A Treatise of Mathematical Instruments - by John Robertson - The 1775 Third Edition - with Notes by David Manthey

A Treatise of Mathematical Instruments


To the Reader (includes a history of the Sector and Parallel-Rules)

I.	Of the common portable instruments and cases.
II	Of compasses.
	Of the bows.
III.	Of the black-lead pencil, feeder, and tracing point.
	To trace or copy a drawing.
IV.	Of the drawing pen and protracting pen.
V.	Of the different parallel rules, and their use.
	1st. In drawing of parallel right lines.
	2d. In the dividing of right lines into equal parts.
	3d. In the reduction of right-lined figures to right-lined triangles of equal area.
VI.	Of the protractor, and its use.
	1st. In plotting and measuring of right-lined angles;
	2d. In drawing of lines at right angles to each other;
	3d. In inscribing of regular polygons in a circle;
	4th. In describing of regular polygons on given right lines.
VII.	Of the plane scale, and its several lines.
	Construction of the scales of equal parts.
	Their use, joined with the protractor, in plotting of right-lined figures.
	Construction of the other lines of the plane scale, viz. 1st. Chords; 2d. Rhumbs; 3d. Sines; 4th. Tangents; 5th. Secants; 6th. Half Tangents; 7th. Longitude; 8th. Latitude; 9th. Hours; 10th. Inclination of Meridians.
VIII.	The uses of some of the lines on the plane scale.
	A table, shewing the miles in one degree of longitude to every degree of latitude.
IX.	Of the sector and its lines.
X.	Of the construction of the single scales on the sector.
XI.	Of the construction of the double scales on the sector.
XII.	Of the uses of the double scales.
	The use of the line of lines.
	1st. To two right lines given, to find a 3d proportional.
	2d. To three right lines given, to find a 4th proportional, &c.
	3d. To set the scales of lines at right angles to one another.
	4th. Between two right lines to find a mean proportional.
	5th. To divide a right line into equal parts.
	6th. To delineate the orders of architecture.
	Some terms in architecture explained.
	Of the Five Orders, and the general proportions in each.
	To draw the mouldings in architecture.
	Table for describing the Ionic volute.
	Uses of some tables for drawing the orders.
	To delineate any of the orders by the tables.
	Three tables, shewing the altitudes and projections of every moulding and part in the pedestals, columns, and entablatures of each order; according to the proportions given by Palladio.
XIII.	Some uses of the scales of polygons.
XIV.	Some uses of the scales of chords.
	To delineate the station lines of a survey.
XV.	Some uses of the logarithmic scales of numbers.
XVI.	Some uses of the scales of logarithmic sines, and logarithmic tangents.
XVII.	Some uses of the double scales of sines, tangents, and secants.
	To find the length of the radius to a given sine, tangent, or secant.
	To find the degrees corresponding to a given sine, tangent or secant.
	To a given number of degrees, to find the length of the versed sine.
	To set the double lines to any given angle.
	To describe an Ellipsis.
	To describe a Parabola.
	To describe a Hyberbola.
	To find the distance of places on the terrestrial globe.
XVIII.	The use of some of the single and double scales on the sector, applied in the solution of all the cases of plane trigonometry.
	Case I. When among the things given, there be a side and its opposite angle.
	Case II. When two sides and the included angle are known.
	Case III. When the three sides are known.
XIX.	The construction of the several cases of spherical triangles, by the scales on the sector.
	Case I. Given two sides, and an angle opposite to one of them.
	Case II. Given two angles, and a side opposite to one of them.
	Case III. Given two sides, and the included angle.
	Case IV. Given two angles, and the included side.
	Case V. Given the three sides.
	Case VI. Given the three angles.
XX.	The use of the sector in drawing the perspective representations of objects.
	To find, in the picture, the place of a point.
	To find the perspective of a line, angle, &c.
	To find the representation of a triangle, a square and any regular polygon.
	Of the circle and its diameter.
XXI.	Of the proportional compasses, and the construction of the scales put on them.

APPENDIX.
Of the callipers, and what they contain.
I.	Of the measures of convex diameters.
II.	Of the weights of iron shot.
III.	Of the measures of concave diameters.
IV.	Of the weights of shot to given gun bores.
V.	Of the degrees in the circular head.
VI.	Of the proportion of troy and averdupoise weights.
VII.	Of the proportion of English and French feet and pounds.
VIII.	Factors useful in circular and spherical figures.
IX.	Of the specific gravities and weights of bodies.
	Some uses of the table.
X.	Of the quantity of powder used in firing of cannon.
XI.	Of the number of shot or shells in a finished or broken pile.
XII.	Concerning the fall of heavy bodies.
XIII.	Rules for the raising of water.
XIV.	Of the shooting in cannon and mortars.
XV.	Of the lines of plans or superficies.
XVI.	Of the line of solids.
XVII.	Of ship guns and sea mortars.
	Names of the parts of a cannon.
	Table of the British establishment of cannon and their shot.
	Table of the parts of a cannon in calibres of the shot.
	To delineate a piece of cannon.
	Of the parts of a truck carriage.
	Tables of the parts of a truck carriage in calibres of the shot.
	Construction of the elevation and plan of a truck carriage.
	Of sea mortars.
	The dimensions of their parts in calibres of the shell.
	To delineate a sea mortar.
	Of the parts of a sea mortar bed.
	Precepts for the delineation.

NOTES.
I.	Preface to the notes
II.	Biographical note on John Robertson
III.	On the different editions of the Treatise
IV.	About this printing
V.	On the Notation used in the Treatise
VI.	On Mathematics
VII.	On Palladio and architecture
VIII.	On surveying
IX.	On spherical trigonometry and navigation

Eleven Plates, and a Plate fronting the Title page.

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A Treatise of Mathematical Instruments

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