The seaman's companion being a plain guide to the understanding of arithmetick, geometry, trigonometry, navigation, and astronomy. Applied chiefly to navigation: and furnished with a table of meridional parts, to every third minute: with excellent and easie ways of keeping a reckoning at sea, never in print before. Also, a catalogue of the longitude and latitude of the principal places in the world with other useful things. The third edition corrected and amended. By Matthew Norwood, mariner.

Title

The seaman's companion being a plain guide to the understanding of arithmetick, geometry, trigonometry, navigation, and astronomy. Applied chiefly to navigation: and furnished with a table of meridional parts, to every third minute: with excellent and easie ways of keeping a reckoning at sea, never in print before. Also, a catalogue of the longitude and latitude of the principal places in the world with other useful things. The third edition corrected and amended. By Matthew Norwood, mariner.

Author

Norwood, Matthew.

Publication

London :: [print]ed by Anne Godbid, and John Playford, for William Fisher, at the Postern-Gate near Tower-Hill; Robert Boulter, at the Turks-Head and Ralph Smith, at the Bible in Cornhill; Thomas Passinger, at the Three Bibles on London-Bridge; and Richard Northcot, next St. Peter's-Alley in Cornhill, and at the Anchor and Mariner, on Fishstreet-Hill.

[1678]

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Link to this Item

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Cite this Item

"The seaman's companion being a plain guide to the understanding of arithmetick, geometry, trigonometry, navigation, and astronomy. Applied chiefly to navigation: and furnished with a table of meridional parts, to every third minute: with excellent and easie ways of keeping a reckoning at sea, never in print before. Also, a catalogue of the longitude and latitude of the principal places in the world with other useful things. The third edition corrected and amended. By Matthew Norwood, mariner." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A52487.0001.001. University of Michigan Library Digital Collections. Accessed May 4, 2024. content_copy

Contents

• title page
• TO THE READER.
• THE CONTENTS.
• OF ARITHMETICK.
  • table
  • The Use of the Table to number.
  • Addition.
  • The Characters used in Arithmetick.
  • Addition of Degrees and Minutes.
  • Addition of Hours and Minutes.
  • Subtraction.
  • Subtraction of Degrees and Minutes.
  • Subtraction of Time.
  • The TABLE.
  • Multiplication.
  • Division.
  • Reduction.
  • The Proof of Reduction.
  • The Golden Rule, or Rule of Three.
    • question - 1
      • Arithmetically.
      • Geometrically.
    • question - 2
    • question - 3
    • question - 4
  • The Rule of Interest, and Interest upon Interest.
  • The Rule of Fellowship.
• GEOMETRY.
  • Geometrical Definitions.
  • PROP. I. To raise a Perpendicular from the middle of a Line given
  • PROP. II. To divide a Line into two equal Parts by a Perpen∣dicular.
  • PROP. III. To raise a Perpendicular to the end of a Line given
    • Another way.
  • PROP. IV. To let fall a Perpendicular from a Point to a given Line.
  • PROP. V. To draw a Line parallel to a Line given.
  • PROP. VI. To draw a Line parallel to a given Line, from any Point assigned.
  • PROP. VII. To make a Square of a Line given.
  • PROP. VIII. To make a Square, whose Length and Bredth is given.
  • PROP. IX. To make a Diamond Figure of a Line, and an Angle given.
  • PROP. X. To make a Rhomboiades of two given sides, and an Angle included.
  • PROP. XI. To find the Center of a Circle.
  • PROP. XII. To find the Center of a Circle, of a Triangle, or any three Pricks that be not in a streight Line.
  • PROP. XIII. To divide the Circumference of a Circle into 2, 4, 8, 16, 32 equal parts.

  • The Projection of the Mariners Compass.

  • The Projection of the Plain Scale.

    • For the Line of Chords.
    • For the Points of the Compass.
    • For the Lines of Sines.

