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Author: Sturmy, Samuel, 1633-1669.
Title: The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.
Series: Early English books online text creation partnership. Navigations series.
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Print source: The mariners magazine, or, Sturmy's mathematical and practical arts containing the description and use of the scale of scales, it being a mathematical ruler, that resolves most mathematical conclusions, and likewise the making and use of the crostaff, quadrant, and the quadrat, nocturnals, and other most useful instruments for all artists and navigators : the art of navigation, resolved geometrically, instrumentally, and by calculation, and by that late excellent invention of logarithms, in the three principal kinds of sailing : with new tables of the longitude and latitude of the most eminent places ... : together with a discourse of the practick part of navigation ..., a new way of surveying land ..., the art of gauging all sorts of vessels ..., the art of dialling by a gnomical scale ... : whereunto is annexed, an abridgment of the penalties and forfeitures, by acts of parliaments appointed, relating to the customs and navigation : also a compendium of fortification, both geometrically and instrumentally / by Capt. Samuel Sturmy.
Sturmy, Samuel, 1633-1669.
London: Printed by E. Cotes for G. Hurlock, W. Fisher, E. Thomas, and D. Page ..., 1669.
URL: https://name.umdl.umich.edu/A61915.0001.001
How to cite: For suggestions on citing this text, please see Citing the TCP on the Text Creation Partnership website.

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title page
To the most August and Most Serene MAJESTY OF CHARLES II. King of Great-Britain, France, and Ireland, Defender of the Faith, &c.
To the Honourable SOCIETY of MERCHANT-ADVENTURERS Of the CITY of BRISTOL. TO THE MASTER, WARDENS, and ASSISTANTS OF THE SAID SOCIETY. To my Honoured Friends Sir Robert Cann and Sir Robert Yeomans, Knights and Baronets, Sir Humfry Hooke, Sir Henry Creswick, Sir John Knight, and Sir Thomas Langton, Knights, John Willoughby and John Knight, Esquires.
To my much Honoured Patron, Sir JOHN SHAW Knight and Baronet: And to the rest of the Honourable FARMERS OF HIS MAJESTIES CUSTOMS, Sir John Wolstenholme, Sir Robert Vyner Knights and Baronets; Sir Edmond Turner Knight, Edward Backwell and Francis Millington Esquires. External, Internal, and Eternal Happiness be wished.
TO THE Courteous Reader.
To his Ingenious and Industrious Friend Capt. SAMUEL STURMY. A double Acrostick.
To His Worthy Friend the Author Captain SAMUEL STURMY. On his BOOK Entituled, The MARINER'S MAGAZINE.
To his Judicious Friend the Author Capt. SAMUEL STURMY, ON HIS MAGAZINE of ARTS.
In Praise of his Dear Friend the Author, for his ART, Capt. SAMUEL STURMY.
The AUTHOR to HIS BOOK.
THE AUTHOR'S COMPLAINT.
AN INDEX, SHEWING, The CONTENTS of the SEVEN BOOKS OF THE MARINER'S MAGAZINE.
TO THE Truly Industrious, and Highly Deserving of English-men Captain SAMUEL STURMY. On his Excellent and Elaborate Treatise, Entituled, THE MARINERS MAGAZINE, &c.
A FRIENDLY ADVERTISEMENT TO THE Navigators and Mariners of ENGLAND.
ERRATA.
In the First, Second, Third, and Fourth Books.
In the Fifth and Sixth Books.
In the Seventh Book.
notice
THE AUTHOR Implores Aid of GOD'S EVERLASTING FOUNTAIN.
scale
The Compleat MARINER, OR NAVIGATOR. The First Book.
CHAP. I. The Argument or Description of the Art of Navigation in general.
CHAP. II. Of what is needful first to be known in the Practick Part of the Compass, and how to divide the Circles and Parts.
How to divide the Circles of the Mariners Compass.
The Moons Motion, and the Ebbing and Flowing of the Sea.
A Ʋseful Variation-Compass.
PROPOSITION I. The Moon being 16 days old, I demand upon what Point of the Compass she will be at 8 of the Clock at night.
proposition 6
PROPOSITION VII. The Moon being 16 days old, I demand, What a Clock it will be Full-Sea at Bristol, Start-point, Waterford, where an East-by-South Moon on the Change-day makes the Full-Sea?
PROPOSITION VIII. The Moon being 16 days old, I desire to know at what hour it will be Full Sea at London, Tinmouth, Amsterdam, and Rotterdam, where a S. W. and N. E. Moon makes a Full-Sea upon the Change-day.
PROPOSITION IX. At Yarmouth, Dover, and Harwich, where a S. S. E. Moon maketh Full-Sea on the Change-day, the Moon being 9 days old, I demand the time or hour of Full-Sea that day in the aforesaid Places.
PROPOSITION X. At St. Andrews, Dundee, Lisbone, and St. Lucas, where a South-West-and-by-South Moon makes High-Water or Full-Sea on the Change-day; The Moon being 28 days old, I demand the time of Full-Sea that day in these Places.
How to find the Golden Number or Prime, according to the Julian, English, or Old Account.
How to find the Epact, according to the Julian, English, or Old Account, and what it proceedeth from.
A Rule to find the Change, Full, and Quarters of the Moon.
How to finde the Age of the Moon at any time for ever.
To finde what Sign the Moon is in, by which is gathered, what the Moon differeth from the Sun.
How to find what Sign the Moon is in more exact; with the Moon's Motion for every day of her Age.
To know the time of the Moon's Rising, Southing, and Setting.
PROP. I. How to find when it is Full-Sea in any Port, Rode, Creek, or River.
PROP. II. The Moon 16 days old, I demand, What a Clock it will be Full-Sea at Bristol, Start-point, and Waterford, where E. b. S. Moon maketh Full-Sea on Change-day?
PROP. III. The Moon being 25 days old, I demand, What a Clock it will be Full-Sea at London, Tinmouth, Amsterdam, and Rot∣terdam, where it flows S. W?
PROP. IV. The Moon being 9 days old, I desire to know the hour of Full-Sea at Quinborough, Southam. and Portsmouth.
PROP. V. The Moon 5 days old, I demand the time of Full-Sea at Rochester, Malden, Blacktail, where S. b. W. Moon is Full-Sea.
PROP. VI. The Motion of the Moon, and the Proportion of Time betwixt Tyde and Tyde.
THE Mariners Magazine; OR, STURMY's Mathematical and Practical ARTS. The Practick Part of Navigation, in working of a Ship in all Weathers at Sea.
PROP. I. The Wind is fair.
Right afore the Wind, and a fresh Gale.
The wind vereth forward, and scanteth.
The wind blows Frisking.
It bloweth a Storm.
A very hollow grown Sea.
The Storm is over, let us turn to Windward.
The Man of War in her Station.
THE GEOMETRICAL DEFINITIONS.
I. A Point is that which hath no Parts.
II. A Line is a supposed Length, with∣out Breadth or Thickness.
III. The Ends or Bounds of a Line are Points.
IV. A Right Line is the shortest of all Lines, drawn from any two of the said Points,
V. A Superficies is a Longitude, having only Latitude.
VI. The Extremes of a Superficies are Lines.
VII. A Plain Superficies lieth equally between his Lines.
VIII. An Angle is when two Lines are extended upon the same Superficies, so so that they touch one another in a Point, but not directly.
IX. A Right Angle is that which is produced of a Right Line, falling upon a Right Line, and making two equal Angles on each side the Point where they touch each other.
