Author:  Partridge, Seth, 16031686. 
Title:  The description and use of an instrument called the dovble scale of proportion by which instrument, all questions in arithmetick, geometry, trigonometry, astronomy, geography, navigation, fortification, gunnery, gaging vessels, dialling may be most accurately and speedily performed without the assistance of either pen or compasses / by Seth Partridge. 
Publication Info:  Ann Arbor, Michigan: University of Michigan, Digital Library Production Service 2011 December (TCP phase 2) 
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Print source: 
The description and use of an instrument called the dovble scale of proportion by which instrument, all questions in arithmetick, geometry, trigonometry, astronomy, geography, navigation, fortification, gunnery, gaging vessels, dialling may be most accurately and speedily performed without the assistance of either pen or compasses / by Seth Partridge. Partridge, Seth, 16031686. London: Printed by William Leybourn for William Wright ..., 1661. 
Notes: 
Advertisement: p. 188.
Errors in paging: p. 78 omitted in numbering only; p. 55 misprinted 57.
Reproduction of the original in the Huntington Library.

Subject terms:  Sliderule  Early works to 1800. 
URL:  http://name.umdl.umich.edu/A56521.0001.001 
Contents 

title page
To the Right Worshipful, Sir RICHARD COMBE Knight, The Authour presents these, with his other best Services.
To the Reader.
THE Double Scale of Proportion.
CHAP. I. The Instrument described.
CHAP. II. The Ʋse and application of the double Scale of Numbers upon the Instru∣ment, in the principal Rules of Arithmetick.
PROBLEM I. Of Multiplication.
Two numbers being given to be multiplyed together, to find their Product, by the double lines.
How to square any number, or to multiply a num∣ber by it self, as also to cube any number.
PROBLEM II. Of Division.
PROBLEM III. Of Reduction of Fractions.
PROBLEM IV. Of Continual Proportionals.
PROBLEM V. Of the Rule of Proportion direct.
PROBLEM VI. The Rule of Proportion Inverse.
PROBLEM VII. Of Duplicated Proportion.
1 Of the Proportion of Lines to Superficies.
2 Of the Proportion of Superficies to Lines.
PROBLEM VIII. Of Triplicate Proportion.
PROBLEM IX. A Company of men laying down several sums of money together into one stock, wherewith they trade and get gain; to find out how much each mans part of the gain must be, answerable to his part of money laid down in stock.
PROBLEM X. Of Interest and Annuities.
To find the Interest of any sum of money, af∣ter any rate by the 100 propounded.
Of Interest of money continued from year to year.
Of Annuities.
A Sum of money being due at a certain time to come, to find what it is worth in present money, to take in.
CHAP. III. The Ʋse of the double Scale of Num∣bers in Superficial measure, as Board, Glasse, Land, and the like.
PROBLEM I. The length and breadth of any square, or long square Superficies being given, to find the Content thereof.
PROBLEM II. The breadth and length of any Superficies being given in one kind of measure, to find the Con∣tent in another kind of measure.
PROBLEM III. The breadth of a Superficies being given in one kind of measure, and the length in another, to find the Content in the greater measure.
PROBLEM IV. The length and breadth of a Superficies being gi∣ven in feet, to find the Content in yards.
PROBLEM V. The breadth of any Superficies being given in in∣ches or feet, to find how much in length will make a superficial foot.
PROBLEM VI. The length and breadth of a plot of land being given in chains, to find the Content in Acres.
PROBLEM VII. The Content of a piece of land being measured by one kind of perch, to find the Content there∣of, after another kind of perch.
PROBLEM. VIII. The one side of any piece of land being given, to find how much in breadth the other way will make an acre of land.
PROBLEM. IX. A plot of land being laid down, and cast up by any Scale, to find how much it will contain by any other Scale, either greater or lesser.
PROBLEM. X. The Diameter of a circle being given, to find the Circumference.
