DIY History | Transcribe | Scholarship at Iowa | Eccentricity of the Sextant by Frederic Furbish, 1893 | Eccentricity of the Sextant by Frederic Furbish, 1893, Page 114

Transcribe
Translate

Eccentricity of the Sextant by Frederic Furbish, 1893

Eccentricity of the Sextant by Frederic Furbish, 1893, Page 114

of (a + b)[superscript]2[/superscript] [illegible?][or or on][/illegible?] (a + c)[superscript]2[/superscript] we mean the sum of all the numbers in the columns headed (a + b)[superscript]2[/superscript] [or or on][/illegible?] (a + c)[superscript]2[/superscript] as written below the double line.

     In the second column we have (a + b)[superscript]2[/superscript] = 6.50885747. The sum of the column of b[superscript]2[/superscript]s is 0.25287910 , known as b[superscript]2[/superscript] or [bb] .

     Substitute these numbers in formula (1) and we have

ab = (1/2)
{ (a + b)[superscript]2[/superscript] - a[superscript]2[/superscript] - b[superscript]2[/superscript] }
{ 6.50885747 - 4.61455381 - 0.25287910 }

ab = (1/2)
{ (a + b)[superscript]2[/superscript] - a[superscript]2[/superscript] + b[superscript]2[/superscript] }
{ 6.50885747 - (4.61455381 + 0.25287910 }

ab = (1/2)
{ 6.50885747 - 4.86743291 }

ab = (1/2)
{ 1.64142456 } = 0.82071228 .

Of course we do not put all this work on the blank. Under (a + b)[superscript]2[/superscript] we write the sum of a[superscript]2[/superscript] and b[superscript]2[/superscript] , as will be observed, draw a double line beneath this and perform the subtraction. The result and its' half are written in the same space the latter below the former.

Saving...

of (a + b)[superscript]2[/superscript] [illegible?][or or on][/illegible?] (a + c)[superscript]2[/superscript] we mean the sum of all the numbers in the columns headed (a + b)[superscript]2[/superscript] [or or on][/illegible?] (a + c)[superscript]2[/superscript] as written below the double line. In the second column we have (a + b)[superscript]2[/superscript] = 6.50885747. The sum of the column of b[superscript]2[/superscript]s is 0.25287910 , known as b[superscript]2[/superscript] or [bb] . Substitute these numbers in formula (1) and we have ab = (1/2) { (a + b)[superscript]2[/superscript] - a[superscript]2[/superscript] - b[superscript]2[/superscript] } { 6.50885747 - 4.61455381 - 0.25287910 } ab = (1/2) { (a + b)[superscript]2[/superscript] - a[superscript]2[/superscript] + b[superscript]2[/superscript] } { 6.50885747 - (4.61455381 + 0.25287910 } ab = (1/2) { 6.50885747 - 4.86743291 } ab = (1/2) { 1.64142456 } = 0.82071228 . Of course we do not put all this work on the blank. Under (a + b)[superscript]2[/superscript] we write the sum of a[superscript]2[/superscript] and b[superscript]2[/superscript] , as will be observed, draw a double line beneath this and perform the subtraction. The result and its' half are written in the same space the latter below the former.