Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.

Title

Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor.

Author

Taylor, John, mathematician.

Publication

London :: Printed by J.H. for W. Freeman,

1687.

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Subject terms

Mathematics -- Early works to 1800.

Link to this Item

https://name.umdl.umich.edu/A64224.0001.001 content_copy

Cite this Item

"Thesaurarium mathematicae, or, The treasury of mathematicks containing variety of usefull practices in arithmetick, geometry, trigonometry, astronomy, geography, navigation and surveying ... to which is annexed a table of 10000 logarithms, log-sines, and log-tangents / by John Taylor." In the digital collection Early English Books Online. https://name.umdl.umich.edu/A64224.0001.001. University of Michigan Library Digital Collections. Accessed May 7, 2025. content_copy

Contents

• frontispiece
• title page
• dedication
• THE PREFACE TO THE READER.
• To the READER.
• to the reader
• To his learned and ingenious Friend Mr. John Taylor, in the deserved Praise of his Excellent Book intituled The saurarium Mathema∣ticae.
• To the Learned Authour my much respected Friend Mr. John Taylor on his Herculean labours in the Composure of this Excellent Mathematical Treasury.
• An Acrostick on the Name of my much respected and ingenious Friend Mr. John Taylor.
• ADVERTISEMENTS.
• The Contents.
• Arithmetick.
  • CHAP. I. Of ARITHMETICK.
    • SECTION I. The Explication of some Arithmetical Pro∣positions.
      • PROPOSITION I. To three numbers given, to find a fourth in a Di∣rect proportion.
      • PROP. II. To three numbers given, to find a fourth in an Inversed proportion.
      • PROP. III. To three numbers given, to find out a fourth in a Duplicate proportion.
      • PROP. IV. To three numbers given, to find a fourth in a Triplicate proportion.
      • PROP. V. To two numbers given, to find out a third, fourth, fifth, sixth, &c. Numbers in a continual pro∣portion.
      • PROP. VI. Between two numbers given, to find out a mean Arithmetical proportional.
      • PROP. VII. Between two numbers given, to find out a mean Musical Proportional.
      • PROP. VIII. How to find the Square-Root of any whole num∣ber, or Fraction.
        • NOTE.
        • To Extract the Square-Root of a Vulgar or Deci∣mal Fraction, and a Mixt-number.
      • PROP. IX. How to find the Cube-Root of any whole Num∣ber, or Fraction.
        • NOTE.
        • To Extract the Cube-Root, of any Vulgar or De∣cimal or Mixt Fraction consisting of a Whole Number and a Fraction.
  • CHAP. II. The Explication, and use of the Ta∣bles of LOGARITHMS.
    • SECT. I. The Explication of the Tables of the Lo∣garithms, and of parts proportional.
      • PROP. I. Any Number given under 10000, or 100000, to find the Logarithm corresponding thereunto.
      • PROP. II.
      • PROP III. A Logarithm propounded to find the whole, or Mixt number, corresponding thereunto.
        • NOTE.
    • SECT. II. Of the Admirable use of the Logarithms in Arithmetick.
      • PROP. I. To Multiply one number by another.
      • PROP. II. To Divide one number by another.
      • PROP. III. To find the Square-Root of a Number.
        • NOTE.
      • PROP. IV. To find the Cube Root of any Number.
      • PROP. V. A Summ of Money being forborn for any number of years, to find how much it will amount unto, reckoning Interest on Interest, according to any Rate propounded.
      • PROP. VI. A Summ of Money being to be paid hereafter, to find what it is worth in eady Money.
      • PROP. VII. A yearly rent, or Annuity to continue any number of years, to find what it is worth in ready Money, at any Rate of Interest propounded.
  • CHAP. III. The Explication of the SINES, TANGENTS, and SE∣CANTS.
    • SECT. I. Of Right Signs, Tangents, Secants, Co∣sines, Tangents, and Secants: Of any Arch, or Angle of a Triangle.
      • PROP. I. To find the right Sine, or Tangent of any Arch or Angle of a Triangle containing any number of Degrees and Minutes.
      • PROP. II. To find the Co-Sine or Co-Tangent of any Arch, or Angle propounded.
      • PROP. III. To find the Secant of any Arch or Angle propounded.
  • CHAP. IV. Of GEOMETRY.
    • SECT. I. The Explication of some Geometrical Pro∣positions.
      • PROP. I. To erect a perpendicular on any part of a line assigned.