X. An Obtuse Angle is that which is greater than a Right Angle.
XI. An Acute Angle is less than a Right Angle.
XII. A Limit or Term is the End of every Thing.
XIII. A Figure is that which is contained under one Limit or Term, or many.
XIV. A Circle is a plain Figure contained under one Line, which is called a Circumference; unto which all Lines drawn from one Point within the Figure, and falling upon the Circumference thereof, are equal one to the other.
XV. A Diameter of a Circle is a Right Line drawn by the Center thereof, and ending at the Circumference, on either side dividing the Circle into two equal Parts.
XVI. A Semicircle is a Figure contained under the Diameter, and that part of the Circumference cut off by the Diameter.
XVII. A Section or Portion of a Circle, is a Figure contained under a Right Line, and a part of the Circumference, greater or less than a Semicircle.
XVIII. Right-lined Figures are such as are contained under Right Lines.
XIX. Three-sided Figures are such as are contained under three Right Lines.
XX. Four-sided Figures are such as are contained under four Right Lines.
XXI. Many-sided Figures are such a• have more Sides than four.
XXII. All Three-sided Figures are called Triangles.
XXIII. Of Four-sided Figures, A Quadrat or Square is that whose Sides are equal, and his An∣gles right, as the Figure A.
XXIV. A Long Square is that which hath right An∣gles, but unequal Sides, as the Figure B.
XXV. A Rhombus is a Figure Quadrangular, having equal Sides, but not equal or right Angles, as the Figure C.
XXVI. A Rhomboides is a Figure whose opposite Sides are equal, and whose opposite Angles are also equal: but it hath neither equal Sides, nor equal Angles, as the Figure D.
XXVII. All other Figures of Four Sides are called Trapezia's.
XXVIII. Such are all of Four Sides, in which is ob∣served no equality of Sides or Angles, as the Figures L and M, which have neither equal Sides nor Angles, but are described by all Adventures, without the observa∣tion of any Order.
XXIX. Parallel or Aequi-distant Right Lines, are such which being in one and the same Superficies, and produced infinitely on both sides, do never in any part concur; as you may see by the two Lines AB, CD.
XXX. A Solid Body is that which hath Length, and Breadth, and Thickness, as a Cube or Die; and the Limits and Extremes of it are Superficies, as the Figure I.
XXXI. Axis is the Diameter about which the Sphere or Globe is turned.
XXXII. The Poles of a Sphere are the Extremes or Ends of the Diame∣ter, and are terminated in the Superficies of the Sphere.
XXXIII. A Sphere is defined by Euclid to be made, when the Diameter of a Semi-circle remaining fixed, the Semicircle is turned about, till it be returned to the Place whence it began to move at first.
Geometrical Theoremes.
Geometrical Problems.
PROBLEM I. Ʋpon a Right Line given, how to erect another Right Line which shall be perpendicular to the Right Line given.
PROBL. II. How to erect a Perpendicular on the end of a Right Line given.
PROBL. III. How to let fall a Perpendicular upon any Point assigned, upon a Right Line given.
PROBL. IV. How to make an Angle equal to an Angle given.
PROBL. V. A Right Line being given, how to draw another Right Line which shall be parallel to the former, at any distance required.
PROBL. VI. To divide a Right Line into any number of equal Parts.
PROBL. VII. A Right Line being given, how to draw another Right Line parallel thereunto, which shall also pass through a Point assigned.
PROBL. VIII. Having any three Points given which are not scituated in a Right Line, How to find the Center of a Circle which shall pass directly through the three Points given.
PROBL. IX. How to describe a Circle in a Triangle, that shall only touch the three Sides; and to find the Centre.
PROBL. X. How to lay down a Triangle in a Circle, and to find the Center of the Circle in the Triangle.
PROBL. XI. Any three Right Lines being given, so that the two shortest together be longer than the third, To make thereof a Triangle.
PROBL. XII. Having a Right Line given, How to make a Geometrical Square, whose Sides shall be equal to the Right Line given.
PROBL. XIII. Two Right Lines being given, How to find a third which shall be in pro∣portion unto them.
PROBL. XIV. Three Right Lines being given, To find a fourth in proportion to them.
PROBL. XV. How to work the Rule of Proportion by a Scale of equal Parts, and such other Conclusions as are usually wrought in Lines and Numbers, as in Mr. Gunter's 10 Prob. 2 Chap.
PROBL. XVI. To divide a Right Line given, into two parts, which shall have such pro∣portion one to the other as two given Right Lines.
PROBL. XVII. How to divide a Triangle into two parts, according to any proportion as∣signed, by a Line drawn from any Angle thereof; and to lay the les∣ser part unto any Side assigned.
PROBL. XVIII. The Base of the Triangle being known, To perform the foregoing Problem Arithmetically.
PROBL. XIX. How to divide a Triangle (whose Area or Content is known) into two Parts, by a Line drawn from an Angle assigned, according to any Proportion required.
PROBL. XX. How to divide a Triangle given into two parts, according to any Propor∣tion assigned, by a Line drawn from a Point limited in any of the Sides thereof; and to lay the greater or lesser part towards any Angle assigned.
PROBL. XXI. To perform the foregoing Problem Arithmetically.
PROBL. XXII. How to divide a Triangle (whose Area or Content is known) into two Parts, by a Line drawn from a Point limited, into any Side thereof, according to any number of Acres, Roods, and Perches.
PROBL. XXIII. How to divide a Triangle according to any Proportion given, by a Line drawn parallel to one of the Sides given.
PROBL. XXIV. To perform the foregoing Problem Arithmetically.
PROBL. XXV. To divide a Triangle of any known Quantity into two Parts, by a Line Parallel to one of the Sides, according to any Number of Acres, Roods, and Perches.
PROBL. XXVI. From a Line given, To cut off any Parts required.
PROBL. XXVII. To find, a Mean Proportional between two Lines given.
PROBL. XXVIII. How to finde two Lines, which together shall be equal in Power to any Line given; And in Power the one to the other, according to any Propor∣tion assigned.
PROBL. XXIX. How to divide a Line in Power according to any Proportion given.
PROBL. XXX. How to enlarge a Line in Power, according to any Proportion assigned.
PROBL. XXXI. To enlarge or diminish a Plot given, according to any Proportion required.
PROBL. XXXII. How to make a Triangle which shall contain any Number of Acres, Roods, and Perches, and whose Base shall be equal to any (possible) Num∣ber given.
PROBL. XXXIII. How to reduce a Trapezia into a Triangle, by a Line drawn from any Angle thereof.
THE Mariners Magazine; OR, STURMY's Mathematical and Practical ARTS. The Second Book.
The ARGUMENT.
A DESCRIPTION OF INSTRUMENTS. CHAP. I. Of Instruments in general.
The Scale of Longitude.
SINES.
TANGENTS.
A SECANT.
Versed Sines.
CHAP. II. A Description of what Instruments of Brass, Steel, Iron, and Wood, you must be provided with before you can make Instruments for Mathe∣matical Uses.
CHAP. III. The Explanation of the other half of the former Semicircle; being a De∣scription of the Fundamental Diagram, of the Dialling-Scale on the Ma∣thematical Ruler.
How to make the Diagram.
CHAP. IV. The Scales or Lines on the Back-side of the Mathematical Ruler, are these: A Line of Numbers, A Line of Artificial Tangents, A Line of Sines, A Meridian Line according to Mercator's or Mr. Wright's Projection; and the Scale of Equal Parts, by which the Numbers were taken off for the Graduating these Scales; and a Line of Longitude or Equinoctial, with a Scale of Reduction, as followeth.
part 1
II. How to make the Line of Artificial Tangents on the Ruler.
III. A Table for the Division of the Line of Artificial Tangents to 45 Deg. and the Minutes fit to be set thereon.
IV. How to make the Scale or Line of Artificial Sines to 90 Deg. and Minutes fit to be set thereon.
V. How to make a Meridian Line according to the true Sea-Chard, or Mercator and Mr. Wright's Projection.
VI. How to Calculate a Table, and by it how to take out the Numbers, and make a Scale of Reduction, to be used in Surveying of Land.
