A Description of The Admirable Table of Logarithms - Chap. 1 - p. 2

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A Description of the Admirable Table of Logarithms

(Page 2)

 

  In the second mement form C to D. In the third moment from D to E, & so forth infinitely, describing the line ACDEF, &c. The spaces AC, CD, DE, EF, &c. And all the rest being equall, and described in equall moments (or times.) This line by the former definition shall be said to increase equally.
 
A Corollary or consequent. Therefore by this increasing, quantities equally differing, must needes be produced, in times equally differing.
As in the Figure before, B went forward from A to C in one moment, and from A to E in three moments. So in sixe moments from A to H: and in 8 moments from A to K. And the differences of those moments, one and three, and of these 6 and 8 are equall, that is to say two.
So also of those quantities AC, and AE, and of these, AH, and AK, the differences CE, and HK are equall, and therefore differing equally, as before.
 
2. Definition A line is said to decrease proportionally into a shorter, when the poynt describing the same in æquall times, cutteth off parts continually of the same proportion to the lines from which they are cut off.

For examples sake. Let the line of the whole sine aZ be to bee diminished proportionally: let the poynt diminishing the same by his motion be b: and let the proportion of each part to the line from wch it is cut off, be as QR to QS.

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