      • PROP. II. To Erect a Perpendicular, on the End of a Line.
      • PROP. III. From a Point above to let fall a Perpendicular on a Line.
      • PROP. IV. To draw a right line Parallel to a right line, at a∣ny distance assigned.
      • PROP. V. To Protract an Angle of any Quantity of Degrees propounded.
      • PROP. VI. To measure an Angle already protracted.
      • PROP. VII. To divide an Angle into two Equal parts.
      • PROP. VIII. To divide a right line into any Number of Equal or Unequal parts; or like to any divided line propounded.
        • CASE II.
      • PROP. IX. How to Protract or lay down any of the Regular Figures, called Polygons.
        • CONSTRUCTION I.
        • CONSTRUCTION II.
        • CONSTRUCTION. III.
      • PROP. X. To divide a line according to any assigned pro∣portion.
      • PROP. XI. To two lines given, to find a third proportional to each of them.
      • PROP. XII. To three lines given to find out a fourth proportio∣nal unto them.
      • PROP. XIII. To find a mean proportional Line between any two right lines given.
      • PROP. XIV. To find two mean proportional Lines between any two right Lines given.
      • PROP. XV. To make a Geometrical square equal to divers Geo∣metrical squares.
      • PROP. XVI. To make a Circle equal to divers Circles propounded.
    • SECT. II. Of Planometry, or the way to measure any plain Superfice.
      • PROP. I. To find the superficial Content of a Geometrical square.
      • PROP. II. To find the superficial content of a Parallelogram, or long Square.
      • PROP. III. To find the superficial Content of any Right-lined Triangle.
      • PROP IV. To find the superficial Content of a Rhombus.
      • PROP. V. To find the superficial content of a Rhomboides.
      • PROP. VI. Te find the superficial Content of any Poligon, or many equal sided Superficies.
      • PROP. VII. To find the superficial Content of a Circle.
      • PROP. VIII. By the Diameter of a Circle given, to find the Cir∣cumference.
      • PROP. IX. By the Circumference of a Circle given, to find the Diameter.
      • PROP. X. By the Content of a Circle given, to find the Cir∣cumference.
      • PROP. XI. By the Content of a Circle given, to find the Dia∣meter.
      • PROP. XII. By the Diameter of a Circle given to find the side of a square equal thereto.
      • PROP. XIII. By the Circumference of a Circle given, to find the side of a square equal to it.
      • PROP. XIV. By the Content of a Circle given to find the side a square equal to it.
      • PROP. XV. By the Diameter of a Circle given, to find the side of an Inscribed square.
      • PROP. XVI. By the Circumference of a Circle given, to find the side of an Inscribed Square.
      • PROP. XVII. o find the Superficial Content of an Oval, or El∣leipsis.
      • PROP. XVIII. To find the Superficial Content of any Section, or Portion of a Circle.
    • SECT. III. Of STEREOMETRY, or the way how to measure any Regular Solid.
      • PROP. I. To find the solid Content of a Cube.
      • PROP. II. To find the solid Content of a Parallelepipedon.
      • PROP. III. To find the solid Content of a Cylinder.
      • PROP. IV. To find the solid Content of a Pyramid.
      • PROP. V. To find the solid content of a Cone.
      • PROP. VI. By the Diameter of a Globe to find his solid Content.
      • PROP. VII. By the Circumference of a Sphere, or Globe, to find his solid Content.
      • PROP. VIII. By the Axis of a Globe, to make a Cube equal there∣unto.
      • PROP. IX. By the Circumference of a Globe, to make a Cube equal thereunto.
      • PROP. X. By the solid Content of a Sphere or Globe, to make a Cube equal thereunto.
      • PROP. XI. A Segment of a Sphere being given to find the solid Content thereof.
  • CHAP. V. Of TRIGONOMETRY. Or the Doctrine of Triangles.
    • SECT. I. Some general Maxims, belonging to plain or Right-lined Triangles.
    • SECT. II. Of Plain Rectangled Triangles.
      • PROP. I. Two Angles and the Base of a Rectangled Trian∣gle given, to find the other parts.
      • PROP. II. The Hypothenuse, Base, and one of the Angles Of a Rectangled Triangle given, to find the o∣ther parts thereof.
      • PROP. III. In a Rectangled Triangle, the Base, and Cathetus given to find the other parts thereof.
