Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.

A Table of Randoms for Mortar-Pieces, to the 12 Points of the Gunner's Quadrant, cal∣culated by Diego-Uffano-Zutphen.

583	570	534	468	377	248	100
6	5	4	3	2	1	0
.	.	.	.	.	.	.	☉
6	7	8	9	10	11	12
583	570	534	468	377	248	000

Now suppose the Mortar to be placed at ☉, the Pricks in the middle line representeth the several Randoms, numbred with the Degrees of the Quadrant, forward and backward, unto which the several Randoms are set; so you see that the Mortar being levelled point blank, throweth the Bomb 100 Paces, if the Mortar be mounted one Point, it throws the Bomb 248 Paces, &c. untill 'tis mounted to the 6th. point,

583 Paces, which is the utmost Random: Now if the Mortar be mounted higher to 7, 8, 9, &c. Points, the Randoms decrease again as before they did increase: as you see in the Table.

But in those latter Randoms there lieth a great mistake, as shall be made palpably appear. For if as they are distant from the sixth Point you make them equal to one another, then the Random of the 12 points, must be equal to the Random of 0 point, or the Level Random, which is 100 Paces from the Mortar. Now it is con∣trary to all Art and Reason, to think that if the Mortar be elevated to the 12th. point, i. e. bolt upright, it should shoot the Bomb 100 Paces from the Mortar; no, it cannot be; but according to all Reason the Bomb must fall down either on, or near the Mortar, and not 100 Paces dis∣tant, as is most erroneously conceived; the like errour is in the following Table of our said Author; but because Mr. Phillipps in his Ma∣thematical Manual hath amply demonstrated their Errours, I therefore shall say no more to the Errours that have been a long time gene∣rally conceived and embraced as a truth, but now are removed.

A Table of Randoms for Mortar-Pieces, to every Degree of the Quadrant.

The Degrees of Mounture.	0	The Paces of the Random.	100	The Degrees of Mounture.	89	The Degrees of Mounture.	23	The Paces of the Random.	480	The Degrees of Mounture.	66
1	122	88	24	490	65
2	143	87	25	500	64
3	164	86	26	510	63
4	185	85	27	518	62
5	204	84	28	525	61
6	224	83	29	531	60
7	243	82	30	536	59
8	263	81	31	540	58
9	280	80	32	543	57
10	297	79	33	549	56
11	315	78	34	552	55
12	331	77	35	558	54
13	347	76	36	562	53
14	362	75	37	568	52
15	377	74	38	573	51
16	393	73	39	577	50
17	406	72	40	580	49
18	419	71	41	581	48
19	432	70	42	582	47
20	445	69	43	583	46
21	457	68	44	584
22	460	67	45	585

The most exact Tables of Randoms for the Mortar, that I have seen or can find in any An∣cient, or Modern Author, is this following Ta∣ble, calculated by the experience and trial of that Famous Inginier Tomaso Moretii of Brescia, Inginier to the most serene Republique of Venice, in his Works Intituled, Trattatu delle Artiglieria, printed 1665. Where he supposeth the utmost

Random, equal to 10000, according to which proportion he framed this following Table.

A Table of the several Randoms of each Degree of the Quadrant, the greatest Equal to 10000.

Elev.	Elev.	Elev.	Elev.
1°	349	89°	23°	7193	67°
2	698	88	24	7431	66
3	1045	87	25	7660	65
4	1392	86	26	7880	64
5	1736	85	27	8090	63
6	2079	84	28	8290	62
7	2419	83	29	8480	61
8	2756	82	30	8660	60
9	3090	81	31	8829	59
10	3420	80	32	8988	58
11	3746	79	33	9135	57
12	4067	78	34	9272	56
13	4384	77	35	9397	55
14	4695	76	36	9511	54
15	5000	75	37	9613	53
16	5299	74	38	9703	52
17	5592	73	39	9781	51
18	5870	72	40	9848	50
19	6157	71	41	9903	49
20	6428	70	42	9945	48
21	6691	69	43	9976	47
22	6947	68	44	9994	46
45	10000	45

The Use of the Precedent Table is explained by these following Propositions.