required shewing that the weight of that other Bullet of 8 inches diameter is 72 pounds Example 2. If a Gun of 5 inches diameter require for her due charge 16 pound of powder How much powder will a Gun of 4 inches diameter in the bore require for her due charge of the same powder Place 5 on the first to 4 on the second and then against 16 on that first is 12,8 on the second and next against 12,8 on the first is 10,24 on the second and thirdly against that 10,24 on the first is 8,2 on the second which third number 8,2 is the answer to the question shewing that 8 pounds and 2 tenth parts of a pound of powder is a due charge for a Gun of 4 inches bore PROBLEM IX A Company of men laying down several sums of money together into one stock wherewith they trade and get gain to find out how much each mans part of the gain must be answerable to his part of money laid down in stock LEt five men whose names let be represented by these five letters A B C D E make a stock of 300 pounds of which stock A put in 84 pounds B put in 72 pounds C put in 48 pounds D put in 54 pounds and E put in 42 pounds which all together make the 300 pounds Now at the end of a time having traded therewith they gained clearly 50 pounds And let it be demanded what portion of the gain each man must have according to his proportion of mony laid down in stock The Rule to answer this demand is thus As 300 the whole stock To 50 pounds the whole gain So is each mans portion of the stock To his portion of the gain Therefore Set 300 the stock on the first to 50 the gain on the second and then against each mans particular portion laid down being sought out on the first is his portion of the gain on the second As against 84 the portion laid down by A on the first is 14 his portion of the gain on the second and against 72 the portion of B is 12 pounds his portion of the gain against 48 the portion of C is 8 pounds his portion of the gain against 54 the portion of D is 9 his portion of the gain and against 42 pounds on the first the portion of E is 7 pounds on the second his portion of the 50 pounds gain Thus much is each mans several portion of the 50 pounds gain all which several portions of the gain added together make up the whole gain of 50 pounds Thus upon our lines can we work that rule of Arithmetick called The Rule of Fellowship which is when diverse men adventure a stock of money together and therewith trade and either gain or lose a certain sum of money to find each mans portion of the gain or losse answerable to his portion of money put into the stock PROBLEM X. Of Interest and Annuities To find the Interest of any sum of money after any rate by the 100 propounded WHat is the Interest of 65 pounds for a year after the rate of 8 in the 100 By the rule of Proportion the question is thus resolved As 100 is to 108 So is 65 to the fourth term Set 1 or 100 on the first to 108 on the second and then against 65 on the first is 70,2 on the second which is 70 pounds 4 shillings so much doth the principal and interest arise unto in a year that is to say five pounds and four shillings And without stirring the Instrument against any other sum of Principal on the first is the Principal and Interest thereof on the second As against 40 pounds is 43 pounds 4 shillings and against 80 pounds is 86 pounds and 8 shillings From whence it appeareth that 3 pounds 4 shillings is the Interest of 40 pounds for a year and 6 pounds 8 shillings the Interest of 80 pounds for a year In like manner against 27 pounds 14 shillings Principal or 27,7 is 29 pounds 18 shillings and a little more Or else work thus Set 1 or 100 back to 8 and then against 65 on that first is 5,2 on the second and against 40 pounds on the first is 3,2 on the second So the Interest of the one is 5 pounds 4 shillings and of the other 3 pounds 4 shillings If the rate of the Interest proposed be 6 in the 100 then set 100 on the first to 106 on the second and then against 65 pounds on the first is 68 pounds 18 shillings on the second which is the Principal and Interest together of 65 pounds for a year Or Set 100 on the first to 6 on the second and then against 65 on the first is 3,9 on the second this 3,9 is 3 pounds 18 shillings the Interest alone of 65 pounds for a year and so of any other Of Interest of money continued from year to year The increase or Interest of money from year to year for many years is in continual proportion to the Principal as 100 is to its Interest as if 40 pounds were to be continued at Interest for many years at the rate of 6 in the 100. Set 100 on the first to 106 on the second and then against 40 on the first is 42,4 on the second that is 42 pounds 8 shillings so much is the first years Principal and Interest And now if you look 42,4 on the first you shall have right against it 44,9 and more that is 44 pounds 18 shillings and more for the Principal and Interest of two years and against 44,9 on the first is 47,6 and better on the second that is 47 pounds 12 shillings 8 pence the Interest and Principal of 40 pounds in three years Again against 47,6 on the first is 50,45 and better that is 50 pounds 9 shillings 7 pence So much is the Principal and Interest together of 40 pounds at the end of 4 years and so forth to as many years as is required Of Annuities When lands are sold at certain years purchase according to the yearly rent to find what their value upon the purchase will be Set 1 on the first to the number of years purchase on the second and then against their yearly rent on the first is the value of the purchase on the second Example Let a house and land worth 16 pounds a year be set to sale at 14 years purchase and demand made how much money it will arise unto at that rate Set 1 on the first to 14 the number of years purchase on the second and then against 16 the yearly rent on the first is 224 on the second which is 224 pounds So much money doth the purchase arise unto of 16 pounds a year bought at 14 years purchase If the price of the lands be given and that it cost after 14 years purchase to find what yearly rent it was sold at In this case Set 14 on the first to 1 on the second and then against the sum of money