CHAP. V. A Table for the Division of the Artificial Rhomb, or Points, Halfs, and Quarters on the Travis-Scale.
The Description of the Travis-Scale.
CHAP. VI. How to make a Quadrant which will resolve many Questions in Astrono∣my, by the help of an Index; and also very useful in Navigation.
The Use of the Quadrant in Astronomy.
SECT. I. Having the Latitude of the Place of the Sun's Declination, It is required to find the Time of the Sun-Rising and Setting.
SECT. II. Having the Latitude of the Place, and the Distance of the Sun from the next Aequinoctial Point, To find the Amplitude.
SECT. III. Having the distance of the Sun from the next Aequinoctial Point, To find his Declination.
SECT. IV. Having the Latitude of the Place, and the Declination of the Sun, To find the Sun's true Amplitude from the true East and West.
SECT. V. The Ʋse of the Quadrant and Variation-Compass in the First Book, on the Instrument of the Moon for shifting of Tydes.
SECT. VI. To know the Variation by the Quadrant.
SECT. VII. To finde the Number of Miles answering to one Degree of Longitude, in each several Degree of Latitude.
I. To find how many Leagues do answer to one Degree of Latitude, in every several Rhomb.
II. By one Latitude, Rhomb, and Distance, To find the difference of Latitudes.
III. By the Rhomb and both Latitudes, To find the Distance upon the Rhomb.
IV. By the distance and both Latitudes, To find the Rhomb.
V. By the difference of Meridians, and Latitude of both Places, To find the Rhomb.
VI. By the Rhomb and both Latitudes, To find the difference of Longi∣tude, or departure from the Meridian.
CHAP. VII. How to make a most Ʋseful Protractor.
CHAP. VIII. The Projection of the Nocturnal.
The Ʋse of the Nocturnal.
CHAP. IX. How to use the Pole-Star's Declination and Table, and thereby to get the Latitude.
CHAP. X. How to make a most Ʋseful Instrument of the Stars, and by it to know most readily when any of 31 of the most notable Stars will come to the Meridian, what Hour of the Night, at any time of the Year, at the first sight.
How to know the Hour of the Night any Star comes to the Meridian in any Latitude.
How to know what Stars are in Course at any time or Day of the Year.
How to know the Hour of the Night, by the Stars being on the Meridian.
CHAP. XI. Of the Crosiers.
CHAP. XII. How to make the Cross-Staff.
CHAP. XIII. How to use the Cross-Staff.
To Work your Observation.
Rules for Observation in North Latitude.
Rules for Observation in South Latitude.
Rules for Observing the Stars.
CHAP. XIV. A Description of the Back-Staff or Quadrant.
The Ʋse of the Back-Staff or Quadrant.
Observe these Rules for North Latitude.
Directions for Observation in South Latitude.
The Ʋse of the Fore-Staff in South Latitude for the Sun and Stars.
CHAP. XV. Directions for Observing the Stars.
CHAP. XVI. The Description and Ʋse of the most Ʋseful Quadrant for the taking Alti∣tudes on Land or Sea, of the Sun or Stars, backwards or forwards, or any other Altitude of Hills, Trees, Steeples, or Castles, or any thing what∣ever.
PROPOSITION I. For Back-Observation at Sea.
PROP. II. Any Point being given, To find whether it be level with the Eye, or not.
PROP. III. To find the Height of an House, Steeple, Tower, or Tree, from the Ground, at one Observation; and the length of the Ladder which will Scale it.
PROP. IV. The Distance being given, To find the Altitude.
PROP. V. The Distance being given, To find the Distance from the Eye to the top of the Tower.
PROP. VI. Some part of the Distance being given, To find the Distance from the Eye or Hypotenuse.
PROP. VII. Some part of the Distance being given, To find the Altitude.
PROP. VIII. To do the same thing by the Quadrant, and Scale of Equal Parts, another way.
PROP. IX. Part of the Distance being given, To find the Remainder of the Distance.
PROP. X. By the Height of the Sun, and the Length of the Shadow, To find the Height of any Tree, Tower, or Steeple.
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THE Mariners Magazine; OR, STURMY'S Mathematical and Practical ARTS. The Third Book.
CHAP. I. Of the Nature and Quality of Triangles.
CHAP. II. Containing the Doctrine of the Dimensions of Right-Lined Triangles, whether Right-Angled or Oblique-Angled; and the several Cases therein resolved, both by Tables, and also by the Lines of Artificial Num∣bers, Sines, and Tangents.
Of Right-Angled Plain Triangles.
CASE I. In a Right-Angled Plain Triangle, The Base and the Angle at the Base being given, To find the Perpendicular.
A GENERAL RULE.
To resolve the same Work by the Line of Sines and Numbers.
CASE II. The Base and the Angle at the Base being given, To find the Hypothenusa.
By the Line of Numbers and Sines.
CASE III. The Hypothenusal and Angle at the Base being given, To find the Perpendicular.
By the Line of Sines and Numbers.
CASE IV. The Hypothenusal and Angle at the Base being given, To find the Base.
By the Line of Sines and Numbers.
CASE V. Let the Perpendicular be the Difference of Latitude 253 Leagues, and the Angle at C, S. W. b. W. 1 deg. 45 min. Westerly, or 58 deg. Let it be given to find the Hypothenusal or Distance upon the Rhomb.
By the Line of Numbers.
CASE VI. The Hypothenusal or Distance Sailed, and the Perpendicular or Diffe∣rence of Latitude given, To find the Rhomb or Angle ABC.
By the Line of Numbers.
CASE VII. The Hypothenusal, and the Parallel of Longitude, and the Radius given, To find the Rhomb or Course Sailed.
By the Lines of Sines and Numbers.
Of Oblique-Angled Plain Triangles.
CASE VIII. Having two Angles, and a Side opposite to one of them, To find the Side opposite to the other.
By the Line of Sines and Numbers.
By the Line of Numbers and Sines.
CASE IX. Two Sides, and an Angle opposite to one of them being given, To find the Angle opposite to the other.
By the Line of Sines and Numbers.
CASE X. Having two Sides, and the Angle contained between them given, To find either of the other Angles.
By the Line of Sines and Numbers.
CASE XI. Two Sides and their Containing Angle given, To find the third Side.
By the Line of Sines and Numbers.
CASE XII. Three Sides of an Oblique Triangle being given, To find the Angles.
By the Line of Sines and Numbers.
book 4
THE AUTHOR TO HIS Fourth Book.
THE Compleat Sea-Artist; OR THE ART OF NAVIGATION. The Fourth Book. CHAP. I. Of Sailing by the Plain Chard, and the Ʋncertainties thereof; And of Navigation.
The First Proposition. Questions of Sailing by the Plain, Ordinary Sea-Chart.
I. Sailing 57 Leagues upon the first Rhomb, How much shall I alter my Parallel of Latitude?
By the Traverse-Scale.
By the Artificial Sines and Numbers on the Ruler.
By the Tables of Artificial Sines and Numbers, by the Fourth Case of Plain Triangles.
II. Sailing 57 Leagues upon the first Rhomb, How far am I de∣parted from the Meridian of the Place from whence I came?
By the Traverse-Table.
By the Traverse-Scale.
By the Tables of Sines and Numbers, by the Fourth Case of Plain Triangles.
