Jacques Ozanam was a mathematician famous for his popular math texts. These included a math dictionary, a course of mathematics, and a text on mathematical and physical recreations. The last of these went through at least 18 editions over 2 centuries.
Ozanam's dialing was instructive and entertaining - it includes innovative ideas such as a geographic sundial showing the time anywhere in the world, various universal horizontal dials, and the first suggestion that one's own body could be the gnomon of an analemmatic dial. His texts also cover altitude, azimuth, lunar, reflection, refraction, portable and stereographic projection dials – all in addition to the standard instruction in drawing sundials on any plane.
This treatise is from the 1712 English translation (by the noted Newtonian scholar J.T. Desaguliers) of Ozanam's 1693 Course of Mathematics. The addendum is a 1708 English translation of the set of Problems of Dialling included in the 1st edition (1694) of his Recreations Mathematical & Physical.
This can be ordered from LuLu Books: Ozanam: A Treatise of Gnomonicks (1712)
Samuel Foster, Elliptical, Or Azimuthal Horologiography (1654). This brilliant work, far ahead of its time, details Foster's development of analemmatic, circular, and diametral sundials and their generalizations. The title appeared earlier in compressed format as part of The Analemmatic Sundial Sourcebook – it is now available here as a separate volume within the Shadow Catcher Series.
This can be ordered from LuLu Books: Foster: Elliptical or Azimuthal Horologiography (1654)
Samuel Sturmy, The Art Of Dialling By The Gnomical Scale (1679). This is the seventh book from Sturmy's very popular The Mariners Magazine. The work originally appeared in 1669, and subsequently went through 3 more editions, “diligently revised and carefully corrected” by mathematician John Colson. This is the second edition.
Unlike other entries in this Shadow Catcher Series, this reprint is done with modern fonts; the graphics are facsimile reproductions.
This can be ordered from LuLu Books: Sturmy: The Art of Dialling By the Gnomical Scale (1679)
Thomas Strode- A NEW AND EASIE METHOD TO THE ART OF DYALLING.
CONTAINING I. All Horizontal Dyals, all Upright Dyals, Reflecting Dyals, Dyals without Centres, Nocturnal Dyals, Upright Declining Dyals, without knowing the Declination of the Plane. II. The most Natural and Easie Way of Describing the Curve-Lines of the Suns Declination on any Plane. The like never before Published. By Thomas Strode, Esq; of Maperton in the County of Somerset. LONDON. Printed, by H.C. for J. Taylor, at the Ship, and T. Newborough, at the Ball, in St. Paul's Church-Yard, MDCLXXXVIII. 1688. (72 pages)
"To The Reader. Courteous Reader, This was chiefly composed for some near Relations; but the Method being Natural, Easie, and not Common, I think I ought to communicate, and not to Bury it with me. I do not Publish this as to prefer it before Trigonometrical Calculation of Dyals, for no way can be Exacter than that; but this is to save that Labour in Young Beginners, lest they should be dejected with the tediousness of the other: And this Discourse but little short in Exactness with that...
"The Method of drawing the Parallels of the Suns Declination, will give (if I am not deceived) a Diversion to those of the Highest Forms in the Mathematicks, being not Extant (as I have great reason to believe) in any Author; being grounded on such Paradoxes in the Conicks, That some of them on the first View will hardly be admitted; for with Gratefulness, I do acknowledge, That I received Seeds and Plants from some eminent Persons of the Royal Society, since deceased; but being removed into my barren Soil, and Cultivated and Manured according to the new Husbandry, produced Fruit beyond my Expectation, whereof this is part; besides their Geometrical way of Delineating their Curves, I have for the Latitude of London, in a Direct South Dyal, given the Distances of the Points of the Hyperbole on Parallels to the Transverse Axe, from the Conjugate, which by a Diagonal Scale will quickly be placed."
This can be ordered from LuLu Books: Strode: A New and Easie Method To the Art of Dyalling (1688)
Gilbert Clerke. THE SPOT-DIAL, Very useful to shew the Hour within the House.
"Together with Directions how to find a true Meridian, the Azymuth and Declination; and how to draw a Dial upon a Staff, upon the Cieling, upon any Pillar or Globe. Never Before Published. By Gilbert Clerke. London, Printed by J.M. for Walter Kettilby at the Bishop's-Head in St. Paul's Churchyard, 1687." (30 pages, 1.3 MB)
Clerke (1626-1697?) gave private lessons in the mathematical arts and produced custom-made sundials. In 1682 he published Oughtredus explicatus, an edition of William Oughtred’s famous 1647 algebra textbook Clavis Mathematica. Clerke added a section on dialling, in which he described his invention of the spot-dial. Some years later, he was prevailed upon to write this brief English treatment of the dial. “I did not think to have written any more of Dialling, having delivered my Mind sufficiently at the End of my Oughtredus Explicatus; but being desired by a Neighbour Gentleman to make a fuller Description of the Spot-Dial, which I mention there…, I have now undertaken it, according to that Gentleman’s Desire, having had much Experience (since that writing was extant) both of the best wayes of drawing the Dial, and of the best Materials, and so much as I believe, that little will be added by him, that comes after, to what I shall here say. The Use of this Dial is to see the Hour by the Rays of the Sun passing through a Hole, and terminated in a Glass set in a Frame within the House against the Window, the Ground of it is the same with that of the Sun’s Light passing through a Hole in the Window, and intercepted by a String, and of the Ceiling-Dial, where the Reflecting-Glass is supposed to be a Point in the Style.”
