Mathematicks are now become a popular Study, and make a part of the Education of almost every Gentleman. Indeed, they are so useful, so entertaining and extensive a Branch of Knowledge, that it is no wonder they should gain Ground; and that uncommon Countenance they now find, must be esteemed as an Instance of the Felicity of the Age, and the good Sense of the People. Mathematicks have wherewith to gratify all Tastes, and to employ all Talents. Here the greatest Genius has room to exert his utmost Faculties, and the meanest will not fail to find something on a Level with his. Their Theory, affords a noble Field for the Speculative Part of Mankind; and, their Practice, an ample Province for the Men of Action and Business.
The Masters in Mathematicks have not been wanting in their Respect to the rest of Mankind: They have frankly communicated their Knowledge to the World; and have published Treatises on every Branch of their Art: Insomuch, that a Man who has a Disposition to this Study, will find himself abundantly supplied with Helps, to what Part soever he applies himself There seems, then, but little wanting to Mathematicks, considered as a Science: If there be any Defect, it is when considered as an Art. I mean, Mathematicks appears more accessible, as well as more extensive, on the Side of their Theory than on that of their Practice. Not that the latter has been less laboured by Authors than the former, but because a sufficient Regard does not seem to have been had to the Instruments, whereon it wholly depends.
Mathematical Instruments are the Means by which those Sciences are rendered useful in the Affairs of Life. By their Assistance it is, that subtile and abstract Speculation is reduced into Act. They connect, as it were, the Theory to the Practice, and turn what was bare Contemplation, to the most substantial Uses. The Knowledge of these is the Knowledge of Practical Mathematicks: So that the Descriptions and Uses of Mathematical Instruments, make, perhaps, one of the most serviceable Branches of Learning in the World. The Way then to render the Knowledge of Mathematicks general and diffusive, is by making that of Mathematical Instruments so: With a View of which kind, our Author seems to have engaged in the following Traitise; at least, it was from a View of this kind, that I undertook to translate it.
The Design of the Work, however useful, yet seems to be New among us. Particular Authors have indeed touched on particular Parts: One, for Instance, having described the Globe; another the Sector; and a third the Quadrant: but for a general Course, or Collection of Mathematical Instruments, I know of none that has attempted it. It is true, in Harris’s Lexicon, we have the Names of most of them; and in Moxon’s Dictionary the Figures of many: But the Accounts given of them in both are so short, same, and deficient, that there is but little to be learned from either of them.
I chose M. Bion&rsuo;s Book for the Ground-Work of mine, as judging it better to make use of a good safe Model provided to my Hands, than run the Risque of proceeding upon my own Bottom. The French Instruments described by him, are, in the main, the same with those used among us. Such English Instruments as he has omitted, I have been careful to supply: And throughout, have taken the Liberty not only to make up his Deficiencies, but amend his Errors.
Those who desire an Inventory of the Work, have it as follows:
It is divided into Eight Books, and each of these subdivided into Chapters. To the whole are prefixed Preliminary Definitions necessary for the understanding of what follows.
In the First Book are said down the Construction and Principal Uses of the most simple and common Instruments, as Compasses, Ruler, Drawing-Pen, Porte-Craion, Square, Protractor. And to these I have added five other Articles, of the Carpenter’s Joint-Rule, the Four-foot Gauging-Rod, Everard’ Sliding-Rule, Coggeshall’s Sliding-Rule, the Plotting-Scale, an improved Protractor, the Plain-Scale, and Gunter’ Scale.
The Second Book contains the Construction and Principal Uses of the French Sector, (or Compass of Proportion) those of various Gauging-Rods. To this Book I have added the Construction and principal Uses of the English Sector.
The Subject of the Third Book is very much diversified. Under this are found the Construction and Uses of several curious and diverting as well as useful Instruments; particularly Compasses of various kinds, Parallel-Rules, the Parallelogram or Pentagraph, &c. Under this Head are also laid down several Things not easily to be met with elsewhere: As, the Manner of arming Load-Stones; the Composition of divers Microscopes, with several other curious Amusements. To the first Chapter of this Book I have added the Descriptions and Uses of the Turn-up Compasses and Proportional Compasses, with the Sector-Lines upon them, as also the Manner of projecting them.
In the Fourth Book you have the Construction and Uses of the principal Instruments used in taking Plots, measuring or laying out Lands, taking Heights, Distances, accessible or inaccessible; Staffs, for instance, Fathoms [or Toises], Chains, Surveying-Crosses, Recipient-Angles, Theodolites, Semi-Circles, the Compass, with their Uses in Fortification. To this Book I have added three Articles of the English Theodolite, Plain-Table, Circumferentor, and Surveying-Wheel. What I have there added of the Uses of those Instruments, though but short, yet I flatter myself will be found more Instructive than much larger Accounts of them in the common Books of Surveying.
The Fifth Book contains the Construction of several different kinds of Water-Levels; with the Manner of rectifying and using them, for the Conveyance of Water from one Place to another. In this Book are also found the Construction and Uses of Instruments for Gunnery: And to these I have added the Construction and Use of the English Callipers.
In the Sixth Book are contained the Construction and Uses of Astronomical Instruments; as the Astronomical Quadrant, and Micrometer, with an Instrument of Mr de la Hire’s for shewing the Eclipses of the Sun and Moon, and Mr Huygens’s Second Pendulum-Clock for Astronomical Observations. In this is also shewn the Manner of making Celestial Observations according to Mr de la Hire and Cassini. To this Book I have added four Chapters, containing the Description and general Uses of the Globes, with the manner of making them: The Description and Uses of the Ptolemaick and a Copernican Sphere, the Orrery, and a Micrometer, better than that described by the Author, and of Gunter’s Quadrant.
The Seventh Book contains the Construction and Uses of the Sea-Compass, the Azimuth-Compass, Sea-Quadrant, Fore-Staff, and other Instruments for taking Altitudes at Sea; as likewise the Construction and Uses of the Sinical-Quadrant, and Mercator’s Charts.
In the Eighth Book are found the Constructions and Uses of all kinds of Sun-Dials, whether fixed or portable, with the Instruments used in drawing them; as also a Moon-Dial, Nocturnal, &c. To this is subjoined a short Description of the principal Tools used in making Mathematical Instruments: And, lastly I have added, byway of Appendix, the Construction of the great Eclipse of the Sun, that will happen May the 11th, 724, by the Sector.
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