By the Artificial Lines on the Ruler.
III. Sailing upon the fifth Rhomb, until I alter my Latitude 1 deg. 35 min. I demand how far I have Sailed?
By the Line of Sines and Numbers.
IV. Sailing upon the fifth Rhomb, until I have altered my Latitude 31 67/100, or 1 deg. 35 min. How much am I departed from my first Meridian?
By the Traverse-Table.
By the Line of Sines and Numbers.
By the fourth Case of Plain Triangles.
V. Sailing upon some Rhomb between the South and the West 57 Leagues, and finding I have altered my Latitude 1 deg. 35 m. I demand upon what Point I have sailed.
By the Traverse-Table.
By the Line of Sines and Numbers on the Scale.
By the fifth Case of Plain Triangles.
VI. Sailing upon some Rhomb between the South and the West 57 Leagues, and finding I have altered my Latitude 1 deg. 35 min. I demand my Departure from my first Meridian.
By the Traverse-Table.
By the Sixth Case of Plain Triangles.
By the Line of Numbers.
CHAP. II. What must be observed by all that keep Account of a Ship's Way at Sea; And to find the true Point of the Ship at any time, according to the Plain Chart.
CHAP. III. A Formal and Exact Way of Setting down and Perfecting a Sea-Reckoning.
CHAP. IV. How to Correct the Account, when the Dead Latitude differs from the Observed Latitude.
The First EXAMPLE.
RULE II.
By the Traverse-Scale.
RULE III.
By the Traverse-Scale.
The Fourth PRECEPT, CASE, or EXAMPLE.
By the Traverse-Scale.
CHAP. V. How to allow for known Currents, in Estimating the Ship's Course and Distance.
QUESTION I. A Ship Sails 40 Leagues more than her Difference of Latitude, and is departed from the Meridian 80 Leagues, I demand her Diffe∣rence of Latitude.
QUEST. II. A Ship Sails 20 Leagues more than her Difference of Latitude, and but 10 Leagues more than her Departure from the Meridian, I demand her Distance Sailed.
QUEST. III. Two Ships Sail from one Port; The first Ship Sails directly South, the second Ship Sails W. S. W. more than the first by 35 Leagues, and then were asunder 76 Leagues; The Question is, How ma∣ny Leagues each Ship Sailed.
By the Artificial Tables of Sines and Numbers.
QUEST. IV. Two Ships Sailed from one Port: The first Sails S. S. W. a certain Distance; then altering her Course, she Sails due West 92 Leagues: The second Ship Sailing 120 Leagues, meets with the first Ship. I demand the second Ship's Course and Rhomb, and how many Leagues the first Ship Sailed S. S. W.
QUEST. V. Two Ships Sail from one Port 7 Points asunder: The one Sails in the S. W. Quadrant, and departs from the Meridian 57 Leagues; and the other Sailed in the S. E. Quadrant, and was departed from the Meridian but 25 Leagues, and then are both fallen into one Latitude; I demand the Rhomb or Courses of each Ship.
QUEST. VI. From the Port at A I Sail S. S. W. unto B, and from B I Sail N. W. b. W. unto C, and from C I Sailed unto my first Port at A, E. b. N. Now having Sailed in all 120 Leagues, I would know how many Leagues I have Sailed upon each Point.
Arithmetically, By the Table of Natural Sines in the Sea-mans Kalendar.
CHAP. VII. The Disagreement betwixt the Ordinary Sea-Chart, and the Globe; And the Agreement betwixt the Globe and the True Sea-Chart, made after Mercator's Way, or Mr. Edward Wright's Projection.
PROBLEM I. How to find by the following Tables what Meridional Parts are con∣tained in any Difference of Latitude.
PROBL. II. The Latitudes of two Places being given, and Difference of Longi∣tude of both Places, To find the Rhomb and Distance.
By the Tables.
Therefore, By the Second Case of Plain Triangles.
By the Fifth Case of Plain Triangles.
PROBL. III. The Latitude of two Places, and their Distance given; To find the true Course and Point, or Place you are in, by Mercator's Chart.
Secondly, For the Difference of Longitude.
PROBL. IV. Sailing 1154 Leagues upon the 4 ¼ Rhomb from the Meridian, or 48 deg. 33 min. from the South Westerly, I demand the Departure from the Meridian.
PROBL. V. Both Latitudes and the Meridian Distance of two Places being given, To find the Difference of Longitude, and Course and Distance on the True Sea-Chart.
By the Line of Numbers.
By the Artificial Lines on the Scale.
By the Scale.
PROBL. VI. By the Difference of Longitude, and one Latitude, and the Course, To find the other Latitude and Distance run.
By the Artificial Lines on the Scale.
PROBL. VII. By the Course and Distance, and one Latitude, To find the other La∣titude, and Difference of Longitude.
CHAP. VIII. How to divide a Particular Sea-Chart, according to Mercator and Mr. Wright's Projection.
CHAP. IX. The Projection of the Meridian-Line by Geometry, and how to make a Scale of Leagues for to measure Distances in any Latitude.
How to make the Scale of Leagues.
CHAP. X. The Way of Sailing by a Great Circle.
CHAP. XI. How to find the true Distance of Places, one of them having no Latitude: The other having Latitude and Difference of Longitude less than 180 Degrees, To find
The First Scituation.
problem 1
How to do these Questions Geographically.
By the Tables.
PROBL. II. How to find the Great Circle's greatest Latitude N. or S. or Obliquity.
The second Scituation.
PROBL. III.
How to do these Questions Geographically.
How to find the Obliquity.
PROBL. IV.
The Third Scituation. One Place having North Latitude, and the other Place having South La∣titude, of different Quantities, and the Difference of their Longitudes less than 90. As I omit one Place having North Latitude, as Lundy, 51 deg. 22 min. the other South Latitude, as the Rio de la Plata, 35 deg. 00 min. Difference of Longitude betwixt them 45 deg. 55 min. I demand the Distance, the Angle of Position, and the greatest La∣titude or Obliquity of the Great Circle that passeth over these two Places.
PROBL. V.
Geographical Questions. Two Ships being at Sea, their Difference of Longitude was 53 deg. Now upon a day they observed the Sun being between them; the North Ship found the Sun's Meridian Height 33 deg. and the South Ship 77 deg. the middle Latitude between them was 15 deg. North of the Aequi∣noctial Line: I demand the Angle of Position, and Distance from the North Ship to the South?
The Fourth Scituation.
PROBL. VII. The Latitude of two Places being given, together with the Difference of Longitude, To find,
CHAP. XII. How to describe the Globe in Plano, by the Mathematical Scale.
The Four Scituations that are in the Globe.
The First Scituation.
The Second Scituation.
The Third Scituation.
The Fourth Scituation.
CHAP. XIII. By Arithmetick how to Calculate exactly for any Degrees and Minutes of Obliquity; What Degree and Minute of Latitude the Great Circle shall pass through for any Degree and Minute of Longitude, from the Point of Obliquity, or of its Intersection with the Aequinoctial.
RULE I.
RULE II.
RULE III.
CHAP. XIV. How by the Scale of Tangents to make a Part of the Globe in Plano, where∣by you may trace out the Latitudes to every Degree of Longitude; or eve∣ry 5 or 10 Degrees, as neer as you will desire, without Calculation.
CHAP. XV.
RULE IV. By the Latitude, and Difference of Longitude from the Obliquity, to find the true Great Circle's Distance.
RULE V. By the Obliquity of the Great Circle, to find the true Latitude to any Quantity of a Great Circle's Distance, from the Point of his greatest Obliquity.
