Question.

If a Saker of foure inches diameter weigh 1600 pound weight, what will a Culuering weigh that is sixe inches diameter?

Resolution.

Some would thinke that the rule of proportion plain∣ly wrought, would answer this question: but in that they are deceiued, for the content of solide bodies being massie, are Sphericall or Cubicall inproportion, there∣fore you must multiply the diameters of euery peece cubically, & set downe the weight of the peece knowne in the middle number, and so working according to the rule of proportion, you shall find out the true weight of the greater peece.

Example.

4 inches the diameter of the lesser peece, multiplied cubically, ariseth 64 inches. Likewise the cubicke num∣ber Page  32 of the diameter of a Culuering of 6 inches high, is 216 inches: then framing the rule of proportion, I say, if 64 being the cube of 4 yeeld 1600 pound weight, (be∣ing the weight of a Saker of 4 inches bore) what will 216 being the cubicke number of 6 inches, so multiply∣ing 216 by 1600, ariseth 345600. which deuided by 64 yeeldes in the quotient 5400 pound weight, so much weigheth the Culuering of 6 inches diameter.

In working by the conuerse rule of proportion, you may not onely prooue this conclusion, but also may find out the weight of any lesser peece of ordinance, by know∣ing the weight of a greater.

Example.

If 216 being the cube of 6 inches, yeeld 5400 pound in weight, what will 64 being the cube of 4 inches? so multiplying 5400 by 64 there ariseth 345600. which de∣uided by 216, the quotient is 1600 pound weight, shew∣ing the true weight of the Saker of 4 inches diameter, as before.

Or if the diameters of the peeces whose weight you would know, containe both whole numbers and broken, in reducing each diameter into his proper fraction, and multiplying the same cubically, setting down the weight of the peece knowne, in the middle place, for the second number, and multiplying and deuiding as afore is taught, the quotient will shew you your request, as the conclusion following will teach you.

Question.

If a demy Culuering of 5 inches ¼ diameter weigh 2600 pound weight, what will a Cannon of 7 inches ¾ diameter?

Resolution.

I reduce the diameter of each peece into his proper fraction, and I find that the broken number of 5 inches ¼ diameter containeth 21/4, which multiplied cubically ari∣seth 9261/4. Likewise I reduce the diameter of the Cannon, being 7 inches ¾ into his fraction, and it is 31/4;, whose cube is 29791/4;: then 1 set an vnite I vnder 2600, and it doth re∣present a fraction thus 2600/1. Now to find out the weight of the greater peece, I set down these 3 new made fracti∣ons in the order of whole numbers, and working by the rule of proportion, I finde the greater peece weigheth 8363 pound, and almost ¾ of a pound: for in multiplying 29791 by 2600, there ariseth 77456600, the which aug∣mented by the denominator 4 maketh 309826400 for the deuidēt or number to be deuided. Likewise the fracti∣on of the lesser peece being 9261, multiplyed by his denominator 4, makes 37044 for a deuisor, which deui∣dent being deuided by the deuisor, yeeldeth in the quo∣ent 8363 pound, and certaine partes of a pound, so much will a Cannon of 7 inches ¾ weigh being proportionall in mettall to the other peece.