      • PROP. IV. The Base, and Hypothenuse, with the Angle be∣tween them given, to find the other parts of a Rect-angled Triangle.
    • SECT. III. Of Oblique-Angled Plain Triangles.
      • PROP. I. Two Angles, and a side opposite, in an Oblique-Ang∣led Triangle given, to find the other parts there∣of.
      • PROP. II. Two sides, and an Angle opposite to one of them in an Oblique-angled Triangle given, to find the other parts thereof.
      • PROP. III. Two Sides of an Oblique-angled Triangle, with the Angle included between them given, to find the other parts thereof.
      • PROP. IV. The three sides of an Oblique-angled Triangle gi∣ven, to find the Angles.
        • I. In the Triangle CDB.
        • II. In the Triangle ADB.
    • SECT. IV. Of Spherical Rectangled Triangles.
      • PROP. I. Case 1. A Side and an Angle adjacent thereunto being gi∣ven, to find the other Side.
      • PROP. II. Case 2. A Side and an Angle adjacent thereunto being gi∣ven, to find the other Oblique-angle.
      • PROP. III. Case 3. A Side and an Angle adjacent thereunto being given, to find the Hypothenuse.
      • PROP. IV. Case 4. A Side and an Angle opposite thereunto being given, to find the other Oblique-angle.
      • PROP. V. Case 5. A Side and the opposite Angle given, to find the Hypothenuse.
      • PROP. VI. Case 6. A side and the opposite Angle given, to find the other side.
      • PROP. VII. Case 7. The Hypothenuse, and an Oblique Angle given, to find the side adjacent thereunto.
      • PROP. VIII. Case 8. The Hypothenuse, and an Oblique-angle given, to find the opposite Side.
      • PROP. IX. Case 9. The Hypothenuse, and an Oblique-angle given, to find the other Oblique-angle.
      • PROP. X. Case 10. The sides given, to find the Hypothenuse.
      • PROP. XI. Case 11. The sides given, to find an Angle.
      • PROP. XII. Case 12. The Hypothenuse, and a side given, to find the o∣ther side.
      • PROP. XIII. Case 13. The Hypothenuse, and a Side given, to find the contained Angle.
      • PROP. XIV. Case 14. The Hypothenuse, and a Side given, to find the oppo∣site Angle.
      • PROP. XV. Case 15. The Oblique Angles given, to find either Side.
      • PROP. XVI. Case 16. The Oblique-angles given, to find the Hypothenuse.
    • SECT. V. Of Oblique-angled Spherical Triangles.
      • PROP. I. Case 1. Two Sides, and an Angle opposite to one of them given, to find the other opposite Angle.
      • PROP. II. Case 2. Two Angles and a Side opposite to one of them gi∣ven, to find the Side opposite to the other.
      • PROP. III. Case 3. Two Sides and an Angle included between them being known, to find the other Angles.
      • PROP. IV. Case 4. Two Angles, and their Interjacent side being known, to find the other sides.
      • PROP. V. Case 5. Two Sides and an Angle opposite to one of them gi∣ven, to find the third side.
      • PROP. VI. Case 6. Two Angles and a Side opposite to one of them gi∣ven, to find the third Angle.
      • PROP. VII. Case 7. Two Sides and an Angle opposite to one of them gi∣ven, to find the Included Angle.
      • PROP. VIII. Case 8. Two Angles and a Side opposite to one of them be∣ing known, to find the Interjacent Side.
      • PROP. IX. Case 9. Two Sides and their Included Angle being known, to find the third Side.
      • PROP. X. Case 10. Two Angles and their Interjacent Side known, to find the third Angle.
      • PROP. XI. Case 11. Three Sides given, to find an Angle.
      • PROP. XII. Case 12. Three Angles given, to find a Side.
  • CHAP. VI. Of ASTRONOMY.
    • SECT. I. Of Astronomical Definitions.
    • SECT. II. Of Astronomical Propositions.
      • PROP. I. The Distance of the Sun from the next Equinoctial point (either Aries or Libra) being known, to find his Declination.
      • PROP. II. The Sun's place given, to find his Right-Ascen∣sion.
      • PROP. III. To find the Sun's place or longitude from Aries, his Declination being given.
      • PROP. IV. By knowing the Suns Declination, to find his Right Ascension.
      • PROP. V. By knowing the Latitude of a Place, and the Suns Declination, to find the Ascensional Difference.
      • PROP. VI. To find the Suns Oblique Ascension or Descension.
      • PROP. VII. By knowing the Suns Declination, and the Latitude of a Place, to find the Suns Amplitude.
