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The construction of the wonderful canon of logarithms

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Construction <strong>of</strong> <strong>the</strong> Canon. 43<br />

logarithm is required. <strong>The</strong> complement <strong>of</strong> <strong>the</strong><br />

half arc is 55 degrees 20 minutes, and its logarithm<br />

1954370 is given. Wherefore add 6931469<br />

to 665143, making 7596612, subtract 1954370,<br />

and <strong>the</strong>re remains 5642242, <strong>the</strong> required logarithm<br />

<strong>of</strong> an arc <strong>of</strong> 34 degrees 40 minutes.<br />

58. When <strong>the</strong> <strong>logarithms</strong> <strong>of</strong>all arcs not less than 45 degrees<br />

are given, <strong>the</strong> <strong>logarithms</strong> <strong>of</strong> all less arcs are very easily<br />

obtained.<br />

From <strong>the</strong> <strong>logarithms</strong> <strong>of</strong> all arcs not less than 45<br />

degrees, given by hypo<strong>the</strong>sis, you can obtain (by<br />

57) <strong>the</strong> <strong>logarithms</strong> <strong>of</strong> all <strong>the</strong> remaining arcs decreasing<br />

down to 22 degrees 30 minutes. From<br />

<strong>the</strong>se, again, may be had in like manner <strong>the</strong> <strong>logarithms</strong><br />

<strong>of</strong> arcs down to 11 degrees 15 minutes.<br />

And from <strong>the</strong>se <strong>the</strong> <strong>logarithms</strong> <strong>of</strong> arcs down to<br />

5 degrees 38 minutes. And so on, successively,<br />

down to I minute.<br />

59. To form a logarithmic table.<br />

Prepare forty-five pages, somewhat long in<br />

shape, so that besides margins at <strong>the</strong> top and<br />

bottom, <strong>the</strong>y may hold sixty lines <strong>of</strong> figures.<br />

Divide each page into twenty equal spaces by<br />

horizontal lines, so that each space may hold three<br />

lines <strong>of</strong> figures. <strong>The</strong>n divide each page into<br />

seven columns by vertical lines, double lines being<br />

ruled between <strong>the</strong> second and third columns and<br />

between <strong>the</strong> fifth and sixth, but a single line only<br />

between <strong>the</strong> o<strong>the</strong>rs.<br />

Next write on <strong>the</strong> first page, at <strong>the</strong> top to <strong>the</strong><br />

left, over <strong>the</strong> first three columns, "o degrees";<br />

and at <strong>the</strong> bottom to <strong>the</strong> right, under <strong>the</strong> last<br />

F 2 three

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