PREFACE

TO THE COMPREHENSIVE MATHEMATICS.

ON presenting this work to the public, it may be proper to state that it has been designed and written mainly for the practical man. It contains a vast array of Numerical, Arithmetical, and Mathematical facts, tables, data, formulas, and rules, pertaining to a great variety of subjects, and applicable to a diversity of ends, as well as much information of a more general nature, valuable to the artisan, and commercial classes; thus meeting the wants, in an eminent degree, of the lovers of the exact sciences, and the practical wants of students in the mathematics.

The facts and data alluded to have been gathered, with much care and patience, from a great variety of sources, or derived, often by toilsome investigations, from known and accredited truths. The care that has been taken in respect to these, it is thought, should secure for this particular department reliance and trust.

The tables, which are numerous, have, with few exceptions, been composed and arranged expressly for the work, and a confidence is felt that they may be relied on for accuracy.

From the valuable works of Dr. Ure, Adcock, Gregory, Grier, Brunton; from the publications of the transactions of London, Edinburgh, and Dublin Philosophical Societies; and from the publications by the Smithsonian Institute, much valuable information has been gained, relating mainly to machinery and the arts; and to these sources the author feels indebted.

The conciseness with which the work has been generally written would, perhaps, be found an objection, were it not that all the propositions and problems of intricacy are accompanied with examples and illustrations, and, in the matters of Geometry, additionally accompanied with diagrams. The whole, it is thought, will appear clear to him who consults it. A prominent feature in the design has been to produce a useful work, and one which in the way of price shall be readily accessible to all.

PREFACE

TO THE UNIVERSAL MODERN CAMBYST, AND FOREIGN
AND DOMESTIC COMMERCIAL CALCULATOR.

This work is composed of the first five sections of the author's
“COMPREHENSIVE MATHEMATICS." It was thought advisable
to publish this portion of that work in a separate form on account
of price; more especially as it contains all of a commercial nature
treated of in that work. Indeed, the contents of that work were
arranged expressly to this end. The Table of Contents in both
works is the same: the work being stereotyped, this could not
well be avoided. The Table of Contents, therefore, in either
work, is that of the "COMPREHENSIVE MATHEMATICS;" and
the first five sections thereof, that is, Section I., Section II., Sec-
tion III., Section A., and Section B., is that of the "Universal
Modern Cambyst, and Foreign and Domestic Commercial Calcu-
lator."

PREFACE

TO THE TIN-PLATE AND SHEET-IRON WORKERS' MONITOR.

This work is composed of Section VI. of the author's "COM-
PREHENSIVE MATHEMATICS," with portions of other sections of
that work. It embraces all that is contained in the last-mentioned
work of special interest to the Tinsmith, as such. It may be re-
lied on for accuracy in all particulars, and is believed to be the
first and only reliable work of the kind ever published. It is pub-
lished in separate form on account of price, and with the view of
affording apprentices and students every possible facility of obtain-
ing it. It contains over 100 pages, nearly 50 diagrams, and step-
by-step directions for constructing, mechanically, not less than 30
unlike and different patterns, embracing all of the more difficult
and complicated in use, and several of new and beautiful designs.

To Reduce a Fraction in a lower,

78
to an equivalent in a given high-
er denomination
To Reduce a Fraction to Whole
Numbers in lower given denom-
79
inations