RULE VI. By the Great Circle's Distance from the Point of Obliquity, and the Latitude given; To find the Difference of Longitude betwixt the Place and the Meridian of greatest Obliquity.
RULE VII. By the Difference of Longitude from the Obliquity, and Latitude given; To find the Great Circle's Distance from the Point and Me∣ridian of greatest Obliquity.
RULE VIII. By the Great Circle's Distance from the Obliquity, and the Latitude given; To find the Rhomb.
RULE IX. To find how far a Man should sail upon a Rhomb, before he change his Course a Point Half a Point, or a Quarter of a Point.
RULE X. By the Great Circle's Distance, and the Difference of Latitude given; To find the Rhomb.
RULE XI. By the Rhomb, and Distance upon it given, To find the Difference of Latitude.
RULE XII. By the Obliquity of the Great Circle, and the Latitude given; To find the Difference of Longitude from the Meridian of Obliquity.
RULE XIII. By the Latitude, and Difference of Longitude from the Obliquity given; To find the Great Circles Distance from the Meridian of Obliquity.
RULE XIV.
RULE XV. By the Latitude, and Difference of Longitude given: To find the Di∣stance upon a Course of East or West.
RULE XVI. By the Difference of Latitude, and Rhomb sailed on; To find the Distance. You have it in the Fourteenth Rule before-going.
RULE XVII. By the Latitude, and Distance sailed upon an East or West Course, To find the Difference of Longitude; as 20 Leagues sailed in Latitude 51 deg. 22 min.
CHAP. XVI. How to make the most true Sea-Chart, and the Ʋse thereof in Mercator's and Great Circle Sailing, called a General Chart.
CHAP. XVII. How to keep a Sea-Journal, that so every Sea-man, Navigator, and Mari∣ner, may not be ashamed to shew their Account to any Artist, and by it benefit themselves and others.
By the Traverse-Scale.
CHAP. XVIII. A Description of the following Table of the Latitude and Longitude of Places, and the way how to find both.
A TABLE OF THE LONGITƲDE and LATITƲDE Of the most Notable Places, That is, HARBOURS, HEAD-LANDS, and ISLANDS OF THE WORLD. Newly Corrected, and Composed after a new manner, by beginning the said Longitude at the Meridian of the most Southern Port of England, the Lizard.
title page
frontispiece
The AUTHOR to his Fifth BOOK.
The ART of Surveying of Land By the SEA-COMPASS: The DESCRIPTION of the COMPASS, and STAFF, and CHAIN. The Fifth Book.
CHAP. I.
SECT. I. Mr. Gunter's Chain.
SECT. II. Cautions to be used, and to be observed in the use of any Chain.
SECT. III. How to reduce any Number of Chains and Links into Feet and Yards.
SECT. IV. How to cast up the Content of any piece of Land in Acres, Roods and Perches by Mr. Gunter's Chain.
SECT. V. How to Measure a Long Square Piece of Ground by a Chain of 20 Links to a Perch, according to Mr. Wing.
SECT. VI. To Measure a Long Square piece of Ground.
By the Line of Numbers.
SECT. VII. To Measure a Triangular Piece of Ground.
By the Line of Numbers.
SECT. VIII. To Measure a piece of Ground of Four unequal sides called a Trapezia.
By the Line of Numbers.
SECT. IX. To Measure a Piece of Ground which is a perfect Circle.
By the Line of Numbers.
SECT. X. To Measure a Ground being a true Oval.
By the Line of Numbers.
SECT. XI. To Measure a piece of Ground lying in form of a Sector of a Circle.
By the Line of Numbers.
SECT. XII. To Measure a piece of Ground that is a Segment, or part of a Circle.
By the Line of Numbers.
SECT. XIII. Having a Plot of Ground with the Content in Acres, To find how many Perch of that Scale was contained in one Inch, whereby it was Plotted.
By the Line of Numbers.
SECT. XIV. A Piece of Ground being measured by the Statute-Perch of 16 ½ Feet, To know how many Acres it is, it being measured by a Perch of 21 Foot, which is the Irish Perch.
By the Line of Numbers.
By the Line of Numbers.
CHAP. II. How to take the Plott of a Field at one Station taken in the middle thereof by the Azimuth-Compass.
Now by the Protractor in the Second Book described.
The manner how the Field-Book must be Ruled.
CHAP. III. How to take the Plott of a Field at one Station taken in any Angle thereof, by the Sea-Compass.
CHAP. IV. How to Measure any Piece of Ground be it never so Irregular; And how to reduce the Sides into Triangles or Trapezias, and to cast up the Content thereof in Acres and Perches.
CHAP. V. How to find the just Quantity or Content of any Piece of Ground in any Form.
CHAP. V. How to take the Height of any Island, or Mountain in the Sea by an Example made by the Author of the Height of Tenariff.
CHAP. VI. How to find the Distance of a Fort, or Walls of a City, or Castle, that you dare not approach for fear of Gun-Shot; Or the Breadth of a River or Water, that you cannot pass, or Measure over it, made by 2 Stations, with the Quan∣tity of the Angle at each Station.
SECT. I. How to take the Breadth of a River.
SECT. II. Being upon the Top of a Hill, Tower, Steeple, or a Ships Top-Mast-Head, there observing the Angle of distance from you, To find the true distance thereof.
SECT. III. By the way of your Ship, and any 2 Angles of Position, to find the Distance of any Island, Cape, or Head-Land from you.
CHAP. VII. How to take the Distance of divers places one from the other, remote from you, according their true Situation in Plano, and to rotract (as it were) a Mapp thereof by the Compass and Pplain-Scale.
The ART of Gaging of Vessels. CHAP. VIII. The Ʋse of the Line of Numbers, and the Lines on the Gaging Rod or Staff, and the Rules in Arithmetick in Gaging of all sorts of Vessels, (viz.) to Gage a Cube-Vessel, to Mea∣sure any Square-Vessel, and a Cylinder-Vessel; Also, Bar∣rels, Pipes, or Hogsheads; to Measure a Vessel part out, to Measure a Brewers-Tun, or a Mash-Fat, to Measure a Cone-Vessel, to Measure a Rising or Convex Crown; and also a Convex or Falling Crown in a Brewers-Copper; also a Brewers Oval Tun.
PROBL. I. The true Content of a Solid Measure being known, To find the Gage-Point of the same Measure.
PROBL. II. The Description of the Gaging-Rod, or Staff.
PROBL. III. The Description of Symbols of words for Brevity in Arithmetick.
PROBL. IV. How to Measure a Cubical Vessel.
For Beer or Ale by the Line of Numbers.
For Wine.
The Arithmetical way.
PROBL. V. How to Measure any Square Vessel.
By the Line of Numbers for Ale.
For Wine.
How to Work the same without the Gage-Point.
For Wine-Gallons.
The Mathematical way.
PROBL. VI. How to Measure a Cylinder Vessel.
For Wine.
The Arithmetical way.
PROBL. VII. How to Measure a Globe-Vessel.
For Ale.
For Wine.
The Arithmetical way.
PROBL. VIII. How to Measure a Barrel, Pipe, Butt, Punching, Hogshead, or small Cask.
Then for Ale.
For Wine.
The Arithmetical way.
Arithmetick thus.
By the Diagonal Line on the Rod or Staff.
PROBL. VIII. By the Line of Segments on the Rod or Staff, and also by a Table, How to find the Quantity of Liquor in a Cask that is part full.
Example.
The first Rule of Proportion.
Then again.
PROBL. IX. How to Measure a Brewers Tun, or a Mash-Fat.
By the Line of Numbers.
The Arithmetical way by the Mean-diameter.
