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:
Again, One T. Browne, a Maker of Mathematical Instruments, made it in a
Serpentine or Spiral Line, composed of divers Concentrick Circles,
thereby to enlarg the divisions, which was the contrivance of one Mr.
Milburn a Yorkshire Gentleman, who writ thereof, and communicated his
Uses to the aforesaid Brown, who (since his death) attributed it to
himself: But whoever was the contriver of it, it is not without
inconvenience; for it can in no wise be made portable; and besides
(instead of compasses) an opening Joynt with thirds [threads] must be
placed to move upon the Centre of the Instrument, without which no
proportion can be wrought.
This Mr. Milburn is probably the person named in the diary of the
antiquarian, Elias Ashmole, on August 13 [1646?]; “I bought of Mr. Milbourn
all his Books and Mathematical Instruments.”[8] Charles Hutton[9] says that
Milburne of Yorkshire designed the spiral form about 1650. This date is
doubtless wrong, for Thomas Browne who, according to Leybourn, got the
spiral form of line from Milbourn, is repeatedly mentioned by William
Oughtred in his Epistle[10] printed some time in 1632 or 1633. Oughtred
does not mention Milbourn, and says (page 4) that the spiral form “was
first hit upon by one Thomas Browne a Joyner, . . . the serpentine
revolution being but two true semicircles described on severall
centers.”[11]