Western and Oriental Manuscripts and Miniatures | 06 December 2017

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Lot no.


Leaf from a mathematical text on the properties of circles

Sold for £3000

Est: £1000–1500

Leaf from a mathematical text on the properties of circles , with discussion of various Greek authorities’ methods of calculating the area of a circle, with simple mathematical diagrams in upper border, in Latin, illustrated manuscript on parchment [France (probably Paris), thirteenth century]

Single leaf, with double column of 68 lines in a tiny and much abbreviated script, quotations underlined in red, paragraph marks in red, simple red and dark blue initials, two small diagrams in upper margin of (i) a circle within a square, and (ii) a circle within a square, with another smaller square within its body, trimmed down outer upright edge removing blank margin there, inner edge torn with damage to edge of one text column, scuffs and stains, all from reuse as a pastedown in a later book, overall fair and presentable condition, 265 by 180 mm.

Any witness to a scientific or mathematical text from the Middle Ages is of the greatest rarity. The text here opens beneath the diagrams with paraphrased discussions of how to calculate the area of a circle, naming its sources as “Ypocrete” (Hippocrates of Chios, c . 470-410 BC., his work on this subject is the only part of his writings to survive, buried within those of Simplicius; he favoured the division of the square into a number of crescent-shaped parts, and the calculation of their total volume) and “Brisso” (Bryson of Heraclea, late fifth century BC., who is now known primarily from Aristotle’s criticism of his method for calculating the area of a circle, by drawing a polygon within a circle, deducing the area of that, doubling its sides and repeating until the polygon and circle are indistinguishable; he and Aristotle also fell out over Bryson’s assertion that there was no such thing as bad language). The text goes on to note the work of one “Zenone” (most probably Zenodorus, c. 200-140 BC.), who considered in his now mostly lost treatise ‘On isometric figures’ , the proposition that “ A circle is greater than any regular polygon of equal contour”.

Western and Oriental Manuscripts and Miniatures

Wednesday 06 December 2017, 2.00pm

Bloomsbury London
Bloomsbury House
24 Maddox Street


Saturday 2 December
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Sunday 3 December
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