3027756 1009252 3027756 2018504 25231300 Square, 254647.399876 Common Multiplier, .7854 1018589599504 1273236999380 2037179199008 1782531799132 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. 3 The The eye containing 12 su perficial inches, or 14 of a Square of the diameter, 9 foot must be reduced to the Common multiplier, 7.854 decimal of a foot and sub tracted from the area which Area including the eye, 7.0686 ||will give a new area, 00180 La reduce 144)12.0000.0833 432 .480 432 Area including the eye, Area of the eye, . 48 7.0686 feet, .0833 6.9853 Here 6.9853 is an area given to find the diameter. When found, we will call it “ a new diameter." See Rule under Lesson 15. New Area. ✓ 6.98,53(2.64 Root of the new area. 4 46)298 Common multiplier, 1.12837 2.64 524). 2253 451348 2096 677022 225674 . 157 New diameter, 2.9788968 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. 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. 2)8.87382614505024 Carried forward. B's part must be equal to half the new area after the eye was deducted. ✓ 4.43,69,13,07,25,25,12 Root, (2.1063981 or B's diame ter, which subtracted from the 41)43 new diameter gives a remainder 41 for A's part. 4206)26913 25236 Suppose a ship sail 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 4000 Square, 16000000 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. The longest leg is 6000 miles, Half the longest leg is 3000 miles. The hypothenuse is 7211 The sum of the hypothenuse and half 10211 Short leg. 4000 alf} 10211)344000(33 degrees. 30633 37670 .7037 60 minutes in a degree. 10211)422220(41 minutes. [Continued. 10211)422220(41 minutes 40844 .13780 ..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° 56 19 Navigators calculate by Points: 114, 11.25, or 11 de. grees 15 minutes make 1 point, 32 points the whole circle or 360 degrees. 11.25 degrees. 32 points. 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 ? Answer, 13 and 48. RULES. 1. Square their sum, 61x61=3721 2. Subtract 4 times their product, 624x4=2496 from their square. 3. Extract the square root of the remainder, v12,25(35 65)325 |