The First Book of the Cross-StaffCHAPT. I. Of the Description of the Cross-StaffThe Cross-Staff, is an Instrument well known to our Seamen, and much used by the ancient Astronomers and others, serving Astronomically for observation of the Altitudes and Angles of distance in the Heavens; Geometrically for Perpendicular Heights and Distances on Land and Sea. The Description and several Uses are extant in Print by Gemma Frisiess in Latine, in English by D. Hood. I differ something from them both, in the Projection of this Staff, but so as their Rules may be applied onto it, and all their Propositions be wrought by it; and therfore referring the Reader to their Books, I shall be brief in the Explanations of that which may be applied from their unto mine, and so come to the Use of those Lines which are of my Addition, not extant heretofore. The necessary parts of the Instrument are Five; (1) the Staff; (2.) the Cross; And (3.) the three Sights. The Staff which I made for my own use, is a full Yard in lenght, so that it may serve for measure.
Thus there are seven Lines inscribed on the Staff: there are Five Lines more inscribed on the Cross.
For the Inscription of these Lines. The first for measure is equally divided ito Inches, and theth parts of Inches. The Tangent on the Staff for observation of Angles, with the Tangent of 20 and the Tangent of 30 on the Cross may all three be inscribed out of the ordinary Table of Tangents. The Staff being 36 Inches in length; the Radius for the Tangent on the Staff will be 13 Inches and 103 parts of 100: so for the whole Line will be a Tangent of 70 gr. and must be numbered by their Complements, and the Double of their Compliments, the Tangent of 10 gr. being numbered with 80 and 160. The Radius for the Tangent of 20 on the Cross, will be 36 Inches, and the whole Line between the Sights a tangent of 36 gr. 3 m according as it is numbered, The Radius for the Tangent of 30 on the Cross will be 22 Inches and 695 parts of 1000: so the whole Line between the sights will contain a Tangent of 49 gr. 6 m. in such sort as they are numbered. The Meridian Line may be inscribed out of the Table which I set down for this pupose in the Use of the Sector. The Line of Numbers may be inscribed out of the first Chiliad of Mr. Briggs Logarithms: and the rest of the Lines of Proportion out of my Canon of Artificial Sines and Tangents, and in recompence thereof this book will serve as a Comment to explain the use of my Canon. | |
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