Author:  Leybourn, William, 16261716. 
Title:  Arithmetick: vulgar, decimal, instrumental, algebraical.: In four parts: conteining I Vulgar arithmetick, both in whole numbers and fractions, in a most plain and easie method. II Decimal arithmetick, with the ground and reason thereof, illustrated by divers examples. III Instrumental arithmetick, exactly performing all questions of what nature soever in a decimal way, by scales, with much more ease and facility then can be effected, either by vulgar or decimal arithmetick, the work of reduction being wholly avoided. Nothing in this kind having been hitherto published by any. IV Algebraical arithmetick, conteining an abridgement of the precepts of that art, and the use thereof, illustrated by examples and questions of divers kinds. Whereunto is added the construction and use of several tables of interest and annuities, weights and measures, both of our own and other countries. / By William Leybourn. 
Publication Info:  Ann Arbor, Michigan: University of Michigan Library 2011 April (TCP phase 2) 
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Arithmetick: vulgar, decimal, instrumental, algebraical.: In four parts: conteining I Vulgar arithmetick, both in whole numbers and fractions, in a most plain and easie method. II Decimal arithmetick, with the ground and reason thereof, illustrated by divers examples. III Instrumental arithmetick, exactly performing all questions of what nature soever in a decimal way, by scales, with much more ease and facility then can be effected, either by vulgar or decimal arithmetick, the work of reduction being wholly avoided. Nothing in this kind having been hitherto published by any. IV Algebraical arithmetick, conteining an abridgement of the precepts of that art, and the use thereof, illustrated by examples and questions of divers kinds. Whereunto is added the construction and use of several tables of interest and annuities, weights and measures, both of our own and other countries. / By William Leybourn. Leybourn, William, 16261716., Billy, Jacques de, 16021679. London: Printed by R. and W. Leybourn, and are to be sold by George Sawbridge at the Bible on Ludgatehill, 1660. 
Subject terms: 
Arithmetic
Mathematics
Algebra

URL:  http://name.umdl.umich.edu/A88112.0001.001 
Contents 

title page
frontispiece
TO THE READER.
publisher's advertisement
The Contents.
text
part 1
Numeration.
Addition.
Addition of numbers of diverse Denominations. 1 Addition of English Money
2 Addition of Troy Weight.
3 Addition of Avoirdupois little Weight.
4 Addition of Avoirdupois great weight.
section
1 Of Liquid Measures.
2 Of Dry Measures.
3 Of Long Measures.
4 Of Time.
5 Of Apothecaries Weights.
The Proof of Addition.
Other Examples proved.
Subtraction.
Subtraction of Numbers of diverse Denominations, 1 Of English Money.
The Proof of Subtraction.
Other Examples in Weight and Measure.
Questions performed by Addition and Subtraction.
Multiplication.
The use of the Table of Multiplication, and the manner how it is to be read.
Other Examples for Practice.
Compendiums in Multiplication.
The Proof of Multiplication.
To multiply by any of the nine Digits without charging the memory.
Questions performed by Multiplication only.
Division.
Example. 1.
Example 2.
A Second way of Division.
Example.
A Third way of Division.
Other Examples for Practice.
proof
A Fourth way of Division.
The Proof of this Division.
Other Examples for Practice proved.
Questions performed by Division only.
Reduction.
Example 1.
Example 2.
Example 1.
Example 2.
Progression.
Geometrical Progression.
A Question resolved by Geometrical Progression.
THE GOLDEN RULE, Or Rule of Three.
The Rule Direct.
Otherwise.
Note 1.
Note 2.
Question 1.
Question 2.
Question 3.
Question 4.
Question 5.
Question 6.
The Golden Rule Reverse.
Question 1.
Question 2.
Note 1.
Note 2.
Question 3.
Question 4.
The Golden Rule Compound of five Numbers.
Question 1.
Question. 2.
Of Fractions.
Numeration.
Multiplication.
Example 1.
Example 2.
Example 3.
Division.
Example 1.
Example 2.
Example 3.
Reduction.
Example.
Example.
Fractions of Fractions.
Example.
Proof.
Addition.
Example.
Subtraction.
The Rule of Fellowship.
Example 1.
Example 2.
Example 3.
The Rule of Fellowship with time.
Question 1.
Question 2.
Quest. 3.
Note
Quest. 4.
The Rule of Alligation.
Question 1.