Or thus for Barrels.
The truest Arithmetical way.
Or thus for Barrels.
PROBL. X. How to Measure a Cone-Vessel, such as is a Spire of a Steeple, or the like, by having the Height and the Diameter at the Base.
Then by the Line of Numbers for Barrels of Ale or Beer.
Then thus Work.
The Arithmetical way. For Gallons.
Or thus for Barrels.
An Example.
Work thus.
Now Working as before, for the Contents of each Cone.
PROBL. XI. How to Measure a Segment or portion of a Globe or Sphere, which serves for a Convex Signet or Rising, or Falling Crown in a Brewers Copper.
A Convex Rising Crown.
By the Line of Numbers.
The Arithmetical way for Ale or Beer-Gallons.
PROBL. XII. How to Reduce Ale-measure into Wine; And likewise to Reduce Wine-Gallons into Ale.
For Example.
The Proportion of the backward Rule of 3.
PROBL. XIII. How to Measure a Brewers Oval Tun.
A Brewers Oval Tun.
The Arithmetical way.
How to get the Mean-diameter by the Line of Numbers.
The Arithmetical way, as before, is thus.
By the Line of Numbers for Barrels.
PROBL. XIV. How to Gage a Vessel by Oughtred's Gage-Rule.
The Use is thus.
CHAP. IX. Wherein is shewed both Arithmetically and Instrumentally How to Measure exactly all kind of plain Superficies, as Walls, Timber-work, Roofs of Houses, Tyling, Board, Glass, Wainscot, Pavement, and the like; as also Timber and Stone.
PROBL. I.
As for Example.
The Arithmetical way for Perch.
PROBL. II. How to Measure Boards, Glass, Pavement, Wainscot, and the like.
How to Measure them.
For Example.
PROBL. III. The Mensurations of Solid Bodies of Timber and Stone, and first of Squared-Timber.
By the Line of Numbers.
The Arithmetical way.
For Example.
This is the absolute Arithmetical way.
PROBL. IV. How to find how many Inches in length will make one Foot of Timber, be∣ing alike in the Squares.
By the Line of Numbers.
The Arithmetical way.
By the Line of Numbers.
The Arithmetical way.
PROBL. V. How to Measure Round-Timber five several ways.
By the Line of Numbers.
By the Line of Numbers.
The Arithmetical way.
For Example.
How to Measure a Round piece of Tapering Timber.
PROBL. VI. How to Measure a Pyramedal piece of Timber.
By the Line of Numbers.
The Arithmetical way.
PROBL. VII. How to Measure a Conical piece of Timber.
The Arithmetical way.
CHAP. X. For the Burden of a Ship, or her Tunnage, Take these Rules following.
SECT. I.
SECT. II.
SECT. III. Having the Proportion of any one Ship in Burden, with the length of her Keel-Timbers; To Build another of any Burden according to that.
PROPORTION.
The Arithmetical way.
SECT. IV.
The Arithmetical way.
CHAP. XI. The Application of the Line of Numbers in Common Affairs, as in Reduction of Weight and Measure of Cheese, Butter, and the like.
CHAP. XII. The most Excellent Gunners Scale, Which resolves the Chief Principles of the whole Art of Gunnery, in a very brief and Compendious form, never by any set forth in the like nature before; with divers Excellent Conclusions both Arithmetical, and Geometrical, and Instrumental; and by Tables being framed both with, and without the help of Arithmetick. As also divers Artificial Fire-Works, both for Recreation, and for Sea and Land-Service.
SECT. I. The Qualifications every Gunner ought to have, and the Properties, Duty, and Office of a Gunner.
SECT. II. Who were the Inventors of Gun-powder, and some Principles of Philoso∣phy fit to be known.
SECT. III. The Description and Use of the Gunners Scale, upon which is all sorts of Ordnance, from the Canon, to the Base of their Weight, Lading, Shot, and all other things appertaining to them.
The Use of this side is thus.
As for Example.
As for Example.
The Description of the other side of my Gunner's Scale.
SECT. IV. The Ʋse of the Line of Numbers on the Scale, for the help of such as cannot Extract the Cube and Square-Root.
How by knowing the weight of one Bullet, to find the weight of another Bullet, the height being given.
The Arithmetical way.
By the Tables of Logarithms.
SECT. V. Admit the weight of an Iron Bullet being 30 pound, the Diameter was 6 Inches, the weight being 47 64/100 what may the Diameter be?
SECT. VI. The Geometrical finding the Diameter for the weight of any Shot assigned.
A second Geometrical way.
A third way.
SECT. VII. To find what proportion is between Bullets of Iron, Lead, and Stone, by knowing the weight of one Shot of Iron; to find the weight of any other Shot of Lead, Brass, or Stone of the like Diameter.
As for Example.
By the Rule of Proportion.
SECT. VIII. How by knowing the weight of one Piece of Ordnance, to find the weight of another Piece being of that very shape of the same Metal, or any other Metal.
Example.
The Arithmetical way.
Arithmetical way.
SECT. IX. How to make a Shot of Lead and Stone, the Stone being put in the Mould in which the Leaden Shot should afterwards be cast, to be of the like Dia∣meter and Weight as an Iron Shot is of.
SECT. X. How by knowing what quantity of Powder will load one Piece of Ordnance; to know how much will load any other Piece whatsoever.
The Arithmetical way.
The Arithmetical way.
How to make the true dispert of any true bored Piece of Ordnance.
As for Example.
Another way to Dispert any Piece.
A fourth way to Dispert a Piece of Ordnance.
SECT. XI. How to know whether your Piece be Chamber-bored.
SECT. XII. How to know what Diameter every Shot must be of to fit any Piece of Ord∣nance, or to choose Shot for Ordnance.
SECT. XIII. How to find what Flaws, Cracks, and Honey-combs are in Pieces of Ordnance.
SECT. XIV. How to find whether a Piece of Ordnance be true bored, or not.
SECT. XV. Of Iron Ordnance what quantity of Powder to allow for their Loading.
As for Example.
The Arithmetical way.
The Arithmetical way.
SECT. XVI. To know what quantity of Powder should be allowed to a Piece of Ordnance not truly bored.
The Arithmetical way.
SECT. XVII. How Moulds, Forms, and Cartredges, are to be made for any sort of Ordnance.
SECT. XVIII. How to make Ladles, Rammers; or Spunges for all sorts of Ordnance.
SECT. XIX. How the Carriage of a Piece should be made.
SECT. XX. To know whether the Trunnions of any Piece of Ordnance are placed right.
SECT. XXI. How much Rope will make Britchings and Tackles for any Piece.
SECT. XXII. What Powder is allowed for Proof, and what for Action of each Piece.
SECT. XXIII. The difference between the Common Legitimate Pieces, and the Bastard Pieces, and Extraordinary Pieces.
SECT. XXIV. How Powder is made, and several ways to know whether Powder be de∣cayed or no, by moisture or Age, in part, or in whole.
SECT. XXV. How to make an excellent good Match to give Fire to any Ordnance.
SECT. XXVI. How to make Powder it shall not wast with time, and preserve that as is good to keep it from decaying.
SECT. XXVII. To renew and make good again any sort of Gun-powder that hath lost its strength by long lying, or moisture, or any other means.
SECT. XXVIII. To make Powder of divers Colours, and first to make White Powder.
To make Red Powder.
To make any Coloured Powder.
SECT. XXIX. Of several sorts of Salt-peter, and a way how to make a sort of Salt-peter very excellent, with ease, and less cost than any way.
SECT. XXX. How to Load and Fire a Piece of Ordnance like an Artist.
