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DIGGES, Leonard [DIGGES, Thomas]

A Geometrical practical treatize named Pantometria, diuided into three bookes, longimetra, planimetra, and stereometria

London : printed by Abell Ieffes, 1591


Folio. pp. [viii], 152, 151-195, [iii]. [A]⁴ B-2C⁴. Roman, Italic and Black letter. Decorative woodcut initials and head- and tail-pieces throughout. Fine woodcut mathematical and topographical diagrams and illustrations, including to t-p, depicting the use of geometrical instruments and the process of land-surveying. Large woodcut arms of Sir Nicholas Bacon (the dedicatee, father of Sir Francis Bacon) to verso of t-p, unidentified arms to verso of Cc3, book-labels of Erwin Tomash and Harrison D. Horblit on pastedown. A particularly fine copy, absolutely crisp and clean, with good margins (some deckle edges), in contemporary limp vellum, remains of ties. 

Second and best edition of Thomas Digges’ fundamental mathematical work, revised and expanded from the edition of 1571, and the first description of many important theories and techniques in English. Digges (1546-1595) was the son  of the mathematician and surveyor Leonard Digges (1520-1559), inventor of the theodolite and perhaps also of the telescope. Thomas produced revised or augmented editions of several of his father’s works.

“This edition is essentially identical to the first with two significant additions by Thomas Digges: the Mathematicall discourse of the five Platonicall solides… and the first treatment of the science of ballistics in English. Also added to Book I is a short chapter (three leaves) on surveying in mines. Leonard Digges published a small book on practical surveying in 1556, but this more ambitious work was still in manuscript when he died. Thomas, his son, further extended the work and had it published. The early material is essentially that to be found in the works of such authors as Gemma Frisius and Peter Apian (quadrants, astrolabes with shadow scales, etc.). However this book, and his earlier work Tectonicon, are the first descriptions of the application of these instruments written in English. All of the early instruments rely on the use of right-angle triangles in establishing a survey. Digges deals with a different type of survey instrument in a later part of this volume. This is the first description and illustration of the theodolite–the name being coined by Digges in this work. This device consisted of a table with an angle- sighting device mounted above it. .… Another intriguing feature of this work is that Digges, in Chapter 21 of the first book, discusses the use of various optical devices and claims that: … “ye may by applycation of glasses in due proportion cause any peculiare house, or roume thereof dilate and shew it selfe in as ample fourme as the whole towne firste appeared, so that ye shall descerne any trifle, or read any letter lying there open”… Digges senior had obviously been experimenting with a magnifying lens, and it seems very likely that he invented the telescope about a half-century before it was unambiguously described in Holland in 1608. The first book, titled Longimetra, is a treatise on surveying using the quadrant, square and theodolite. The subsequent books, Planimetra and Stereometra, cover plane and solid geometry and their use in the calculation of area and volume—particularly gauging.” Tomash & Williams 

The Pantometria provides a complete course in practical geometry, from the fundamentals (“A Line is a length without breadth or thicknesse”) to the most complex theorems. Digges provides numerous examples throughout, taking the reader through the steps of each calculation. The work concludes with the first appearance of Digges’ work on ballistics, a new addition to the present edition. “He was able, on the basis of his own and his father’s experiments, to disprove many commonly held erroneous ideas in ballistics but was not able to develop a mathematical theory of his own. These appendixes constitute the first serious ballistics studies in England” (DSB).

A very fine copy of this most important work. 

ESTC S107357. STC 6859; Cockle 16. Spaulding and Karpinski 49. DSB IV, 97 (attributing the Pantometria to Leonard Digges). Tomash & Williams D54 [This copy]. The Geometry of War 45.