William Emerson. DIALLING or The Art of drawing Dials, on All Sorts of Planes whatsoever.
"In Three Parts. Sect. I. The fundamental Principles of Dialling. Sect. II. The Practice of Dialling, illustrated on all sorts of Planes. Sect. III. Of describing the common Furniture of Dials; and the Construction of some useful Dials of other kinds. London. Printed for J. Nourse, in the Strand; Bookseller in Ordinary to his Majesty, 1770." (206 pages, 10.7 MB)
Emerson (1701-82) was a schoolteacher and mathematician. He eventually gave up teaching and lived on the income from a small inheritance so that he could devote his time to study. He became an author well known for his “comprehensive grasp of all existing knowledge in all branches of his subject”. He published a defense of Newton’s Principia and authored a textbook on fluxions (calculus). Even 80 years after his death, “the works of this able mathematician…[were] still in high estimation”. The current work was originally bound with Emerson’s The Mathematical Principles of Geography. "[T]he first section contains the grounds of this art; by shewing, how the several requisites are to be found, by the intersections of the circles of the sphere, with the plane of the dial, from the principles of spherical trigonometry; from which the practical rules are deduced. The second section contains the practice, and that three different ways. 1. Geometrically, by rule and compass, which depends upon the gnomonic projection of the sphere… 2. By trigonometrical calculation, by the tables of sines and tangents, which is the most exact way. 3. By the lines upon Collin’s Dialling scale, which is a method extremely easy and ready. The third section shews the way of making some other sorts of dials; and drawing the furniture upon any common dial; that is the projection of the several circles of the sphere; and inserting therein, such hours as have been used by other nations. And tho’ these things are not absolutely necessary, they may serve sometimes as an ornament for a dial."
This can be ordered from LuLu Books: Emerson: Dialling Or The Art of Drawing Dials (1770)
Samuel Foster. Posthuma Fosteri: THE DESCRIPTION OF A RULER, Upon which is described divers SCALES:
AND The Uses thereof: Invented and written by Mr. SAMUEL FOSTER, LateProfessor of ASTRONOMIE in GRESHAM COLLEDG. By which the most usuall Propositions in Astronomie, Navigation, and Dialling, are facily performed. Also, a further use of the said Scales in Deliniating of far declining dials; and of those that Decline and Recline, three severall wayes. With the deliniating of all Horizontall Dials, between 30, and 60 gr. of Latitude, without drawing any lines but the Houres themselves. LONDON: Printed by ROBERT and WILLIAM LEYBOURN, for NICHOLAS BOURN, at the South entrance into the Royall Exchange. 1652. (90 pages, 9.8 MB)
This book was published posthumously in the year that Foster died. It describes a ruler with 9 scales and gives instructions on how to use the scales to solve many of the standard problems of “astronomie, navigation, and dialling”. In addition to familiar trigonometric scales, the ruler includes two new scales introduced by Foster. The first provides an easy means of laying out horizontal dials between 30º and 60º of latitude without having to draw any auxiliary lines.
Samuel Foster. THE ART OF DIALLING; BY A NEW, EASIE, AND MOST SPEEDY WAY.
"SHEWING, HOW TO DESCRIBE THE Houre-lines upon all sorts of Plaines, Howsoever, or in what Latitude so-ever Scituated; As also, To find the Suns Azimuth, whereby the sight of any Plaine is examined. Performed by a Quadrant, fitted with lines necessary to the purpose. Invented and Published by SAMVEL FOSTER, Professor of Astronomie in Gresham Colledge LONDON, Printed by John Dawson for Francis Eglesfield, and are to be sold at the signe of the Marigold in Pauls Church-yard. 1638." (50 pages, 1.9 MB)
Also, in non-facsimile form, NASS presents with a paragraph-by-paragraph collation with the earlier edition [above] is the second edition of Samuel Foster's THE ART OF DIALLING. This edition provides "several Additions and Variations of the Authors, deduced from his own Manuscript. With a SUPPLEMENT, Performing all the Instrumental Work of the Quadrant, by Calculation. By help of the Canons of Sines and Tangents, which of all ways is the most Exact. By WILLIAM LEYBOURN Philomath. LONDON, Printed by J.R. for Francis Eglesfield at the Marygold in St. Pauls Churchyard. 1675." (60 pages, 0.8 MB)
This can be ordered from LuLu Books: Foster: Art of Dialling (1638)