Example.
Quest. 2.
Example 3.
Question 3.
The Rule of False Position.
Question 1.
Question 3.
Question 3.
The Rule of Ceres and Virginum.
Question 1.
Question 2.
Question 3.
Note.
Question 4.
Example.
Extraction of Roots.
Example.
Here followeth a Table of Roots and their Squares from 1, to 1000.
Extraction of the Cube Root.
section
Some uses of the Square and Cube Root.
Uses of the Square Root.
PROPOSITION. I.
PROPOSITION II.
Ʋse of the Cube Root.
PROPOSITION.
DECIMAL ARITHMETICK. The Second Part. With the ground and reason thereof, illustrated by divers Examples, in all the most usual Rules of Arithmetick.
Proposition 1.
Example 1.
Proposition 2. How to expresse English Coin, in Decimal Numbers.
section
section
section
section
section
section
section
section
section
The use of the foregoing Tables.
PROP. I. How to expresse English Coin in Deci∣mals.
Example.
PROP. II. How to express Troy weight in De∣cimals.
Example.
PROP. III. How to express Averdupois great weight in Decimals.
Example.
PROP. IV. How to expresse Averdupois little weight in Decimals.
PROP. V. How to expresse Liquid Measures in Decimals.
PROP. VI. How to expresse dry measures in De∣cimals.
PROP. VII. How to expresse long measures in De∣cimals.
PROP. VIII. How to expresse the parts of Time in Decimals.
PROP. IX. How to expresse Dozens in Decimals.
PROP. X. A decimal number being given, how to find what Fraction it doth represent.
Example 1.
Example 2.
Examples.
Example.
Of Notation of Decimals.
Addition of Decimals.
Example 1.
Example 2.
Other Examples for practice.
Example 3. In Averdupois little w.
Subtraction of Decimals.
Example 1.
Examples for practice.
Multiplication of Decimals.
Example 1.
Example 2.
Example 3.
Example 4.
Example 5.
Examples for practice.
Division of Decimals.
The Rule for the first varietie.
Example 1. Where the terms given, are both of mixt numbers.
Example 2. One of the terms given, being a whole number the other mixt.
Example 3. The Dividend being a Decimal, and Divisor the whole number.
The Rule for the second varietie.
Example 1.
Example 2.
The Rule for the third variety.
Example.
The Rule for the fourth varietie.
Examples for Practice.
The Rule of three in fracti∣ons Vulgar and Decimal.
1 Question.
The same Question in Decimals.
2 Question.
The same question in Decimals.
The Operation.
The Operation.
An Example in the Rule of Three Reverse.
Examples in the Rule of Proportion, consisting of five numbers.
Question 1.
Quest. 2.
THE THIRD PART Conteining INSTRUMENTAL ARITHMETICK.
Numeration upon the Scales.
Addition.
Subtraction.
Example.
Multiplication by Nepers Bones.
Of Division by the Rods.
Example in the Rule of Three Direct.
Example in the Rule of Three Reverse.
Example in the Double Rule of Three.
Example in Barter.
The tenor of the Question is this.
Example in Fellowship.
The manner of Work.
Examples in Losse and Grain.
Examples in Losse and Gain upon Time wrought by the Double Rule of Three.
An Appendix.
Section 1. Of Exchange of the Coins, Weights, and Measures of one Countrey, with the Goins, Weights and Mea∣sures of another Countrey.
Question 1.
Question 2.
Question 3.
Question 4.
Question 5.
Question 6.
Question 7.
A Table shewing what one pound of Avoirdupois weight at London, maketh in divers eminent Cities, and other remarkable places.
The use of the preceding Table.
A Table shewing what one pound Weight in divers forreign Cities, and remarkable places, maketh at London of Avoirdupois Weight.
The use of the foregoing Table.
A Table reducing English Ells to the Measures of divers forreign Cities and remarkable places.
The use of this Table.
A Table reducing the Measures of divers forreign Cities and remarkable places, to English Ells.
The use of this Table.
Section 2. Concerning Interest and Annuities.
The first Table shewing what one pound being forborn any number of years under 31, will amount unto, accounting interest upon interest, after the rate of 6 per cent.
The use of this Table.
The Second Table, sheweth what one pound Annuity will amount unto, being forborn any number of years under 31, at 6 per cent. interest upon interest, the Annuity being to be paid yearly.
The use of this Table.
