First use of π as 3,14... (18th C)

 

Humans have long known that a special relationship exists between the diameter and circumference of a circle. As early as 2000 BCE, some had even found numbers to represent this relationship. By this date, the Babylonians knew that the circumference of a circle was always approximately 3 1/8 times larger than its diameter, while the Egyptians put the value at 4(8/9)2

Hindu astronomy books known as the Siddhantas tell us that by 380 CE the Hindus had arrived at 3 177/1250, or 3.1416, as a constant value for the circumference/diameter ratio, and in the fifth century CE Chinese mathematicians determined that the constant must be greater than 3.1415926 and less than 3.1415927. 

The Mayas likely also knew of this ratio, and, given their sophisticated methods of calculation, had probably determined its value with a high degree of accuracy. However, it may be impossible to know for certain, as Diego de Landa, Bishop of Yucatan, burned most of the Mayas’ written records in the 1560s, believing that they were filled with “‘superstition and lies of the devil’.

Although knowledge of the constant ratio between a circle’s circumference and its diameter—the ratio we now call “pi”—is ancient, the use of the Greek letter “π” to represent it is not. Use of the π symbol is usually dated to William Jones’ work Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics, published in 1706 and shown above (direct link to the book in that amazing resource called archive.org)

After spending some time in the Royal Navy as the mathematics master on a man-of-war, Jones worked as an itinerant teacher and then private tutor in London, and later edited and published editions of several of Isaac Newton’s works. His Synopsis Palmariorum Matheseos consists of two major sections, the first dealing with “Numeral and Literal Arithmetick” and the second with the “Principles of Geometry.” 

Jones uses the π symbol several times throughout the second part, in both diagrams and equations. Although Jones is generally credited as the first to clearly set the letter π equal to the value 3.14 . . ., he may actually have borrowed this use of the π symbol from the writings of the astronomer John Machin, who had calculated π out to one hundred decimal places, and whose work Jones cites elsewhere in his Synopsis. Regardless of which man used the π symbol first, mathematicians adopted the symbol as standard only after the noted mathematician Euler used it in his writings, approximately thirty years after the publication of Jones’ work.

William Jones, Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics. London: Printed by J. Matthews for J. Wale, 1706.

X 510 J72S 

Selected Bibliography & Other sources

Arndt, Jörg, and Christoph Haenel. Pi –Unleashed. Trans. Catriona Lischka and David Lischka. Berlin: Springer, 2000. Print.

Beckmann, Petr. A History of Pi. 2nd ed. Boulder: Golem, 1971. Print. (Basically all historical references I mention on this post about the "PI" number for Babilonians, Hindus, Mayas, etc are deep/well explained on this book). Also available at amazon, see link here to buy for less than 15 USD

As usual, wikipedia for William Jones BIO; archive.org (this time the book is not high res and only B/W no color but...)

The Rule of Saint Benedict, 13th(¿?) C.

The wonderful historiated initial below comes from the opening of a copy of the La regle saint Benoit, a French translation of the Rule of Saint Benedict. The illustration shows Saint Benedict addressing four attentive nuns. The artist incorporates suggestive details that give the scene a liveliness that is surprising for so small a picture. scene:: The nun closest to Benedict points to a passage, as if asking for clarification. Benedict holds his book closed, appearing to keep his place with his index finger as he pauses to answer a question.

 

 

Decorated initials are among the most striking features of manuscripts, but they were not widely attested until the Middle Ages. Books were rarely decorated in the ancient world because, even though literacy rates were higher, oratory remained the principal means of delivery while the physical books and scrolls were relegated to supporting roles.

During the Middle Ages, with the influence of Christianity, the book became important both symbolically and practically as an instrument of textual transmission. Decorated initials helped to reveal the structure of a text by emphasizing the beginnings of works, sections and verses. Historiated initials such as this one tended to be reserved for major divisions, while smaller initials might break a text into sections. A memorably decorated initial would help a reader locate its associated text. This is especially so when it reflected the text’s meaning, as in this case, where the initial introduces the sentence, Escoute fille les coma[n]demens de ton maître [Listen, daughters, to the commandments of your teacher]. It may seem odd that the initial, so appealing to the eye, introduces the injunction to “listen.” It reflects a cultural milieu in which the reception of texts was both auditory and visual.

This particular copy of the Rule I could find was produced in northeastern France toward the end of the thirteenth century. It also contains other devotional works, including Li livres des tribulations, Chanson d’amors de pure povreteit, and three short treatises. The French has feminine inflections, suggesting that the book was made for a female readership. An inscription pasted into the book by Claude de Grilly, a nun at the Abbey of Sainte-Glossinde, suggests the book may have been made for that convent.  JC

A couple of sources beeeelow... (sorry, is late while typing this after a hard day at job hehe) ::

• Benedict, Saint, Abbot of Monte Cassino. La regle saint Benoit. ([Lorraine, approximately 1275-1300]). Pre-1650 MS 0098. University of Illinois

• Link provided to an Ebay seller (digital-scriptorium) that has auctions on ebay for a digitized copy of an 8th Century Rule of San Benedict of Nursia, probably this was one of the first editions commissioned.

NYPL’s NEW Digital Collections

The New York Public Library made a recent and exciting announcement --it has made available more than 180,000 images of public domain material from its collection as high-resolution downloads. The idea is to “facilitate sharing, research and reuse by scholars, artists, educators, technologists, publishers, and Internet users of all kinds.”

Images hail from every nook of the NYPL’s rich holdings, from medieval manuscripts to Federal Art Project and Farm Security Administration photographs. Looks nice, I still have to check max resolution available on those sources but... some samples below (links to source provided on images caption):

Henry David Thoreau’s holograph draft manuscript of “Wild Apples,” 1850-1860.

Text with illuminated miniatures, c. 1500-1525.

Chromolithograph map, “Linguistic stocks of American Indians north of Mexico,” 1891.

Photograph by Berenice Abbott, “Oyster Houses, South Street and Pike Slip, Manhattan,” 1935.