      • PROP. VIII. By knowing the Suns Declination and Amplitude, from the North part of the Horizon, to find the Latitude.
      • PROP. IX. By knowing the Latitude of a place, and the Sun's Declination, to find at what time the Sun will be on the true East or West Points.
      • PROP. X. By knowing the Sun's Declination, and Latitude of a place, to find his Altitude at six a Clock.
      • PROP. XI. By knowing the Latitude of a place, and the Sun's Declination, to find the Azimuth at six.
      • PROP. XII. By knowing the Latitude of a place, and the Sun's Declination, to find the Sun's Altitude when he i on the true East or West points.
      • PROP. XIII. To find the Sun's Altitude at any time of the day.
      • PROP. XIV. By knowing the Latitude of a Place, with the Sun's Declination, and Altitude, to find the Hour of the Day.
      • PROP. XV. To find the Time of the Sun's Rising or Setting, and consequently the Length of the Day or Night.
      • PROP. XVI. The Sun's Declination, Altitude and Azimuth known, to find the Hour of the Day.
      • PROP. XVII. By knowing the Sun's Declination, Altitude, and Hour from Noon, to find the Azimuth.
      • PROP. XVIII. By knowing the Latitude of a place, the Altitude of the Sun, and the Hour from Noon, to find the Angle of the Sun's Position.
      • PROP. XIX. By knowing the Sun's Altitude, Declination, and Azimuth; to find the Latitude.
      • PROP. XX. To find the length of the Crepusculum, or Twilight
      • PROP. XXI. To find the Quantity of the Angles, which the Cir∣cles of the 12 Houses make with the Meri∣dian.
      • PROP. XXII. To find the Right Ascension of the Point in the Equinoctial: and also the Point in the Ecliptick; called Medium Coeli or Cor Coeli.
      • PROP. XXIII. To find the Angle of the Ecliptick with the Meri∣dian.
      • PROP. XXIV. To find the Angle of the Ecliptick with the Ho∣rizon.
      • PROP. XXV. To find the Amplitude Ortive of the Ascendent, or Horoscopus.
      • PROP. XXVI. To find the Ascendent degree of the Ecliptick, or the Cuspis of the first House.
      • PROP. XXVII. To find the Distance of the Cuspis of any House, from Med. Coeli.
      • PROP. XXVIII. To find the parts of the Angle of the Ecliptick with the Meridian, cut with an Arch perpendicular to the Circle of any of the Houses.
      • PROP. XXIX. To find the Pole's Altitude, above any of the Circles of the Houses.
      • PROP. XXX. By knowing the Latitude and Longitude of any fixed Star, to find his Right Ascension and De∣clination.
      • PROP. XXXI. By knowing the Pole's Altitude, to find when any fixed Star shall be due East or West.
      • PROP. XXXII. By knowing the Poles Altitude, to find the Eleva∣tion of any fixed Star above the Horizon, being due East or West.
      • PROP. XXXIII. To find out the Horizontal Parallax of the Moon.
      • PROP. XXXIV. The Horizontal Parallax of the Moon being known, to find her Parallax in any apparent Latitude.
      • PROP. XXXV. By knowing the Moon's Place in the Ecliptick, (having little or no Latitude) and her Paral∣lax of Altitude, to find the Parallaxes of her Longitude and Latitude.
      • PROP. XXXVI. How by knowing the Refraction of a Star, to find his true Altitude.
        • EXAMPLE.
  • CHAP. VII. Of GEOGRAPHY.
    • SECT. I. Of GEOGRAPHICAL Definitions.
    • SECT. II. Geographical Descriptions of the Earth.
      • part - 1
      • ASIA.
      • AFRICA.
      • AMERICA.
    • SECT. III. Of Geographical Propositions.
      • PROP. I. How to find the Distance of any two Cities or Places, which differ onely in Latitude.
      • PROP. II. To find the Distance of any two Places which differ only in Longitude.
      • PROP. III To find the Distance of any two Places, which dif∣fer both in Latitude, and in Longitude.
  • CHAP. VIII. of NAVIGATION.
    • SECT. I. Of Plain sailing, or sailing by the Plain Chart.
      • PROPI. The Rumb, and Distance sailed thereon being gi∣ven, to find the Difference of Latitude, and the Departure from the Meridian.
      • PROP. II. By the Rumb and Difference of Latitude given, To find the Distance, and the Departure from the Meridian.
      • PROP. III. By knowing the Distance of the Meridians of two Places, and their Difference of Latitude, to find the Rumb, and Distance.