  • The Projection of the Sphere in Plain Lat. 50 deg.

    • How to Project a Sphere.
  • The Meaning of the Terms used in the following Work.
  • questions
    • QUESTION I. To find the Meridian Altitude of the Sun.
    • QUESTION II. To find the Suns Amplitude of Rising and Setting.
    • QUESTION III. To find the Suns Azimuth at six of the Clock.
    • QUESTION IV. To find the Suns height at six of the Clock.
    • QUESTION V. To find the Suns height being due East or West.
    • QUESTION VI. To find the Difference of Ascension.
    • QUESTION VII. For the time of the Suns Rising or Setting in this Example.
    • QUESTION VIII. To find the hour of the Suns being due East or West.
    • QUESTION IX. To find the time of Day breaking, and Twilight ending.
    • QUESTION X. To find the Continuance of Twilight.
    • QUESTION XI. To find the Length of the longest Day in that Latitude.
      • Latitude Northerly 50 deg. 00 min. Declination 13 deg. 15 min. Southerly.
      • Latitude 51 deg. 30 min. Northerly, Declination 11 deg. 10 min. Northerly, I demand the Suns place and right Ascension.
      • The Ecliptick being thus divided into Signs; we may find the Suns place, and right Ascension.
  • The Meridian Altitude of the Sun being given, and the Latitude, to find the Suns Decli∣nation, as also all the other things before found.
    • Terms of Art used in Navigation.
• PROPOSITIONS of SAILING BY THE PLAIN SCALE.
  • Difference of Latitude and Course given, to find the Distance run, and the Departure from the Meridian.
    • A General Rule.
    • To find the Distance run.
    • For the Departure from the Meridian.
  • Course and Difference of Longitude in miles given, to find the Difference of Latitude and Distance.
  • Course and Distance run given, to find the Difference of Latitude and Departure from the Meridian.
    • By Proportion.
  • Distance run and Difference of Latitude given, to find the Course and Departure from the Meridian.
    • By the Tables.
  • Departure from the Meridian and Distance run given, to find the Course and Difference of Latitude.
    • By the Plain Scale.
  • Difference of Latitude and Departure from the Meridian given, to find the Course and Distance run
    • By Proposition.
  • Difference of Latitude given alone, Difference of Longitude and Distance run in one intire Sum, I demand the Course and Sides several.
    • Demonstration.
    • By the Tables.
  • A TRAVIS.
    • By the Tables.
• OF A RECKONING.
  • Example in the Reckoning following.
    • January the 3d Anno Dom. 1655, we departed from the Lizard, lying in the Latitude of 50 d. 00 m. being bound for Ditiatha, which lies in the Latitude of 16 d. 16 m. it having West Departure from the Meridian of the Lizard 950 Leagues (according to the courses which we then steered) at 4 of the clock, the Lizard bore from us N N E, about 6 leagues distance by estimation.
• CONCERNING the VARIATION OF THE COMPASS.
  • Example.
  • Example, for the laying open of this Error.
• The USE of a PLAIN SEA-CHART.
  • For their bearing one from the other.
  • For the Departure from the Meridian between two Places.
  • For the Difference of Latitude between two Places.
  • To set off any Course from a Place assigned upon a Blank.
• Of OBLIQUE TRIANGLES.
  • Two Sides with an Angle opposite to one of them given, to find the other Angles and Side.
    • By the Tables.
    • Say then for the Angle at B.
    • For the Distance run of the Ship at B, the Side B C.
  • The three Angles of a Triangle given, with one of the Sides, to find the other two sides.
    • By the Tables.
      • First for the Side A B.
      • For the Distance that the Southermost Ship sailed, A O.
  • Two Sides and their contained Angle being given to find the third Side and the other Angles.
    • By the Tables.
      • subsection
      • Proportion.
      • Now for their Distance asunder, C B.
