On the History of Gunter's Scale and the Slide Rule During the Seventeenth CenturyCajori, Florian
History
On the History of Gunter's Scale and the Slide Rule During the Seventeenth Century
Cajori, Florian
Slide-rule
The English editions of this book which appeared in 1623 and 1628 are
devoid of interest. The editions of 1645 and 1658 contain an important
innovation.[7] In the preface the reasons why this instrument has not been
used more are stated to be: (1) the difficulty of drawing the lines with
exactness, (2) the trouble of working thereupon by reason (sometimes) of
too large an extent of the compasses, (3) the fact that the instrument is
not readily portable. The drawing of Wingate’s arrangement of the scale in
the editions of 1645 and 1658 is about 66 cm. (26.5 in.) long. It contains
five parallel lines, about 66 cm. long, each having the divisions of one
line marked on one side and of another line on the other side. Thus each
line carries two graduations: (1) A single logarithmic line of numbers; (2)
a logarithmic line of numbers thrice repeated; (3) the first scale
repeated, but beginning with the graduations which are near the middle of
the first scale, so that its graduation reads 4, 5, 6, 7, 8, 9, 1, 2, 3;
(4) a logarithmic line of numbers twice repeated; (5) a logarithmic line of
tangents; (6) a logarithmic line of sines; (7) the rule divided into 1000
equal parts; (8) the scale of latitudes; (9) a line of inches and tenths of
inches; (10) a scale consisting of three kinds, viz., a gauge line, a line
of chords, and a foot measure, divided into 1000 equal parts.
Important are the first and second scales, by which cube root extraction
was possible “by inspection only, without the aid of pen or compass;”
similarly the third and fourth scales, for square roots. This innovation is
due to Wingate. The 1645 edition announces that the instrument was made in
brass by Elias Allen, and in wood by John Thompson and Anthony Thompson in
Hosier Lane.
Changes introduced by Milbourn
William Leybourn, in his The Line of Proportion or Numbers, Commonly called
Gunter’s Line, Made Easie, London, 1673, says in his preface “To the
Reader:”
The Line of Proportion or Numbers, commonly called (by Artificers)
Gunter’s Line, hath been discoursed of by several persons, and variously
applied to divers uses; for when Mr. Gunter had brought it from the
Tables to a Line, and written some Uses thereof, Mr. Wingate added divers
Lines of several lengths, thereby to extract the Square or Cube Roots,
without doubling or trebling the distance of the Compasses: After him Mr.
Milbourn, a Yorkshire Gentleman, disposed it in a Serpentine or Spiral
Line, thereby enlarging the divisions of the Line.
On pages 127 and 128 Leybourn adds:
Public-domain text, read in full here on John Shaqi.
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