two fecond lines crofs each other, that is the place of the town D; and where the two third lines crofs each other, that is the place of the town.E. Now the distance of each town from your ftations and alfo the distance of the towns from one another may be found by extending from your ftations to the towns and that extent measured on that fcale of equal parts that your stationary diftance was taken from, will give you the diftance of any of the towns from either of your ftations or from one another. But if more exactnefs is required you must work by problem 10th. and you will find the anfwers as below, which were found by logarithms. To find the content of any triangle by having any two fides and the angle included. RULE. Multiply the two fides together, and multiply half the product by the number in the fecond table anfwering to the angle. EXAMPLE. EXAMPLE. Suppofe a triangle as in the following figure, what is its area. N. B. In order to value the fraction of a link in an angle, multiply the difference of any two whole numbers in the table of fines by the frac 3.9 tional part of a link, and add the product to the leffer number till you come to 141 links; but fubtract the value of the difference from the greater number (for the proper factor) if it is greater than 141 links. AC 9.70 AB 6.80 77600 5820 6.80 See the operations of the different angles in the next page. In each product you'll obferve one more decimal pointed off than what are in the factors, in order to produce acres, &c. And here we have worked the queftion three ways, by the 3 different factors belonging to the 3 different angles, and each operation is very nearly the fame; fo that it is a matter of indifference which two fides of a triangle are known (if the angle included is known alfo) to find the area of the triangle; and this is at any time done without having the plan or plot of the triangle. Now let us find the content of the aforemention'd triangle by the old method when the plan is not given, and then we fhall fee how much more trouble fome it is than the new me. thod. See the work in the next page. The Method of Surveying, as it relates to dividing of Land. PROBLEM XIII. To divide a triangular piece of land into any number of equal or unequal parts, by lines proceeding from any point affigned in any file thereof EXAMP. Let ABC be the triangular piece of land, containing 60 acres, to be divided between three men; the first to have 15 acres, the fecond 20, and the third 25 acres; and the lines of divifion to proceed from D. First measure the bafe which is 50 chains; then divide this bafe into 3 parts, thus: firft man's bafe, which fet from A to A Ch. A Ch. E; then fay, As 60 : 50 :: 20: 16.67 for the fecond |