PROBLEM XI. The Circumference of a circle being given, to find the Diameter.
PROBLEM XII. The Diameter of a circle being given, to find the side of a Square equal to it.
PROBLEM XIII. The Circumference of a circle being given, to find the side of a square, equal in Content to that circle.
PROBLEM. XIV. The Diameter of a circle being given, to find the side of a square, that may be inscribed with∣in it.
PROBLEM. XV. The Circumference of a circle being given, to find the side of a square that may be inscribed within it.
PROBLEM. XVI. The Diameter or Circumference of a circle, either of them being given, to find the side of an E∣quilater triangle, to be inscribed within that circle.
PROBLEM. XVII. The Diameter or Circumference of any circle being given, to find the superficial Content.
PROBLEM. XVIII. The Diameter, with the superficial Content of any circle given, to find the Content of any other circle that is twice the Diameter of the first.
PROBLEM. XIX. The Content of a circle being known, to find the Diameter and Circumference.
CHAP. IV. The Ʋse of the double scales in solid measure, such as Timber, Stone, &c.
PROBLEM. I. The side of a square solid being given in inches, or feet, to find how much in length will make a foot solid in inches or feet.
PROBLEM. II. The breadth and depth of an unequal square solid being given in parts of a foot, or in inches, to find how much in length will make a foot.
PROBLEM III. The breadth of a square solid, or the side of a square equal to the Base of any unequal square solid, and the length of the same solid being gi∣ven in inches or feet, to find the Content in feet.
PROBLEM IV. The side of a squared solid given in inches, and the length in feet, to find the Content in feet.
PROBLEM V. The length, breadth and depth of a square solid being given in inches, to find the Content in feet.
PROBLEM VI. The Base of any square solid being given in in∣ches, and the length in feet, to find the Content in feet.
PROBLEM VII. The Diameter of a Cylender given in inches or feet, to find the length of a foot, according to that Diameter.
PROBLEM VIII. The circumference of a Cylinder given in inches, or tenth parts of feet, to find the length to make a solid foot.
PROBLEM. IX. The Diameter and length of a Cylinder given in inches or feet, to find the Content in inches, or tenth parts of feet.
PROBLEM. X. The Diameter and length of a Cylinder given in inches, to find the Content in feet.
PROBLEM. XI. The Diameter of a Cylinder given inches, and the length in feet, to find the content in feet.
PROBLEM. XII. The circumference and length of a Cylinder given in inches, to find the content in inches.
PROBLEM XIII. The circumference and length of a Cylinder given in inches, to find the content in feet.
PROBLEM. XIV. The circumference of a Cylinder taken in inches, and the length in feet, to find the content in feet.
PROBLEM. XV. The Diameters of any vessel at the head, and at the bung, with the length in inches had, to find the content thereof, first in inches, and then in gallons, either of Wine or Beer.
CHAP. V. The Ʋse of the double scales of Num∣bers in Spherical Bodies, such as Globes, Bullets, &c.
PROBLEM. I. The Diameter of any Spherical Body being known, to find the circumference.
PROBLEM. II. The circumference of any Spherical Body being known, to find the Diameter.
PROBLEM. III. The Diameter and circumference of any spheri∣cal Body being known, to find the superficial content.
PROBLEM. IV. The Axis or Diameter of a Globe being known, to find the solid content.
PROBLEM V. The Diameter of a Bullet being given, with the weight; to find the weight of another Bullet of the same metal, but of another Diameter, ei∣ther greater or lesser.
PROBLEM VI. Having the side of a cubick body of silver with the worth thereof, to find the worth of another cubick body of silver, whose side is greater or lesser than that of the body given.
PROBLEM VII. Having the weight of a Bullet of one kind of me∣tal, to find the weight of a Bullet of another kind of metal, being equal in magnitude.
CHAP. VI. The Ʋse of the double Scales in the Measuration of Concave Cylinders, such as great Ordnance.
