Willsfords arithmetick, naturall, and artificiall: or, decimalls. Containing the science of numbers, digested in three books. Made compendious and facile for all ingenious capacities, viz: merchants, citizens, sea-men, accomptants, &c. Together with the theorie and practice united in a sympathetical proportion betwixt lines and numbers, in their quantitites and qualities, as in respect of form, figure, magnitude and affection: demonstrated by geometrie, illustrated by calculations, and confirmed with variety of examples in every species. / By Thomas Willsford, Gent.

Question 3. A Druggist had two sorts of Tobacco; the one was Spanish, at 10 s. the lb; the other Virginia, at 3 s. the pound; of these two sorts, he was to mix 112 lb weight, and so, as that it might be afforded for 8 s. the lb: how much must be taken of either sort?

This second

A	〈 math 〉〈 math 〉	C	〈 math 〉〈 math 〉
B	D.—Lb.	D	Lb
7-112	5	80
		2	32

rule differs much frō the former, which, requires onely a common price, from the totall of severall quantities mixt together; whereas this is confined unto a price and quantity in generall, composed of particulars, from whence the mixture is to be made, and the parts taken, proportionally according to each price, quantity or quality; as in this Example, in the Table at A, where 8 s. is the price determined on; the best Tobacco was 10 s. the pound, the worst 3 s. the pound; which two prices I set one above

another, and couple them together with an arch of a circle; the price set must be alwaies lesser than the greatest price, and greater than the least of the particulars, as here 8 is lesser than 10, and greater than 3: this done the difference between the price set, and each particular must be found, and counter-changed with the number, to which it is coupled, as in the first Table, the difference betwixt 8 & 10 is 2, which is placed against 3. the difference between 8 & 3 is 5, which stands against 10. the summe of the differences is 7, which according to the Rule a∣bove, and the Table, at B, stands in the first place: 112 pound, the quantity to be mixt the second number; and each particular correspondent diffe∣rence the third number: so it is now in the Rule of proportion, as 7 the totall difference, to 112 pound the totall quantity; so will 5 (the particular respective difference for the best price) be to 80 pound, the quantity to be taken of that sort. Again, as 7 to 112 pound, so 2 unto 32 pound the quan∣tity of the worst sort; and thus repeating the Rule of 3, so often as there be particular differences, you will produce particular quantities to them, whose totall must be equall to the summe, or quantity pro∣pounded to be mixt, if otherwise, the operation is false.

Yet least in the mixture of these simples, you should remaine ignorant of the reasons; this questi∣on, and all of this kind hath relation unto the 15 and 16 Axiome, parag. ••7. wherein the totall difference of prices, hath proportion to the totall summe or quantity to be mixt, as the particular difference or parts, have to their respective quantities, but here

another Querie will be made, wherefore these dif∣ferences between the price set, and each particular price is counterchang'd with a greater and a lesser; by the difference of prices, will be discovered the severall quantities in proportion to those differen∣ces; if the difference were equall, the quantities to be taken of all those sorts would prove alike: if the rate or proportion propounded, inclines unto the greater price given, it will have the lesser difference, by how much the neerer it comes to the greatest price, and yet the greater quantity of that sort must be in the mixture; and so consequently the least price (in this case) will have the greatest difference, in which the least quantity is required; and the con∣trary will be found by the rule of 3 direct; as by the last example, and the first table at A, where the price propounded is 8 s. the two prices given are 10 and 3, and the differences are 2 and 5: and being 8 is neerer 10 then 3, the greatest quantity of the best sort will be required; and the lesse of the wor∣ser sort; therefore as 7 to 112, so 5 unto 80, and as 7 to 112, so 2 unto 32.

In the other Table at C admit a composition of the same commodity were to be made at 6 s, with any quantity assign'd, 6 the price propounded is neerer 3 then 10, therefore 3 must have the greater difference, whereby to produce the greater quan∣tity, and the best sort at 10 s. the least difference as 3. the worst sort 4. and so the proportion would have been, as 7 to 112, so 3 unto 48 lb. or as 7 to 112 lb so 4 unto 64 lb both of them making the just quantity of 112 lb and for a farther triall, the price stated, if multiplied into the quantity for to

be mixt, the product will be equall, unto the pro∣ducts of the severall prices, and their respective quantities: as 6 multiplied by 112 lb. produceth 672; so 48 by 10 is 480. and 64 by 3 maketh 192, which added unto 480 the summe is 672, or 33 L. 12 s. as before.