200000.0678626104 LESSON 22. A and B in partnership bought a grindstone which contained 3 feet in diameter; after making an allowance for for the eye, 4 inches by 3, the parties agreed that A should grind off one half first; how many inches of the diameter must A wear off for his part? Answer, 10 inches 5 seconds 7 thirds. First consider we have a diameter given to find the area. See rule 4, under note 2, lesson 16. Area including the eye, 7.0686 ||will give a new area. Here 6.9853 is an area given to find the diameter. When found, we will call it "a new diameter." See Rule under Now we have a new diameter given to form another which will make a circle half as large in area for B's part. See Rule 2, above example 2, under Lesson 16. ~| The new diameter, 2.9788968 2.9788968 238311744 178733808 268100712 238311744 238311744 208522776 268100712 59577936 8.87382614505024 This square of the new diameter must be divided by the proportion 2; that is done to make another circle half as large by extracting the Square Root of the quotient. To 2)8.87382614505024 prove this operation, find the area of B's part by Rule 4, under Note 2, in Lesson 16. B's part must be equal to half the new area after the eye was deducted. Suppose a ship sail LESSON 23. from New-York 4000 miles south, then east 6000 miles; how far will she be from New-York on a direct course, and what will be the course back? Ans. the ship will be 7211 miles from New York, and the course back will be N. 56° 19′ W. See Rules under Lesson 7, One leg of the triangle, 4000 Square, 4000 16000000 Square of the other leg, 36000000 Sum of the squares, ✔ 52,00,00,00(7211 answer. 49 14:).300 284 1441). 1600 1441 14421). 15900 14421 .1479 Rule to find the course. As the sum of the hypothenuse and half the longest leg, is to 86 degrees; So is the short leg, to its opposite angle. 10211)422220(41 minutes. .13780 10211 ..3569 33 degrees and 41 minutes is the angle sought. Subtract this angle from 90, the remainder will be 56 degrees, 19 minutes, the course to steer back. 90° 33 41 56 19 Navigators calculate by Points: 114, 11.25, or 11 degrees 15 minutes make 1 point, 32 points the whole circle or 360 degrees. 11.25 degrees. 2250 3375 360.00 degrees. LESSON 24. The sum of two numbers and their product given to find each number. The sum of two numbers when added together is 61, and their product is 624; what are those two numbers? 3. Extract the square root of the remainder, 12,25(35 9 65)325 325 |