PROBLEM I. The Diameter and weight of any one Cylinder, or Piece of great Ordnance being known, to find the weight of any other Piece of the same me∣tal and shape, either greater or lesser, its Dia∣meter being onely known.
PROBLEM. II. Having the Diameter and weight of any Piece of great Ordnance, of one metal; to find, the weight of another Piece of Ordnance of ano∣ther metal, that retaineth the same shape.
PROBLEM. III. To find the superficial Content of the concave Su∣perficies of any Piece of Ordnance, and also the solid Content of the Concavity thereof.
PROBLEM IV. To know how much of every kind of metal is con∣ned in any Brasse Piece of Ordnance.
PROBLEM. V. By knowing what quantity of powder will load some one Piece of Ordnance, to find how much of the same powder will load any other Piece of Ord∣nance, greater or lesser.
PROBLEM. VI. Knowing how far any Piece of Ordnance will carry her Bullet at pointblank, and at the best of her Randon, to find how far any other Piece of Ordnance will carry her Bullet at her best Randon, her levelrange being known.
PROBLEM VII. By knowing how far any piece of Ordnance will carry a Bullet at the best of her Randon, to find how far she will carry her Bullet at any other degree of Randon.
PROBLEM VIII. To find out how much wide of the mark any Piece of Ordnance will shoot, by knowing how far it is to the mark shot at, and how wide the Pieces mouth lieth from the right line to the mark.
PROBLEM IX. Knowing the quantity of each sort of Ingredients for the making of Gun powder, to find how much of every sort is to be put into any uuantity of powder that shall be required to be made.
CHAP. VII. The Ʋse of the double Scales in For∣tification.
section
How to make a Fort greater than the Fort proposed.
diagram
CHAP. VIII. The Ʋse of the double Scale of Sines in Astronomy.
PROBLEM. I. The Suns greatest declination, with his place or di∣stance from the next Equinoctial point being gi∣ven, to find his present declination for the time given.
PROBLEM. II. The Suns greatest declination, and his present de∣clination for any time proposed being had, to find his distance from the next Equinoctial point, and thereby his place in the Ecliptick.
PROBLEM. III. The Suns declination, and the Latitude of the place being given, to find the Suns Amplitude.
PROBLEM. IV. The Latitude of the place, the Suns greatest decli∣nation with his distance from the next Equino∣ctial point being had, to find his Amplitude.
PROBLEM. V. The Latitude of the place, the Suns place or di∣stance from the next Equinoctial point, with his greatest declination being known; to find what altitude the Sun will have, when he is on the true East or West point.
PROBLEM. VI. The Latitude of the place, and Suns declination being had; to find what altitude the Sun will be of, when he cometh upon the true East or West point.
PROBLEM VII. Having the Suns greatest declination, and his di∣stance from the next Equinoctial point; to find his right ascension.
PROBLEM VIII. The Suns greatest declination, and his present de∣clination, being given for a time; to find his right ascension for that time.
PROBLEM. IX. The Latitude of the place, and the Suns declination known; to find how long the Sun riseth and set∣teth, before or after the hour of six.
PROBLEM. X. The Sun being in the Equinoctial, by knowing his distance from the Meridian, and the latitude of the place; to find the Suns altitude at that time.
PROBLEM XI. The latitude of the place, and the Suns declination Northwards being known; to find the Suns al∣titude, at the hour of six.
PROBLEM. XII. The Latitude and declination of the Sun being known; to find the Suns Azimuth at the hour of six, from the North part of the Meridian.
PROBLEM XIII. The Latitude of the place, and the Suns altitude at the point of his being due East or West; to find the hour and minute when he will be so due East or West.
PROBLEM XIV. The elevation of the Pole, the Suns (or a Stars) declination, and distance from the Meridian for any time being given; to find the Suns al∣titude at that time.
