most accepted theory today is that they were made from bent rules or perhaps cast metal shapes, but we cannot be sure how such consistent, thin and accurate lines were printed” (Kelly). Other challenges included running out of woodcut initial Ss (due every proposition beginning with the same set formula) and a general shortage of capital letters resulting from their use in labeling the over 500 marginal diagrams—all met by Ratdolt to produce the most beautiful scientific book of the incunable period, which became the model for much that followed.
See also Benjamin Wardhaugh, Encounters with Euclid (2021).
Encyclopedia Britannica Euclid | Biography, Contributions, Geometry, & Facts | Britannica
Life
Of Euclid’s life nothing is known except what the Greek philosopher Proclus (c. 410–485 CE) reports in his “summary” of famous Greek mathematicians. According to him, Euclid taught at Alexandria in the time of Ptolemy I Soter, who reigned over Egypt from 323 to 285 BCE. Medieval translators and editors often confused him with the philosopher Eukleides of Megara, a contemporary of Plato about a century before, and therefore called him Megarensis. Proclus supported his date for Euclid by writing “Ptolemy once asked Euclid if there was not a shorter road to geometry than through the Elements, and Euclid replied that there was no royal road to geometry.” Today few historians challenge the consensus that Euclid was older than Archimedes (c. 290–212/211 BCE).
Sources and contents of the Elements
Euclid compiled his Elements from a number of works of earlier men. Among these are Hippocrates of Chios (flourished c. 440 BCE), not to be confused with the physician Hippocrates of Cos (c. 460–375 BCE). The latest compiler before Euclid was Theudius, whose textbook was used in the Academy and was probably the one used by Aristotle (384–322 BCE). The older elements were at once superseded by Euclid’s and then forgotten. For his subject matter Euclid doubtless drew upon all his predecessors, but it is clear that the whole design of his work was his own, culminating in the construction of the five regular solids, now known as the Platonic solids.
A brief survey of the Elements belies a common belief that it concerns only geometry. This misconception may be caused by reading no further than Books I through IV, which cover elementary plane geometry. Euclid understood that building a logical and rigorous geometry (and mathematics) depends on the foundation—a foundation that Euclid began in Book I with 23 definitions (such as “a point is that which has no part” and “a line is a length without breadth”), five unproved assumptions that Euclid called postulates (now known as axioms), and five further unproved assumptions that he called common notions. (See the table of Euclid’s 10 initial assumptions.) Book I then proves elementary theorems about triangles and parallelograms and ends with the Pythagorean theorem.
To see the George reid copy contact DCLG Reading Room 0133