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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1780 Excerpt: ...which should be equal to 2--.0957620 zz 1 Er. too little. Again suppose x = 3.6, then l: x zz 5563025, and xl: x zz 2.0026890 2 +.0026890 zz Z Er. too great. Hence we have 1 num. 3.5 1 er.--.095762 2 num. 3.6 2 er. +.002689 diff. 0.1 sqm.098451 Then Q-'X.ooa689 =.00273 cor..09845 2 num. 3.60000 correct.--,00273 3.59727 = At; Agjain, suppose x zz 3597, then l: x--.55594043 and = 1.9997176, which subtracted from 2, gives--.0002624 the error, too little. Whence 2 num. 3.600, 2 er. +.0026890 3 num. 3.597 3 er. n--.0002824 diff, .003, sum.0029714 Then rp, .002 X.O0O2824 Q Then----2 zz.000285 e cor .0029714 3 num. 3.597 cor. +.000285 x zz 3.597285 as required. 7. If s be the sine of an arch z9 rad. zz 1, and 4sz zz 5, to find s and z. By division sz zz 1.25. The length of 1 degree is zz.01745329 By a few trials, we may find z between 70 and 80 degrees. Suppose z zz 70 deg. then.01745 X 70 zz 1.2215; also S. 70 zz.939 =: s, and sz zz 1.1469, and 1.25--1.1469 zz.1031 the first error, too little. Again, suppose z zz 75 deg. then.01745X75 zz 1.3087, and s zz.966, and sz zz 1.2642; and 1.2642--1.25=0142 the second error, too much. Hence 1 num. 70 1 er.--.1031 2 num. 75 2 er. +.0142 Again, let z zz 74,4 =1 740: 240, s zz.9631626; then.01745329 X 74-4 = 1.298524, and 1.2985245 zz 1.2506895, from which subtract 1.25, then.0006895 zz 3d error, too much. 2 slum. 2 num. 75 2 er. +.0143937 3 num. 74.4 3 er. +.0006895 cliff, .6 diff.-01133105 Then 6X.0006895-01331 3 num. 74.460--cor..031 afid z zz 74.369 zz 740: 22s: 8/; and s zz.9630372. Scholium. There are also other ways of extracting the roots of equations, though not much different from some of the foregoing ones, particularly a method of Sir /. Newton's, which is like the process used in She se...

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