PROBLEM XV. Having the Poles elevation, and the Suns declina∣tion; to find the ascensional difference.
PROBLEM XVI. Having any Planets declination and Latitude, with its distance from the next Equinoctial point; to find its right ascension.
PROBLEM XVII. The Suns greatest declination, with his distance from the next Equinoctial point, being had; to find the Meridian angle, that is, the intersection of the Meridian with the Ecliptick.
PROBLEM. XVIII. The Suns declination and amplitude given; to find the heigth of the Pole.
PROBLEM. XIX. The amplitude of the Sun, and time of his rising being known; to find thereby his declination.
PROBLEM. XX. Having the elevation of the Pole, and the Suns amplitude; to find his declination.
PROBLEM. XXI. Having the hour of the day, the Suns nltitude and declination; to find the Azimuth.
PROBLEM XXII. The Suns declination, altitude, and azimuth being known; to find the hour of the day.
PROBLEM XXIII. The altitude of the Equator, and the Suns, or a Stars declination being given; to find the angle of the Meridian with the Horizon.
CHAP. IX. The Ʋse of the double Scales in Geo∣graphy.
PROBLEM I. Two places lying without the Equinoctial, and ha∣ving both one Latitude, differing onely in Lon∣gitude, being propounded; to find their Di∣stance.
PROBLEM. II. Two places being propounded, which differ in Lon∣gitude, the one lying under the Equinoctial, and the other having Latitude, to find their distance in miles.
PROBLEM. III. Two places having several Latitudes towards one Pole, and differing in Longitude; to find their distance.
PROBLEM IV. Two places, one having North Latitude, and the other South Latitude, and differing in Longi∣tude; to find their distance.
CHAP. X. Of plain right lined Triangles.
PROBLEM. I. In a plain right lined Triangle, right angled, the three angles being known, and one side; to find either of the other sides.
PROBLEM. II. In a plain right lined Triangle oblique angled, the three angles and one side being known; to find either of the other sides.
PROBLEM. III. If two sides of a right lined Triangle, and an Angle opposite to one of them sides being known; to find the angle opposite to the other side.
PROBLEM. IV. Two sides, and the angle included between them, be∣ing a right angle; to find the other two angles.
PROBLEM. V. In any oblique angled Triangle, whether obtuse or acute, having two sides, and the angle inclu∣ded between them; to find the other angles.
PROBLEM. VI. In any right lined Triangle, whether right angled, or oblique angled, any two sides bing known, with the angle included between them; to find the third side.
PROBLEM VII. In a right lined Triangle, the three sides only be∣ing known; to find the Perpendicular, and there∣by the three angles.
PROBLEM VIII. In a right angled Triangle, the Angles and the Hypothenusal being given, to find any one of the sides including the right angle.
CHAP. XI. Of Trigonometria, shewing the use of the double Scales of Numbers, Sines and Tangents, in the resolu∣tion of Triangles, either plain or spherical.
part
PROBLEM. I. The two sides of a rectangled Triangle being given, to find the Base, which is the side opposite to the right angle.
PROBLEM II. The two sides being given, to find either of the ob∣lique angles.
PROBLEM III. One side, and the oblique angle next unto it being given; to find the Base.
PROBLEM IV. The Base, and one of the oblique angles being gi∣ven; to find the other oblique angle.
PROBLEM. V. The Base, and one of the oblique angles given; to find the side next the same angle.
PROBLEM. VI. The Base, and one of the oblique angles given; to find the side opposite to the angle given.
PROBLEM VII. One side, and the oblique angle next it being gi∣ven; to find the other side.
PROBLEM VIII. One side, and the oblique angle next it being known; to find the other oblique angle.
PROBLEM. IX. One side, and the angle opposite to it being known; to find the Base.
PROBLEM. X. One side, and the angle opposite to it being given; to find the other side.
PROBLEM XI. One side, and the angle opposite to it being known; to find the other angle.