The third Table sheweth what one pound being forborn any number of years under 31 is worth in ready money, rebating yearly, after the rate of 6 per cent. interest upon in∣terest.
The making of the Table.
The fourth Table sheweth the present worth of one pound Annuity; to continue any number of years under 31, and payable yearly after the rate of 6 per cent. interest upon interst.
The use of this Table.
The fifth Table sheweth what Annuity payable yearly, one pound will purchase for any num∣ber of years under 31, after the rate of 6 per cent. compound interest.
The use of this Table.
The fourth Part: BEING AN ABRIDGEMENT OF THE PRECEPTS OF ALGEBRA
table
CHAP. I. The Alegorithm of Cossick Numbers, simple, compounded, or diminished.
Sect. 1. Addition of simple Cossick numbers.
Sect. 2. Subtraction of simple Cossick numbers.
Sect. 3. Multiplication of simple Cossick numbers.
Sect. 4. Division of simple Cossick numbers.
Sect. 5. Addition of numbers composed and diminished.
Sect. 6. Subtraction of numbers composed and dimi∣nished.
Sect. 7. Multiplication of numbers composed and di∣minished.
Sect. 8. Division of numbers composed and diminished.
Sect. 9. Algorithm of Fractions.
CHAP. II. The rule of Algebra, with the expli∣cation thereof.
Sect. 1. The rule of Algebra.
Sect. 2. How the Equation must be found.
Sect. 3. How your Equation must be reduced.
Sect. 4. When you must extract the root.
Sect. 5. How to extract the square root of numbers, compound and diminished.
Sect. 6. How to know if the question be impossible, vain, or ill propounded.
CHAP. III. Algorithme of second roots with their use.
Sect. 1. Addition of second roots.
Sect. 2. Subtraction of second roots.
Sect. 3. Multiplication of second roots.
Sect. 4. Division of second roots.
Sect. 5. The extraction and use of second roots.
CHAP. IV. The Algorithme and extraction of the roots of surd & irrational numbers.
Sect. 1. Reduction of surd roots simple to the same de∣nomination.
Sect. 2. Multiplication and Division of surd simple roots.
Sect. 3. How to know whether two surd roots be com∣mensurable or not.
Sect. 4. Addition of simple irrational roots.
Sect. 5. Subtraction of simple irrational roots.
Sect. 6. Addition and Subtraction of surd numbers, composed and diminished.
Sect. 7. Multiplication of numbers surd, composed and diminished.
Sect. 8. Division of surd numbers, compounded or di∣minished.
Sect. 9. Multiplieation of roots universal.
Sect. 10. Division of roots universal.
Sect. 11. Addition and Subduction of roots uni∣versal.
Sect. 12. Extraction of the roots of Binomes and Apotomes.
CHAP. V. The Ʋse of Algebra.
Sect. 1. Questions resolved by one simple Equation.
Question I.
Question II.
Question III.
Sect. II. Questions resolved by an Equation com∣pounded.
Question I.
Question II.
Question III.
Sect. III. Questions resolved by surd numbers.
Question I.
Question II.
Question III.
Sect. IV. Geometrical questions resolved by Algebra.
Question I.
Question II.
Question III.
Sect. 5. Questions resolved by the second Roots.
Question I.
Question II.
Question III.
Sect. VI. Questions resolved indefinitely.
Question I.
Question II.
Question III.
Appendix. Questions in Algebra, most of which require the Rule of Three in their Operation.
Question. I.
Question II.
Question III.
Question IV.
Question V.
Question VI.
Question VII.
Question VIII.
Question IX.
Question X.
Question XI.
Question XII.
Question XIII.
Question XIV.
Question XV.
Question XVI.
Question XVII.
Question XVIII.
Question XIX.
Question XX.
Question XXI.
Question XXII.
Question XXIII.
Some Examples in Algebra con∣cerning Squares.
To finde two numbers in a given Excesse, so as their Squares may have also a given Excesse.
Two numbers being given, to finde another, with which multiplying both the given numbers, makes the grea∣ter number a square, and its lesser the side of that square.
Some Examples relating to Cubes.
To finde a number, which multiplied in it self, and the product multiplied by some given number, may pro∣duce a number in a given proportion to the Cube of the found number.
To divide a given number in two parts, so as that their Cubes may make a given sum, which shall be greater than the quarter part of the Cube described of the given number.
