The description and use of the carpenters-rule: together with the use of the line of numbers (inscribed thereon) in arithmetick and geometry. And the application thereof to the measuring of superficies and solids, gaging of vessels, military orders, interest and annuities: with tables of reduction, &c. : To which is added, the use of a (portable) geometrical sun-dial, with a nocturnal on the backside, for the exact and ready finding the hour of the day and night: and other mathematical conclusions. Also of a universal-dial for the use of seamen or others. With the use of a sliding or glasiers-rule and Mr. White's rule for solid measure. / Collected and fitted to the meanest capacity by J. Browne.

PROB. 13. To find the Cubique Root of a Number under.〈 math 〉〈 math 〉

The Cubique root is always by the first of two mean proportionals be∣tween 1 and the Number given, and therefore to be found by dividing the space between them into three equal Parts: So by this means the root of 1728 will be found to be 12, the root of 17280 is neer 26, the root of 172800 is almost 56, although the point on the Rule representing all the square numbers is in one place, yet by altering the unit it produceth various points and numbers, for their respe∣ctive proper roots. The Rule of find

which is in this manner: You must set (or suppose pricks to be set) pricks under the first figure to the left hand, the fourth figure, the seventh and the tenth; now if by this means the last prick to the left hand shall fall on the last figure, as it doth in 1728, then the unit will be best placed at 1 in the middle of the Line, and the Root, the Square and Cube will all fall forward toward the end of the Line.

But if it fall on the last but 1, as it doth in 17280 then the unit may be placed at 1 in the beginning of the Line, and the Cube in the second length, or else the unit may be pla∣ced at 10 in the end of the Line, and the Cube in the first part of the Line, you may help your self, as in the first Problem of the 2 Chapter.) But if the last prick fall under the last but two, as in 172800, it doth then place the unit always at 10 in the end of the Line, then the Root, the Square, and Cube, will all fall backward, and be found in the second part, between

the middle 1 and the end of the Line. By these Rules it doth appear that the Cube root of 8 is 2, of 27 is 3, of 64 is 4 of 125 is 5, of 216 is 6, of 345 is 7, of 512 is 8, of 729 is 9, of 1000 is 10. As you may see by this following Table of Square and Cu∣bique roots.

Thus you have the chief use of the line of numbers in general, and they that have skill in the rule of three and a little knowledge in plain triangles, may very aptly apply it to their par∣ticular purposes, Yet for their sakes for whom it is intended, I shall in∣large; to some more particular appli∣cations in measuring all sorts of Su∣perficies, and Solids; wherein I do judge it will be most serviceable do them that be unskilful in Arithme∣tick, as before said.

A Table of Square and Cubique Roots.

Root.	Square.	Cube.	Root.	Square.	Cube.	Root.	Square.	Cube.
1	1	1	7	49	343	204	41616	8489664
2	4	8	8	64	512
3	9	2••	9	81	729	439	192721	84604519
4	16	64	10	100	1000
5	25	125	12	144	1728	947	896809	849278123
6	36	216	26	676	17576
			56	3136	175616	1000	1000000	1000000000