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10-19-1925

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THE present Publication being chiefly intended for the American reader, we have taken the liberty of making some alterations, which, it is presumed, will rather prove advanta.geous than otherwise.

Some parts of the work have been abridged, and other parts totally omitted, as being of little or no use to the American Surveyor. These alterations have enabled the Editor to introduce into the body of the work, some matters of considerable importance in the practice of surveying; amongst which, are a complete set of tables of latitude and departure, to the distance of 100, and to every 15 Minutes of the quadrant; a table of logarithms from 1 to 10,000; and a table of artificial sines, tangents, and secants; also an example of calculating the contents of a survey, according to the method commonly practised in the surveyor general's office of this commonwealth,

Philadelphia, 1808.

1.

VYSE'S TUTOR'S GUIDE,

BEING a complete Syftem of Arithmetic; with
Maious Branches in the Mathematics.
In fix Part, viz.

riety of questions.

Arithmetic in all its ufeful Rules, and a great va2 Vulgar Fractions in all their Parts. 3 Deci a fractions, with the Extraction of Roots of 4. Mendifferent Powers; to which is added, Rules, &c. for the eafy Calculation of intereft and annuities, &c. furation of Superfices and Solids, applied to meafuring Artificers' Works, &c. with a collection of Queftions for Exercife. To which is added, the Specific gravity of Metals, &c. 5. Chronology or the Method of finding the feveral Cycles, Epacts Moveables Feafts, Time of High Water, &c.; with a collection of Questions relating to Hiftory; likewife all the moft ufeful Examples on both the Globes. 6. Algebra, wherein the Method of raising and refolving Equations is rendered cafy, and illuftrated with a Variety of Examples and Numerical Questions.

THE KEY TO THE TUTOR'S GUIDE;

OR the Arithmetician's Repofitory: containing Solutions of the Queftions, &c. in the Tutor's Guide. The whole being principally defigned for the Eafe of Schoolmafters; and, with the Guide, furnishes a more complete and extenfive Syftem of Arithmetic than any extant; and will enable all those who are acquainted with the first Principles to attain a competent Knowledge of the feveral Rules with Eafe and Precision, and thereby qualify themfelves to inftruct the children and domestics of a family at leisure hours.

AN INTRODUCTION TO ALGEBRA;

WITH notes and obfervations; defigned for the use of Schools and Places of Public Education. by JOHN BON NYCASTLE, of the Royal Military Academy, Woolwich. The firft American edition.

The American Tutor's Affiftant; or, a compendious fystem of Practical Arithmetic; containing, the feveral rules of that ufeful fcience, concifely defined, methodically arranged, and fully exemplified. The whole particularly adapted to the cafe and regular inftruction of youth in our American schools.

PREFACE.

THE word geometry imports no

more

than to measure the earth, or to measure land; yet in a larger and more proper sense, it is applied to all sorts of dimensions. It is generally supposed to have had its rise among the Egyptians, from the ri ver Nile's destroying and confounding all their land-marks, by its annual inundations, which laid them under the necessity of inventing certain methods and measures to enable them to distinguish and adjust the limits of their respective grounds, when the waters were withdrawn. And this opinion is not entirely to be rejected, when we consider that Moses is said to have acquired this art when he resided at the Egyptian court. And Achilles Tatius in the beginning of his introduction to Aratus's Phanomena, informs us, that the Egyptians were the first who measured the heavens and the earth (and of course the earth first) and

that

that their science in this matter, was engraven on columns, and by that means delivered to posterity.

It is a

matter of some wonder, that though surveying appears to have been the first, or at least one of the first of the mathematical sciences, that the rest have met with much greater improvements from the pens of the most eminent mathematicians, while this seems to have been neglected; insomuch that I have not been able to meet with one author, who has sufficiently explained the whole art in its theory and practice: for the most part, it has been treated of in a practical manner only; and the few who have undertaken the theory, have in a great measure omitted the practice.

to at

These considerations induced me to tempt a methodical, easy, and clear course of Surveying; how far I have succeeded in it, must be determined by the impartial reader the steps I have taken to render the whole evident and familiar are as follow:

In section the first, you have decimal fractions, the square root, geometrical definitions, some necessary theorems and problems; with the nature and use of the tables of logarithm numbers, sines, sines, tangents, and

secants.

The second section contains plane trigonometry right angled and oblique, with its application in determining the measures of inaccessible heights and distances.

The third section gives an account of the chains and measures used in Great-Britain an Ireland; methods of surveying and of taking inaccessible distances by the chain only, with some necessary problems; also a particular description of the several instruments used in surveying, with their respective uses,

The fourth section contains two methods of finding the areas of maps from their ge ometrical construction, more concise than any heretofore made public.

and

The fifth section contains a new, much more concise method of determining the areas of surveys from the field-notes, or by calculation than any hitherto published; and I venture to assert that it is impossible (from the nature of right-lined figures) that any method or methods more concise than this, can be investigated.

To these methods is annexed a short table of difference of latitude and half departure, to every degree and quarter of a degree of the quadrant, the stationary distance being

one

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