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. |

A Treatise of Mathematical Instruments · by John Robertson ·
with Notes by David Manthey

ISBN 1-931468-11-7 · Copyright ©
2002 by David Manthey · 6x9", 284 pages.

[ Overview |
Contents |
Excerpt |
Cover |
Order |
Publisher |
Contact ]

[ Flower-de-Luce Books |
Invisible College Press |
Orbital Central ]