Addition works like multiplication on C/D scales, except that when you use the right
index the result appears on Q′.
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\(\sqrt{3^2+4^2}=5\) |
Set 3 on Q opposite left index of P, read 5 on Q opposite 4 on P.
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\(\sqrt{20^2+99^2}=101\) |
Set 99 on Q opposite right index of P, set hairline to 20 on P,
read 101 under hairline on Q′.
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\(\sqrt{1.2^2+0.5^2}=1.3\) |
Set hairline to left index of P, set 1.2 on Q′ under hairline,
set hairline to 0.5 on P, read 1.3 under hairline on Q′.
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Subtraction works like division on C/D scales, except that when you use the right index the result moves from Q′ to Q.
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\(\sqrt{53^2-45^2}=28\) |
Set 53 on Q opposite 45 on P, read 28 on Q opposite left index of P.
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\(\sqrt{119^2-60^2}=91\) |
Set hairline to 60 on P, set 119 on Q′ under hairline,
read 91 on Q opposite right index of P.
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\(\sqrt{137^2-88^2}=105\) |
Set hairline to 88 on P, set 137 on Q′ under hairline,
set hairline to left index of P, read 105 under hairline on Q′.
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\(\sqrt{117^2-108^2}=45\) |
Set hairline to left index of P, set 108 on Q′ under hairline,
set hairline to 117 on Q′, read 45 under hairline on P.
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Problems involving small values, between 1.415 and 3-ish, can be computed with improved precision by scaling. | ||

\(\sqrt{1.2^2+1.5^2}\approx 1.92094\) | Direct computation gives 1.9(3?). By scaling the arguments to 6 and 7.5 the rule gives 9605 rescaled = 1.921. | |

\(\sqrt{23^2-15^2}\approx 17.4356\) | Direct computation gives 17.(4?). By scaling the arguments to 11.5 and 7.5 the rule gives 8715 rescaled = 17.43. |

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