DIY History | Transcribe | Scholarship at Iowa | Eccentricity of the Sextant by Frederic Furbish, 1893 | Eccentricity of the Sextant by Frederic Furbish, 1893, Page 113

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Eccentricity of the Sextant by Frederic Furbish, 1893

Eccentricity of the Sextant by Frederic Furbish, 1893, Page 113

It is a general rule that the product of two factors is equal to one half (the square of the sum of the factors - the squares of each of the factors). Expressed algebraically this is xy - (1/2) {(x + y)[superscript]2[/superscript] - x[superscript]2[/superscript] - y[superscript]2[/superscript]}.

     Therefore

(1) ab = (1/2) [ (a + b)[superscript]2[/superscript] - a[superscript]2[/superscript] - b[superscript]2[/superscript] ]

(2) ac = (1/2) [ (a + c)[superscript]2[/superscript] - a[superscript]2[/superscript] - c[superscript]2[/superscript] ]

(3) an = (1/2) [ (a + n)[superscript]2[/superscript] - a[superscript]2[/superscript] - n[superscript]2[/superscript] ]

(4) as = (1/2) [ (a + s)[superscript]2[/superscript] - a[superscript]2[/superscript] - s[superscript]2[/superscript] ]

(5) bc = (1/2) [ (b + c)[superscript]2[/superscript] - b[superscript]2[/superscript] - c[superscript]2[/superscript] ]

(6) bn = (1/2) [ (b + n)[superscript]2[/superscript] - b[superscript]2[/superscript] - n[superscript]2[/superscript] ]

(7) bs = (1/2) [ (b + s)[superscript]2[/superscript] - b[superscript]2[/superscript] - s[superscript]2[/superscript] ]

(8) cn = (1/2) [ (c + n)[superscript]2[/superscript] - c[superscript]2[/superscript] - n[superscript]2[/superscript] ]

(9) cs = (1/2) [ (c + s)[superscript]2[/superscript] - c[superscript]2[/superscript] - s[superscript]2[/superscript] ]

At the bottom of the first column of the table of squares we have the sum 4.61455381 which is known as (a[superscript]2[/superscript]) or [aa] and it will be well to state that from this point when we speak

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It is a general rule that the product of two factors is equal to one half (the square of the sum of the factors - the squares of each of the factors). Expressed algebraically this is xy - (1/2) {(x + y)[superscript]2[/superscript] - x[superscript]2[/superscript] - y[superscript]2[/superscript]}. Therefore (1) ab = (1/2) [ (a + b)[superscript]2[/superscript] - a[superscript]2[/superscript] - b[superscript]2[/superscript] ] (2) ac = (1/2) [ (a + c)[superscript]2[/superscript] - a[superscript]2[/superscript] - c[superscript]2[/superscript] ] (3) an = (1/2) [ (a + n)[superscript]2[/superscript] - a[superscript]2[/superscript] - n[superscript]2[/superscript] ] (4) as = (1/2) [ (a + s)[superscript]2[/superscript] - a[superscript]2[/superscript] - s[superscript]2[/superscript] ] (5) bc = (1/2) [ (b + c)[superscript]2[/superscript] - b[superscript]2[/superscript] - c[superscript]2[/superscript] ] (6) bn = (1/2) [ (b + n)[superscript]2[/superscript] - b[superscript]2[/superscript] - n[superscript]2[/superscript] ] (7) bs = (1/2) [ (b + s)[superscript]2[/superscript] - b[superscript]2[/superscript] - s[superscript]2[/superscript] ] (8) cn = (1/2) [ (c + n)[superscript]2[/superscript] - c[superscript]2[/superscript] - n[superscript]2[/superscript] ] (9) cs = (1/2) [ (c + s)[superscript]2[/superscript] - c[superscript]2[/superscript] - s[superscript]2[/superscript] ] At the bottom of the first column of the table of squares we have the sum 4.61455381 which is known as (a[superscript]2[/superscript]) or [aa] and it will be well to state that from this point when we speak