SECT. XXXI. The difference of Shooting by the Metal, and by a Dispert by a Right Range, and at Random, by the Figures following.
SECT. XXXII. How to Order and Direct a Piece, and amend an ill Shot that was made, either by the Metal, Level, Right-line, or Advantage, or Mount.
SECT. XXXIII. Of Shooting upon the Advantage or Random, at a Mark, beyond the Right-line of the Pieces reach, or Right-range of the Shot, and of the Dead-range for every Degree.
Example.
SECT. XXXIV. How to make an effectual Shot out of a Piece of Ordnance at Random.
How to Mount your Piece by your Scalc and Quadrant thereon.
As for Example.
SECT. XXXV. How to find the Right-Line, or Right-Range of any Shot discharged out of any Piece, for every elevation by one Right or Dead-Range given for the Piece assigned.
As for Example.
Work by these Rules.
SECT. XXXVI. To know how much of the Horizontal-Line is contained directly under the Right-Line of any Shot called the Right-Range made out of any Piece at any Elevation assigned.
SECT. XXXVII. Of the violent, crooked, and natural Motion or Course of a Shot discharged out of any Piece of Ordnance assigned.
As for Example.
SECT. XXXVIII. How to make a Gunner's Rule, being an Instrument which will serve to ele∣vate a Piece of Ordnance with more facility than the Gunner's Qua∣drant.
SECT. XXXIX. How to Divide the Gunner's Rule into degr. by help of a Table, sitting it for any Piece from 5 foot long to 14 soot long; and by the help of this Table, any Piece may be Elevated to any degr. without the help of a Quadrant, Ruler, or any other Geometrical Instrument whatsoever.
SECT. XL. How to give Level to a Piece of Ordnance, with the Gunner's Rule at any Degree of Random.
SECT. XLI. How by the Table to give Level to a Piece of Ordnance, without the Gunner's Rule.
SECT. XLII. How to make a Shot at the Enemies Lights in a dark Night.
SECT. XLIII. How to make a perfect Shot at a company of Horse-men, or Foot-men passing by the place where Ordnance doth lie upon a Level-Ground; and also to make a good Shot at a Ship Sailing upon a River.
SECT. XLIV. How to cause the same quantity bosh of Powder and Shot, discharged out of the same Piece, to carry close, or more scattering.
SECT. XLV. How a Shot which sticketh fast within the Concavity of a Piece, that it can∣not be driven home unto the Powder, may be Shot out, without hurt to the Gunner, or hurt to the Piece.
SECT. XLVI. A Piece of Ordnance at the same Elevation, and towards the self-same place, with the like quantity of Powder and Shot, discharged several times, what difference there is in their Ranges.
SECT. XLVII. How to Weigh Ships sunk, or Ordnance under Water: or to know what empty Cask will carry any sort of Ordnance over a River.
SECT. XLVIII. How many Horses, Oxen, or Men will serve to draw a Piece of Ordnance.
SECT. XLIX. How Gunners may take a Plott of their Garrison, and every object near it.
OF ARTIFICIAL FIRE-WORKS, FOR Recreation, AND SEA and LAND-SERVICE. CHAP. XIII.
SECT. I. A Description of the Mortar-Piece, and how to make one of Wood, and Past-Board (for a need,) Brass and Iron ones being wanting.
To make the Mortar-Piece of Wood and Past-Board.
SECT. II. How to fit and prepare Granadoes for the Mortar-Piece.
How to make Fuses.
SECT. III. How to make Granadoes of Canvas for the Mortar.
SECT. IV. How Granadoes are to be Charged in a Mortar, and Fired.
SECT. V. How to make Hand-Granadoes to be hove by Hand.
SECT. VI. How to make Fiery-Arrows or Darts like Death Arrow-Heads.
SECT. VII. How to make Fire-pots of Clay.
SECT. VIII. How to make Powder-Chests.
SECT. IX. How to make Artificial Fire-Works for Recreation and Delight.
SECT. X. To make the Composition for Rockets of any size.
To fill the Rockets with this Composition.
To give Fire to one or two Rockets.
SECT. XI. How to make flying Serpents and Rockets that will run upon a Line, and return again.
SECT. XII. How to make Fire-Wheels, or as some call them Girondles.
SECT. XIII. How to make divers Compositions for Starrs.
SECT. XIV. How to make and use the Starrs.
SECT. XV. How to represent divers sorts of Figures in the Air with Rockets.
SECT. XVI. How to make Silver and Golden Rain, and how to use them.
SECT. XVII. How to make Fire-Lances.
SECT. XVIII. The manner how to make Balloons for the Mortar-Piece.
SECT. XIX. A most precious Unguent for any Burning.
The SALVES.
SECT. XX. Another Salve most Excellent.
TO Cap. SAMƲEL STƲRMY THE AUTHOR, For his Work and VVorth.
title page
THE Denomination of Eight and Forty Constellations of the Fixed STARS; OR, The Rudiments of ASTRONOMY, Put into plain RHYTHMES.
STƲRMY'S MATHEMATICAL and PRACTICAL ARTS The Sixth Book. Wherein is contained a Definition of the Circles of the Sphere, with the manner how to Resolve all the most necessary Propositions thereunto belonging, by a Line of Chords and Signs, or by Chords and Tangents; as also by Calculation by Tables.
CHAP. I.
Circles of the Sphere.
Of the Colures.
CHAP. II. The Projection of the Sphere in Plano, represented by the Analemma, and the Points and Circles before described.
CHAP. III. How to Calculate the Sun's true place.
PROBL. I.
Example.
2. Example.
As for Example.
Example.
Another Example.
Example.
PROBL. II. The Suns Distance from the next Equinoctial-point; and his greatest De∣clination being given, to find the Declination of any Point required.
PROBL. III. Having the Suns greatest Declination, and his Distance from the next Equi∣noctial-Point; to find his Right-Ascention.
Example 2.
Example 3.
Example 4.
PROBL. IV. The Elevation of the Pole, and Declination of the Sun being given; to find the Ascentional-Difference.
PROBL. V. The Suns Right-Ascention, and his Ascentional-difference being given; to find his Oblique-Ascention, and Descention.
PROBL. VI. To find the time of Sun-Rising, and Setting, with the length of the Day and Night.
PROBL. VII. The Elevation of the Pole, and Declination of the Sun being given; to find his Amplitude.
As for Example.
PROBL. VIII. Having the Latitude of the Place, and the Suns Declination, to find the time when the Sun cometh to be due East and West.
PROBL. IX. The Elevation of the Pole, and the Declination of the Sun being given; to find the Suns Altitude when he is due East and West.
PROBL. X. The Elevation of the Pole, and Declination of the Sun being given, to find the Suns Altitude at the Hour of Six.
PROBL. XI. Having the Latitude of the Place, and the Declination of the Sun given; to find the Suns Azimuth at the Hour of Six.
PROBL. XII. Having the Latitude of the Place of the Suns Declination, and his distance from the Meridian being given, to find the Suns Altitude at any Time assigned.
PROBL. XIII. The Suns Altitude, and his Distance from the Meridian, and Declination being given; to find his Azimuth.
PROBL. XIV. The Poles Elevation, with the Suns Altitude and Declination given; to find the Suns Azimuth.
As for Example.
2 Example.
PROBL. XV. To find the Altitude of the Sun by the Shadow of a Gnomon set Perpendicular to the Horizon by Scale and Compasses; as also by Calculation.
As for Example.
PROBL. XVI. Having the Latitude of the Place, the Suns Declination, and the Suns Alti∣tude; to find the Hour of the Day.
PROBL. XVII. Having the Azimuth of the Sun, the Altitude of the Sun, and the Declina∣tion; to find the Hour of the Day.
