The mariners plain scale new plain'd: or, A treatise shewing the ample Uses of a Circle equally divided, or of a Line of chords and equal Parts, Divided into Three Books or Parts. Being contrived to be had either alone, or with the other Parts. I. The first containing Geometrical Rudiments, and shewing the Uses of a Line of Chords. . . II. The second shewing the Uses of a Line of Chords, in resolving all the Cases of Spherical Triangles, by Projecting the Sphere Orthographically. . . III. The third part shewing the Uses of a Line of Chords, in resolving all the Cases of Spherical Triangles Stereographically that is on the Circular Projection with Dyalling, from three Shadows of a Gnomon on a regular Flat, or by two Shadows, &c. . .
The mariners plain scale new plain’d: or, A treatise shewing the ample Uses of a Circle equally divided, or of a Line of chords and equal Parts, Divided into Three Books or Parts. Being contrived to be had either alone, or with the other Parts.
I. The first containing Geometrical Rudiments, and shewing the Uses of a Line of Chords, in resolving of all Proportions relating to Plain or Spherical Triangles, with Schemes suited to all the Cases derived from Proportions, and the full use of the Scale in navigation, according to the particulars in the following Page, and in finding the Variation of the Compass.
II. The second shewing the Uses of a Line of Chords, in resolving all the Cases of Spherical Triangles, by Projecting the Sphere Orthographically, or laying down the Sphere in right Lines, commonly called, The Drawing or Delineating of the Analemma. With an everlasting Almanack in two Verses, &c.
III. The third part shewing the Uses of a Line of Chords, in resolving all the Cases of Spherical Triangles Stereographically that is on the Circular Projection with Dyalling, from three Shadows of a Gnomon on a regular Flat, or by two Shadows, &c.
To which may also be added a Treatise of the Authors, of Dyalling by a Line of Chords, formerly published.
Of great Use to Sea-men, and Students in the Mathematicks.
Four parts in one volume. London: Thomas Johnson for Francis Cossinet, 1659. First edition.
Quarto (7 3/8” x 5 5/16”, 188mm x 136mm): π2 A–H4, 2B–R4, Α2 3B–I4 3K2, 4Α2 4B–E4 4F2 [$2 signed; –A1, 2K2, 4F2; 3E2 signed “F2”]. 154 leaves (34, 64, 36, 20), pp. [12] (blank, title, Navigation title, blank, plate, 2pp. dedication, to the reader, verses, 3pp. contents) 1-56; 21-128; [4] (title, blank, preface, contents) 31-67 [1] (blank); [4] (title, blank, to the reader, contents) 41-36. With 111 woodcuts and 5 engravings all integral with the text, plus 1 folding engraving hors-texte.
Bound in (perhaps later; re-backed to style) mottled calf with a blind double-fillet border and scrollwork corner-ornaments. On the spine, five raised bands. Author and title gilt to red morocco in the second panel. Gilt roll to the edges of the boards. All edges of the text-block speckled red and brown.
Re-backed to style with original label laid down. Craquelure to the upper edge of the back board, with some scuffing below. Tanned generally, with mild foxing throughout. Occasional graphite marginalia. Chipping to the folding plate, not affecting the image. Bookplate of Ted Benttinen laid in at front.
John Collins (1625–1683) began his career as a bookseller’s apprentice, but his path took an unexpected turn with the onset of the English Civil War. During the conflict, Collins joined an English merchant ship and spent seven years in the Mediterranean. In his spare time, he studied mathematics and merchant accounting, gaining the skills that would later help him establish himself as a teacher upon returning to London. In 1659, Collins published The Mariners Plain Scale New Plain’d for the use of the British East India Company’s navy. Prior to this, Collins had written treatises for his personal students, but this publication was well-received, eventually being incorporated into the curriculum for British sailors. The present treatise introduced new methods for measuring a ship’s course or distance using the plain scale — a term first recorded by the Oxford English Dictionary in the present work; a divided line indicating the scale (i.e., its relation to real distance) of the chart — as well as navigating currents, calculating “circle sailing,” and performing arithmetical navigation. Collins was elected a fellow of the Royal Society in 1667 and continued to advance navigational techniques throughout his life. He was a contemporary of Isaac Newton and John Wallis, and remains a key figure in the Scientific Revolution in Britain.
The present example includes the title of the composite volume and title pages for all three parts (including the title for the first part) Navigation by the Mariners Plain Scale new plain’d: or, a Treatise of Geometrical and Arithmetical Navigation… (ESTC R207824); most examples that have sold have this configuration.
Theodore “Ted” Benttinen (1948–2023) was an MIT-educated oceanographer and explorer who went to both poles on research missions. Benttinen amassed a formidable collection of books of exploration, particularly strong in Pacific voyages as well as in polar accounts. The present volume was lot 54 in the Sotheby’s New York 9 December 2024 sale of his library.
ESTC R171445 & R207824; Tomash & Williams, History of Computing C124-126.
Catalogued by GR Murdock.
Item #GRM0007
Price: $7,560