PROBLEM. XII. The Base, and one side known; to find the oblique angle adjoyning to the same side.
PROBLEM XIII. The Base, and one side being given; to find the an∣gle opposite to the same side.
PROBLEM. XIV. The Base, and one side being given; to find the other side.
PROBLEM. XV. The two oblique angles being given, to find the Base.
PROBLEM. XVI. The two oblique angles being given; to find either of the sides.
In Oblique angled spherical Triangles.
PROBLEM XVII. Two angles, and a side opposite to one of them be∣ing given; to find the side opposite to the other.
PROBLEM XVIII. Two sides, and an angle opposite to one of them being known; to find the angle opposite to the other of them.
PROBLEM. XIX. Two sides, and the angle includd between them, being known; to find the other side opposite to that angle.
PROBLEM XX. Two sides, with the angle included between them, being given; to find either of the other angles.
PROBLEM. XXI. Two sides, and one angle next to the side sought be∣ing given; to find the same side.
PROBLEM XXII. Two sides, and an angle adjacent to one of them being given; to find the angle included be∣tween the same sides.
PROBLEM XXIII. Two angles, with the side lying betwixt them being known; to find either of the other sides.
PROBLEM. XXIV. Two angles, with the side lying betwixt them being given, to find the third angle.
PROBLEM. XXV. Two angles, and a side opposite to one of them being given; to find the side adjacent to both the angles.
PROBLEM. XXVI. Two angles, and a side opposite to one of them be∣ing known; to find the third angle.
PROBLEM. XXVII. The three sides being given, to find any one of the angles.
PROBLEM. XXVIII. The three angles being onely known, to find any of the sides.
diagrams
CHAP. XII. The Ʋse of the Instrument in Navi∣gation.
PROBLEM I. Two places being propounded, the one under the Equinoctial, and the other without; to find their Meridional Difference.
PROBLEM. II. Two places having both Northerly, or both South∣erly Latitude; to find their Meridional Dif∣ference.
PROBLEM. III. Two places being situate, the one Southerly, and the other Northerly; to find the Meridional Difference.
PROBLEM IV. The Latitude of two places, and their Difference of Longitude being known; to find the Rumb leading from the one to the other.
PROBLEM. V. The Latitudes of two places being given with the Rumb; to find the distance upon the Rumb.
PROBLEM VI. The Latitudes of two places, and their distance being known; to find the Rumb leading from one to the other.
PROBLEM VII. The Latitude of the place from whence you go, the Rumb you go upon, and the distance gone, being given; to find the Difference of Latitude, and thereby the Latitude of the place you are in.
PROBLEM VIII. The Latitude of the place you are in, and the La∣titude of the place you went from, with the Rumb being given; to find the Difference of Longi∣tude.
PROBLEM. IX. In any Parallel of Latitude, to find how many leagues answer to one degree of Longitude in that Parallel.
PROBLEM X. To find how many miles answer to many degrees of Longitude in any Parallel.
PROBLEM XI. Upon any Rumb proposed, to find how many leagues do answer to one degree of latitude in the Me∣ridian, or of any great circle.
CHAP. XIII. The Ʋse of the double Scales of Sines and Tangents on the Instrument, in Dialling.
PROBLEM. I. To find the distance of the hours from the Line of twelve a clock, in Horizontal Dials, made for an oblique Sphere.
PROBLEM II. A Dial being made, and the Elevation for which it was made not being known; to find for what Latitude it is made.
PROBLEM III. To find the distances of the hourlines, from the line of 12 a clock in a direct South Dial, for any Elevation propounded.
PROBLEM. IV. In a vertical Dial inclining, having the Eleva∣tion of the Pole above the Plane; to find the distance of the hourlines from the hourline of 12 a clock.
PROBLEM. V. In any erect declining Dial, to find the distance of the Styll from the Substyll, and of the Substyll from the Meridian.
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