  • The three Sides of a Triangle given, to find the Angles.
    • I have resolved the Demands, which are as followeth.
      • By Proportion.
      • A General Rule in Oblique Triangles.
    • Example.
      • For the Angle C B A.
    • Example.
  • QUESTION V.
    • By the Tables
      • For A I.
      • For R I.
      • For A O.
  • Two Sides and a contained Angle being given, to find the third Side and the Course (that each Side runs upon) pro∣vided that no Course be named, only the half of the Compass that you sail in (or the quarter which is most commonly) and the Difference of Latitude that is made between the extent of the two Sides.
    • By Proportion.
    • Then for the Ships Distance asunder, C A.
  • Two Sides of an oblique Triangle being given in one Sum, and the other Side alone, with an Angle opposite to one of the Sides, to find the Sides several, and the other Angles.
    • By the Tables.
      • First then for B I the Eastermost Ship's run.
      • Lastly, for I A the Westermost Ships run.
  • The three Sides of a Triangle being given in one intire Sum, and the Angles apart, to find the Sides apart.
    • By the Tables the Proportion is,
      • For N B.
      • To find the Ships Distance that sailed S W, correspondent to C N 30 leagues.
      • By the Tables for N s.
      • subsection
  • Three Sides of a Triangle given, to find the Center.
    • Example.
      • For the Distance of the Ships from the Port.
  • QUESTION X.
    • By the Tables.
• A TABLE OF MERIDIONAL PARTS, To every Third MINƲTE.
  • A Declaration of the Table of MERIDIONAL PARTS.
    • Illustration.
    • The Ʋse of the foregoing Tables of Meridional Parts.
    • Example. To find the Meridional Parts answering to any Latitude.
  • QUESTION I.
  • QUESTION II.
    • For the Difference of Latitude A B.
    • For the Difference of Longitude.
  • QUESTION III. The Latitudes of two places, and the Distance between them given, to find the Course and Difference of Longitude.
  • QUESTION IV.
  • QUESTION V.
    • For the Difference of Latitude in parts.
    • For the Distance between these Places.
  • Of the Longitude and Latitude of Places.
    • Concerning the foregoing Tables.
  • How to keep a Reckoning of the Longitude and Latitude a Ship makes at Sea.
    • That there be nothing wanting to make me be understood, I will here following do the three first days works in three Examples.
      • example
      • For the second days Work.
      • The third days Work.
      • example
  • tables
  • Rules to find the Latitude, or Poles Elevation by the Meridian Altitude of the Sun or Stars, having the Tables of their Declination.
• OF ASTRONOMY.
  • part
  • part
  • Latitude 50 deg. 00 min. Northerly, Declination 13 deg. 15 m. Northerly, I demand the Meridian Altitude of the Sun.
  • Latitude 50 deg. 0 min. Declination 13 deg. 15 min. Northerly, I demand the Suns Amplitude of Rising and Setting.
  • Latitude 50 deg. Declination 13 deg. 15 min. I demand the Suns Azimuth of Rising or Setting.
  • Latitude 50 deg. Declination 13 deg. 15 min. Northerly, I demand the Suns height at six of the Clock.
  • The same things given, to find the Suns Azimuth at six of the Clock.
  • Latitude 50 deg. 0 min. Declination 13 deg. 15 min. to find the Suns height being due East or West.
  • The Latitude being 50 deg. 0 min. Declination 13 deg. 15 min. I desire to know the Difference of Ascension.
  • The same things given, to find the time of Sun Rising.
  • To find the length of the longest Day in that Latitude before proposed.
  • Latitude 50 deg. 0 min. Declination 13 deg. 15 min. Northerly, I demand the time of the Suns being due East or West.
  • Latitude 50 deg. 0 min. Declination 13 deg. 15 min. I demand the Continuance of Twilight.
  • To find the Suns Place and Right Ascension, provided, the Latitude and Declination be given.
    • For the Suns Right Ascension.
• ADƲERTISEMENT.