Gunnery became a subject for practical mathematics in the 16th century. Printed books and new mathematical instruments dealt with the measurement of shot, the elevation of guns and mortars, and the calculation of the range of fire. Calipers and gauges were devised to measure diameters and indicate weights. Sights and levels enabled the gunner to set appropriate elevations, and there was an enormous range of forms and styles for such instruments, including exotic combinations which could never have served in warfare. More standard patterns were emerging by the 18th century when mathematical instrument makers had become regular suppliers to ordnance departments. The prediction of range in relation to the elevation of a gun was considered the pinnacle of artillery as a mathematical science, and its most difficult problem. From Galileo and Newton to the humble compilers of tables, mathematicians demonstrated the value of their art by studying the fleeting path of the shot through the air.

Gunnery entries in the catalogue:

1.  Niccolò Tartaglia, La nova scientia (1537) and Quesiti et inventioni diverse, (1546)
2.  Gunner's sector, c. 1600
3.  Gunner's folding rule, signed 'Bengamin Jobson 1680'
4.  Gunner's gauge, 1612
5.  Astronomical compendium by Erasmus Habermel, c. 1600
6.  Protractor and gunner's gauge by I. G. Mettel, 18th century
7.  Gunnery and dialling instrument, 1595
8.  Gunner's calipers, c. 1700?
9.  Gunner's calipers by Nicolas Bion, c. 1700
10.  Gunner's calipers by Watkins and Smith, c. 1770
11.  Gunner's sector by Tobias Volkmer, 1618
12.  Bartolomeo Romano, Proteo militare (1595)
13.  Leonhard Zubler, Nova geometrica pyrobolia (1608)
14.  Surveying and gunnery instrument, c. 1600
15.  Gunnery and surveying instrument, 16th century
16.  Gunner's sight, 17th century
17.  Gunnery instrument by Erasmus Habermel, late 16th century
18.  Surveyor's quadrant by Jacobus Lusverg, 1677
19.  Gunner's level and gauge, early 18th century
20.  Gunner's level and sight by Ulrich Klieper, 1578
21.  Gunner's level and sight by Georg Zorn, 1624
22.  Gunner's level and sight, c. 1600
23.  Gunner's level and gauge, signed 'F. F. F. 1629'
24.  Gunner's level and sight by M. E., 1686
25.  Gunner's level and sight by M. K., 1689
26.  Gunner's level by Butterfield, c. 1700
27.  Gunner's level and sight by Picart, c. 1700
28.  Gunner's level, c. 1700
29.  Gunner's level, early 18th century
30.  Gunner's level and sight by W. Burucker, early 18th century
31.  Gunner's level and sight, 1736
32.  Nicolas Bion, Traité ... des instrumens de mathematique (1709)
33.  Folding level and sector by LeMaire fils, c. 1750
34.  Folding level and sector by Clerget, c. 1700
35.  Folding square by John Marke, c. 1670
36.  Gunner's perpendicular by Adams, c. 1790
37.  Daniel Santbech, Problematum astronomicorum et geometricorum (1561)
38.  Gunner's level and sight by I. D., 1621
39.  Gunner's level and sight, 17th century
40.  Henry Phillippes, A Mathematical Manual (1669)
41.  Samuel Sturmy, The Mariners Magazine (1669)
42.  Gunner's rule by John Rowley, c. 1700
Material relating to gunnery also appears on other instruments.
For example, the following instruments carry gunner's gauge scales:
4.  Gunner's gauge, 1612
5.  Astronomical compendium by Erasmus Habermel, c. 1600
6.  Protractor and gunner's gauge by I. G. Mettel, 18th century
7.  Gunnery and dialling instrument, 1595
11.  Gunner's sector by Tobias Volkmer, 1618
12.  Bartolomeo Romano, Proteo militare (1595)
17.  Gunnery instrument by Erasmus Habermel, late 16th century
19.  Gunner's level and gauge, early 18th century
23.  Gunner's level and gauge, signed 'F. F. F. 1629'
52.  Triangulation instrument by Joost Bürgi, c. 1600
53.  Triangulation instrument by Erasmus Habermel, late 16th century

