Question.

I demaund the true cubicke root of 117884.

Resolution.

The pricks placed in order as before, I find there will be Page  7 but 2 figures in the quotient, & that the cubick nūber of 117 is 64, whose cubick root is 4, which 4 I place in the quotient, and his cube 64 being abated from 117, there remaines 53 to be placed ouer the last prick: then tripling the quotiēt 4, ariseth 12 to be set down one place nearer towards my right hand, & then multiplying the quotient by the said triple, doth arise 48 for a deuisor, which I set in his place, drawing a line vnder him as in the former worke you see. And then I make search how oft I can haue 48 in 538, which I can haue many times, but more then 9 times I must not take; and therefore I set downe 9 in the quotient, and multiplying the same by the deui∣sor 48, ariseth 432, to be placed vnder the line vnder the deuisor, then I do multiply the said 9 squarely, ariseth 81, the which multiplied by 12 being the triple of the first quotient, ariseth 972, the which I set down one place nearer towards my right hand; and then I multiply 9 cubickly, ariseth 729 to be set downe yet one place nearer to∣wards my right hand: and adding all those sums together, the totall is 53649, which abated from 53884, rests 235. And thus I affirme, that 49 is the nearest cubicke root in whole numbers of 117884, as here by the worke you may see.

〈 math 〉

Now to find a denominator for the 235 remaining, I square the roote 49, so ariseth 2401. Then I triple the sayd squared number and there ariseth 7203, and then I triple the roote 49, ariseth 147, to which I adde one, and it makes 148. Al which summes ioyned together, makes 7351, aud so the true cubicke roote of 117884 is 49 and 235/7351 partes of an vnite.

Page  8Theormes shewing the true proportion that a bullet of one mettal beareth to the like bullet of a cōtrary met∣tall, as also the proportion that the circumference of any buller or globe &c. beareth to the diameter, and of the superficiall content thereof to the diametrall square thereof, the which according to Archimedes are thus proued.

All circles are equall to that right angled triangle, whose containing sides, the one is equall to the semidia∣meter, the other to the circumference thereof.

The proportion of all circles to the square of their Diameter, is as 11 to 14.

All globes beare together triple that proportion that their Diameters do.

The circumference of any circle, is more nor the tri∣ple of his Dyameter, by such proportion as is lesse then 1/7 and more nor 10/27.

A bullet of iron, to the like bullet of marble stone is in proportion as 15. to 34.

A bullet of lead to the like bullet of iron, is in propor∣tion as 28 is to 19.

A bullet of lead to the like bullet of marble stone is in proportion as 4 to 1.

The Diameter of any bullet &c. is in proportion to the circumference as 7 to 22.