The art of gunnery. Wherein is described the true way to make all sorts of gunpowder, guu-match [sic], the art of shooting in great and small ordnance: excellent ways to take heights, depths, distances, accessible, or inaccessible, either single or divers distances at one operation: to draw the map or plot of any city, town, castle, or other fortified place. To make divers sorts of artificiall fire-works, both for war and recreation, also to cure all such wounds that are curable, which may chance to happen by gunpowder or fire-works. This treatise is composed for the help of all such gunners and others, that have charge of artillery, and are not well versed in arithmetick and geometry : all the rules and directions in this book, being framed both with and without the help of arithmetick. By Nathanael Nye mathematician, master gunner of the city of Worcester.

CHAP. 26.

How by knowing the height and weight of one bullet, to finde the weight of another bul∣let, the height being given.

A Bullet of iron of six inches hie, weigh∣eth thirty pounds; what will the like bullet of seven inches in height weigh? Resolution, first, Multiply six cubically, then multiply seven cubically; then as the cube of six, is in proportion to the cube of seven; so thirty pounds (the weight of a shot of six inches high) is to so many pounds as a shot of seven inches high will weigh.

Example. First, I multiply six cubically, there ariseth two hundred and sixteen, then I multiply seven cubically, which is three hundred forty nine; then I say, as two hundred and sixteen is to three hundred forty three, so thirty (the weight of six inches high) is to forty seven pounds, ten ounces, and one quarter; the weight of a shot seven inches high.

How to help those that cannot abstract the cube root (to resolve this proportion) two se∣veral ways.

The first way is, to learn the use of a Table of cube roots, which I have an∣nexed for the use and help of such as can∣not extract the cube root, because my book should be as profitable an help as any Book ever hath yet been; for by this Table, you may learn to work al∣most any conclusion, as well as if you could extract the Root, and with more case.

An excellent Table to finde the Cube root of any number not exceeding 1000000.

The root.	The cube.
1 ¼	1.95
1½	3.37
1 ¾	5.36
2	8
2 ¼	11.39
2 ½	15.62
2 ¾	20.80
3	27
3 ¼	34.33
3 ½	42.82
3 ¾	52.73
4	64
4 ¼	76.77
4 ½	91.12
4 ¾	107.17
5	125
5 ¼	144.90
5 ½	167.37
5 ¾	190.11
6	216
6 ¼	244.14
6 ½	274.62
6 ¾	307.55
7	343
7 ¼	381.••8
7 ½	421.87
7 ¾	465.48
8	512
8 ¼	561.51
8 ½	614.12
8 ¾	669.92
9	727
9 ¼	791.45
9 ½	857.37
9 ¾	926.89
10	1000
10 ½	115.76
11	1331
11 ½	1520.87
12	1728
12 ½	1953.12
13	2197
13 ½	2460.••7
14	2744
14 ½	30275 25
15	3375
15 ½	3724
16	4096
16 ½	4492
17	4913
17 ½	5359
18	5832
18 ½	6332
19	6859
19 ½	7415
20	8000
20 ½	8615
21	9261
21 ½	9938
22	10648
22 ½	11390
23	12167
23 ½	127••8
24	13024
24 ½	14705
25	15625
25 ½	16581
26	17576
26 ½	18609
27	19683
27 ½	20797
28	21972
28 ½	23149
29	24389
29 ½	25672
30	27000
30 ½	28372
31	29792
32	32768
33	35937
34	39304
35	42125
36	48656
37	50653
38	54872
39	55419
40	64000
41	68921
42	74088
43	79507
44	85184
45	91125
46	97336
47	103823
48	110592
49	117649
50	125000
51	135651
52	140608
53	148877
54	157464
55	167375
56	175616
58	195112
59	205379
60	216000
61	216981
62	238328
63	250047
64	262344
65	274635
66	287496
67	300753
68	314432
69	329199
70	333000
71	357911
72	373348
73	389017
74	405224
75	421875
76	438276
77	456533
78	474522
79	493039
80	512000
81	531441
82	550408
83	571787
84	592604
85	614125
86	646056
87	648303
88	68••472
89	701669
90	729000
91	753571
92	778688
93	804357
94	830584
95	857375
96	884736
97	615673
98	941192
99	970299
100	1000000

To work the last proposition by the Table.

First, In place of multiplying 6 cubical∣ly, finde 6 in the Table, and right against it you shall have 216, which is the cube of 6; then finde 7 likewise under the title Root, and under the title Cube you shall finde 343, the Cube of 7; then consider, that so much as 216 is in proportion to 343, the like proportion 30 is to 47 pounds and ten ounces.

There is much about seven cube inches of iron in one pound; by this rule you may finde 7 thirty times in 216 and 7; you may finde seven to be contained in 343, just forty nine times, but this rule is not so per∣fect as the former, because in subtracting seven out of 216, you shall finde thirty pounds and 6/7 parts, which is too much by the fraction.