Surveying and Rangefinding entries in the catalogue:
43.  Juan de Rojas, Commentariorum in astrolabium (1551)
44.  Astrolabe by Anthoitne Mestrel, 1551
45.  Leonard and Thomas Digges, Pantometria (1571)
46.  Altazimuth theodolite by Humphrey Cole, 1586
47.  Arthur Hopton, Speculum Topographicum: or the Topographicall Glasse (1611)
48.  Circumferentor by W. R., 1667
49.  Levinus Hulsius, Instrumenta mechanica (1605)
50.  Sebastian Münster Rudimenta mathematica (1551)
51.  Benjamin Bramer, Geometrischen triangular Instruments (1648)
52.  Triangulation instrument by Joost Bürgi, c. 1600
53.  Triangulation instrument by Erasmus Habermel, late 16th century
54.  Leonhard Zubler, Novum instrumentum geometricum (1607)
55.  Triangulation instrument by Christoph Trechsler, 1617
56.  Philippe Danfrie, Declaration de l'usage du graphometre (1597)
57.  Graphometer by Baradelle, second half of the 18th century
58.  Leonhard Zubler, Fabrica et usus instrumenti chorographici (1607)

Fortification entries in the catalogue:

59.  Egnatio Danti, Latino Orsini, Trattato del radio latino (1583)
60.  Radio latino by Mancinus, c. 1600
61.  Military surveying instrument, 17th century
62.  Military graphometer and protractor, 17th century?
63.  Surveying instrument and sundial by Paul Carré, 1652
64.  Surveying instrument for fortification by A. Descrolieres, 1579
65.  Military surveyor's protractor by Erasmus Habermel, late 16th century
66.  Military architect's rule, 17th century
67.  Sector by Nicolaus Blondo, 1694
68.  Military architect's rule, 17th century
69.  Military architect's rule, c. 1700
70.  Military protractor by John Marke, c. 1670
71.  Protractor for internal and external angles by John Rowley, c. 1700
72.  Military protractor by Johann Martin Unseld, 1712
73.  Architect's protractor by Joshua Kirby, 1765
74.  Joseph Furtenbach, Mannhafter Kunst-Spiegel (1663)
75.  Philip Staynred, A Compendium of Fortification (1683)
76.  Richard Blome, The Gentlemans Recreation (1686)
77.  Johann Christoph Sturm, Mathesis compendiaria (1714)
Scales of polygons, which could be used in drawing fortification outlines, appear on many of the instruments, not just those above:
2.  Gunner's sector, c. 1600
11.  Gunner's sector by Tobias Volkmer, 1618
14.  Surveying and gunnery instrument, c. 1600
33.  Folding level and sector by LeMaire fils, c. 1750
34.  Folding level and sector by Clerget, c. 1700
35.  Folding square by John Marke, c. 1670
60.  Radio latino by Mancinus, c. 1600
61.  Military surveying instrument, 17th century
62.  Military graphometer and protractor, 17th century?
63.  Surveying instrument and sundial by Paul Carré, 1652
64.  Surveying instrument for fortification by A. Descrolieres, 1579
65.  Military surveyor's protractor by Erasmus Habermel, late 16th century
66.  Military architect's rule, 17th century
67.  Sector by Nicolaus Blondo, 1694
68.  Military architect's rule, 17th century
69.  Military architect's rule, c. 1700
70.  Military protractor by John Marke, c. 1670
72.  Military protractor by Johann Martin Unseld, 1712
73.  Architect's protractor by Joshua Kirby, 1765

As an astronomical instrument, the telescope is one of the most familiar icons of science. Yet when invented it was considered more a military device than a scientific instrument. The first telescopes were announced in the Netherlands in 1608 and were improved by Galileo in 1609. Galileo's astronomical observations brought him European fame, but even before making his discoveries he had already been rewarded for improving the instrument's strategic use. While the telescope, as an optical instrument, is markedly different from the mathematical instruments of the period, its origins were equally bound by contemporary preoccupations with war.

Troop Formations and the Telescope entries in the catalogue:
78.  William Oughtred, The Circles of Proportion and the Horizontal Instrument (1632)
79.  Circles of Proportion by Elias Allen, c. 1635
80.  Military counters, c. 1700
81.  Galilean telescope, modern replica

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