PROBL. XVIII. How to find the Right-Ascension of a Star, and the Declination of a Star; having the Longitude and Latitude of that Star given.
By Calculation.
PROBL. XIX. Having the Declination, and Right-Ascension of a Star; to find the Longi∣tude and Latitude thereof.
PROBL. XX. Having the Meridian-Altitude of an unknown Star, and the distance there∣of from a known Star; to find the Longitude and Latitude of the unknown Star.
PROBL. XXI. To find the Parallax of Altitude of the Sun, Moon, or Stars.
title page
frontispiece
To my much Honoured Friend Isaac Morgan Esq; Collector of his Majesties Customs in the Port of Bristol.
THE Art of Dialling.
THE ARGUMENT.
CHAP. I. The Preface of the kinds of Dials.
CHAP. II. Theorems premised.
CHAP. III. How to make the Polar Dial, and how to place it.
How by Calculation to find the length of the Stile, and Semidiameters of the Parallels of Declination.
How to find by the length of the Stile, the Semidiameter of the Pa∣rallel Circles of Declination.
EXAMPLE I.
EXAMPLE II.
CHAP. IV. How to make the South Aequinoctial Dial, or Polar Plane.
How to calculate the Height of the Stile, and the Points of Hour-distance from the Meridian.
How to find the length of the Tangent between the Substile and the Hour-Points.
CHAP. V. How to make the East Aequinoctial Dial, or the West Lat. 51 d. 30 m.
How to make the West Aequinoctial Dial.
CHAP. VI. Of the kinds of Oblique Dials.
CHAP. VII. How to make the Vertical Horizontal Dial.
CHAP. VIII. A South and North Erect Direct or Horizontal Dial, and how to make it.
CHAP. IX. How to make a South inclining 23 deg. in the Latitude of 51 deg. 30 min.
CHAP. X. How to observe the Declination of any Declining Plane.
How to take the Declination of any Wall or Plane, without the help of a Needle or Loadstone.
How to find the Declination by the Needle, whether the Air be clear or not.
CHAP. XI. How to make a Declining Horizontal Dial, or South erect declining from the South Eastwards 32 deg. 30 min. in the Latitude of 51 deg. 30 min.
To find what Hour or how much Time the Substiler is distant from the Meridian or Inclination of Meridian.
CHAP. XII. How to draw the Hour-Lines in a Declining Horizontal-Dial, or South erect, declining 32 deg. 30 min. from the South Eastward, the Latitude being 51 deg. 30 min.
CHAP. XIII. How to observe the Reclination or Inclination of any Plane.
CHAP. XIV. To draw the Hour-Lines in all Declining, Reclining, Inclining Planes.
To Describe the DIAGRAM.
CHAP. XV. How to make a North and South Reclining Dial.
CHAP. XVI. How to make an East or West Reclining or Inclining Dial.
EXAMPLE.
CHAP. XVII. How to find the Arches and Angles that are requisite for the making of the Reclining Declining Dial.
CHAP. XVIII. How to draw the Reclining Declining Dial.
CHAP. XIX. How to find the Horary Distance of a Reclining Declining Dial.
CHAP. XX. To draw the Proper Hours of any Declining Dial.
CHAP. XXI. To know in what Country any Declining Dial shall serve for a Vertical.
CHAP. XXII. How to find the Arches and Angles which are requisite in a North Decliner Recliner, and a South Decliner Incliner.
CHAP. XXIII. How to draw the Declining Inclining Dial.
CHAP. XXIV. How to know the several sorts of Dials in the Fundamental Diagram.
CHAP. XXV. How other Circles of the Sphere besides the Meridians may be projected upon Dials.
CHAP. XXVI. How to describe on any Dial the proper Azimuths and Almicantars of the Plane.
CHAP. XXVII. How to deal with those Planes where the Pole is but of small Elevation, and how to enlarge the Stile thereof.
CHAP. XXVIII. Another Example, How to Inlarge the Stile in a South Dial, reclining 45 deg. from the Zenith Northward.
CHAP. XXIX. How to make a Vertical Dial upon the Cieling of a Floor within Doors, where the Direct Beams of the Sun never come.
CHAP. XXX. How to make an Ʋniversal Dial on a Globe; and to cover it, if it be required.
CHAP. XXXI. How to make a Direct North Dial for the Cape of Good Hope, in South Lati∣tude 35 d. and Longitude 57 d. to the Eastward of Flores and Corvo.
CHAP. XXXII. How to find the Time of the Night by the Moon shining upon a Sun Dial.
CHAP. XXXIII. How to find the Hour of the Day or Night by a Gold Ring and a Silver Drinking Bowl, or Glass, or Brass, or Iron, or Tin Vessel.
A Good Observation.
CHAP. XXXIV. How to Paint the Dials which you make.
To Paint and Finish the Dials, ready to be set up in their Places.
A Receipt for Red Ink.
How to cleanse a Picture.
To cleanse a Gold Border.
To grind Gold to Write and Paint.
Some Ʋses of the following Tables of Logarithmes, Sines, and Tangents.
PROBL. I. How to find the Logarithmes of any Number under 1000.
PROBL. II. A Logarithme being given, to find the Absolute Number thereunto belonging, by the former Observation; the Characteristick will declare of what Number of Places the Absolute Number consisteth.
PROBL. III. How to find the Logarithme of a Number that consisteth of four Places.
PROBL. IV. Any Number of Degrees and Minutes being given, to find the Artificial Sine and Tangent thereof.
PROBL. V. If any Sine or Tangent be given, to find what Degrees and Minutes answer thereunto.
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Canon Triangulorum Logarithmicus.
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table
table
The Ʋse of the Table of Proportion, for the more ready find∣ing out of any Logarithme, from 10000 to 100000.
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TO ALL Merchants and Factors, and Comman∣ders or Masters of Ships; AND To all other Officers and Mariners: And to all other Honest-minded Men whom this may Concern. SAMUEL STURMY Wisheth Prosperity, Courage, and Wisdom in all Your Lawful Undertakings.
A SUMMARY OF SUCH PENALTIES and FORFEITURES As are Limited and Appointed by Several ACTS of PARLIAMENT Relating to the CUSTOMS and NAVIGATION.
Goods forfeited for being Imported into England or Wales, with∣out any Penalty upon the Ship; these Goods being all English Manufactures.
In what Cases Goods are forfeited for Ʋndue Shipping or Landing.
In what Cases Ship and Goods are forfeited upon Exportation of Goods.
A TABLE OF THE STATUTES Relating to the CUSTOMS, and NAVIGATION, and TRADE, Made in the Reign of King CHARLES the Second.
THE AUTHOR TO His Books.
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A COMPENDIUM OF FORTIFICATION.
To Describe a Fort of Five Bulwarks, or any other; so that the Bastion, or Flanked Angle of 8 Bastions or Bulwarks exceed not 90 Degrees by the Line of Chords.
Of the Works that are in or about Forts of most Importance.
To Draw the Platform of a Fort, beginning with the Capital (or Head) Line; And also to draw the Horn-works.
For the Horn-works.
Now follow two Tables; the one for 12 Bastions, and the other for Forts of 8 Bastions: Whereby you may trace out any Fort by help of a Line of Equal Parts, which shall divide the Side of the Outer Polygon into 10000 parts.
The Ʋse of these Tables.
The Profile or Section of a Fort with a Fausse-Bray and Counterscarp; also Subtrenched.
Of Irregular Fortification.
To make a Scale for Fortification by the Tables.
How to Fortifie a long Curtain with Bulwarks, or a strait Town Wall.