PREFACE.

THE following Sheets contain a large collec

tion of questions in common Algebra; which (fome few excepted) are difpofed in the following order.

1. Such questions, in the folutions of which only Addition and Subtraction of quantities are ufed.

2. Questions, which befide the former operations, require the ufe of Multiplication and Di'vifion.

3. Questions, wherein the doctrine of Proporportion is requifite.

4. Such questions, producing fimple Equations, wherein a more complex process is necesfary: Where any of thefe feemed likely to occur in practice frequently, a general Solution is given.

A 3

5. Ques

5. Questions, producing Equations of fimple

Powers.

6. Questions, that produce adfected quadratic
Equations, folved by completing the Square:
With a few Examples of Dr. Halley's Method
of finding their roots by a-logarithmical Procefs.

7. Quefions, that produce adfected Equa-
tions of higher Powers.

THE method of finding divifors, delivered
in Sir Ifaac Newton's UNIVERSAL ARITHME-
TIC is here principally used; because it seems
beft adapted to find the roots of fuch equa-
tions, when thofe roots are whole numbers,
or rational fractions: There are however,
fome examples of finding the roots of fuch
cubic equations as want the fecond term by a
method fimilar to Cardan's, or by Dr. Halley's
logarithmical procefs depending thereon; but
where neither of thefe methods appeared prac-
ticable, without a previous reduction, one of
Dr. Halley's approximations to the root (called
his rational and irrational theorems) is ufed,
according as this, or that, feemed most ap-
plicable to the given numbers.

8. Indetermined queftions; as well thofe
that are capable of innumerable anfwers, as thofe

where the number of anfwers in integers is limited.

THE folutions of thefe queftions are attempted, for the most part, in a manner different from what has been commonly used; and fome folutions are given at large, which other writers have thought too operofe to be inferted: A few of the questions ufually called Diophantine are introduced toward the end of these, and are folved by the fame principles.

9. Questions, relating to Arithmetical Progreffions, and other feries derived from them: fuch as, their fquares, cubes, &c. the different Series of Figurate numbers; and of thofe Numbers whofe fecond, third, fourth, &c. Differences are equal; the Combinations, Elections, Permutations of Quantities, &c.

10. Questions, relating to Simple Intereft, Difcompt, &c.

11. Questions, relating to Geometrical Progreffions.

12. Questions, relating to Compound Intereft; and to the values of Annuities for Time certain; both in Poffeffion and Reverfion.

13. Quéf

13. Questions, relating to Geometrical Progreffions infinitely decreafing; and to feries of Fractions, the Numerators of which are Numbers, whofe 1st, 2d, 3d, &c. Differences are equal, and their Denominators a Geometrical Progreffion.

14. The Summation of the feveral series of the Reciprocals of Figurate Numbers; and of other Series which can be obtained by a fimilar Process.

15. The feveral Series that are commonly used for making Logarithms, inveftigated by common Algebra.

THESE Series were first exhibited by Mercator, from the Quadrature of the Hyperbola; afterward by Dr. Halley, from the Doctrine of Ratiuncula, and by extracting the Root of an Infinite Power; by others, from the Doctrine of Fluxions, &c. Now, as Beginners in Mathematical Learning cannot foon be acquainted with any of the above Principles; and fince a Table of Logarithms is useful, even at the firft Entranee into these Studies, this Solution obtained by the Affumption of a Series, although it may not give fufficient Satisfaction as to the Invention, will prove the

Truth of thofe Methods which are ufed in conftructing fuch Tables; and by Confequence enable the Operator to correct them if erroneous.

16. Approximations to the Sums of the fe veral Series of the Reciprocals of the ift, 2d, 3d, &c. Powers of an arithmetical Progreffion.

This manner of ranging the questions has been fometimes difpenfed with, when there was an Opportunity thereby of bringing more Matter into lefs Space.

Variety of Authors have been carefully examined to colle Materials for this work; viz. Oughtred, Leybourn, Moore, Kerfey, Wallis, Harriott, Parfons, Newton, Halley, Jones, De Moivre, Ward, Ronayne, Simpfon, &c. of our own Nation; and Defcartes, Alexander, Ozanam, John and James Bernoulli, Wolfius, Euler, &c. of other Nations.

From thefe Authors, and many others, bas been felected much the greater Part of this Work. It is true, neither the Words made use of by an Author in expreffing a Question, nor his Manner of Solution, bave been frilly retained; it hav

ing