      • PROP. IV. Admit two Ships to set sail from one Port, one Ship sails W. S. W. 40', the other W. by N. so far untill she finds the first Ship to bear from her S. E. by E. I demand the second Ships distance from the Port, and their Distance asunder?
      • PROP. V. Two Ships sets sail from two Ports, which lie N. and South of each other, the one sails from the Northermost Port 72 29'/100, and then meets she other Ship, which came from the Southermost Port, on a N. W. Course, and had sailed from thence 56 80'/100 I demand the Rumb on which the first ship made her way, and also the Distance be∣tween the two Ports?
      • PROP. VI. Admit a Ship coming off the Main Ocean and I had sight of a Promontory or Cape, by which it is my desire to sail, I find it to bear from me S. S. E. and distant by Estimation 33', or Miles: But keeping still on my Course S. untill the Evening, having sailed 36' or Miles, I would then know how the Cape bears, and its distance from the Ship?
      • PROP. VII. Two Ports both lying in one Latitude, distant 64' or Miles, the Westermost of those Ports lieth op∣posite to an Island, more Northerly distant there∣from 47' or Miles, which Island is also distant from the Eastermost Port, 34' or Miles, I de∣mand the Course from the Westermost Port to that Island?
    • SECT. II. Of sailing by the true Sea Chart, commonly called MERCATOR'S Chart.
      • PROP. I. To find by the Table, what Meridional parts are contained in any Difference of Latitude.
      • PROP. II By knowing the Latitudes, and the difference of Longitude of any two Places, to find the Rumb, and Distance.
      • PROP. III. By knowing the Latitudes, and distance of two Places, to find the Rumb, and Difference of Lon∣gitude.
      • PROP. IV. By knowing the Latitudes, and Rumb of two Pla∣ces, to find their Distance, and Difference of Longitude.
      • PROP. V. By knowing the Rumb, Difference of Longitude, and one Latitude, to find the other Latitude, and the Distance.
      • PROP. VI. By knowing the Distance, one Latitude, and Rumb, to find the other Latitude, and Difference of Longitude.
    • SECT. III. Of Circular Sailing, or Sailing by the Arch of a Great Circle.
      • PROP. I. Two Places, the one under the Equinoctial, the other in any Latitude given; also their difference of Longitude given, to find.
      • PROP. II. Two Places proposed, the one lying under the Equi∣noctial, the other in any Latitude given; with their distance in a great Circle of the same Places being also known, to find.
      • PROP. III. Two Places lying in one Latitude given, their dif∣ference of Longitude being also known, to find.
      • PROP. IV. Two Places lying both in one Latitude given, and the nearest distance being also known, to find.
      • PROP. V. Two Places proposed lying in one Latitude, and the distance of those Places in their Parallel given; to find.
      • PROP. VI. By knowing the nearest Distance of two Places, their Difference of Longitude, and one of their Latitudes; to find the Direct Position thereof from the other.
      • PROP. VII. By knowing the Latitudes of two places, and like∣wise their Difference of Longitude; to find,
  • CHAP. IX. Of SURVEYING.
    • SECT. I. Of the use of the Protractor.
      • PROP. I. By the Protractor, to Protract an Angle of any quantity of degrees propounded.
      • PROP. II. By the Protractor given, to measure an Angle given.
    • SECT. II. Of the Manifold Use of the Semicircle, in taking the Plots of small Enclosures, Plains, Woods, or Mountains divers Ways.
      • PROP. I. How to take the Plot of a Field, by the Semicircle at one Station taken in any part thereof, from whence all the Angles may be seen, and measu∣ring from the Station unto every Angle thereof.
      • PROP. II. How to delineate on Paper any Observation taken according to the Doctrine of the last Proposition.
      • PROP. III. How by the Semicircle to take the Plot of a Field at one Station in any Angle thereof, from whence you may view all the other Angles, by measuring from the Stationary-Angle, unto all the other Angles.
      • PROP. IV. How to delineate any Observation taken according to the Doctrine of the last Proposition.
      • PROP. V. How by the Semicircle to take the Plot of a Field at two Stations, by measuring from each Station to the visible Angles: the Field being so Irregu∣lar that from no one Place thereof, all the Angles can be seen.
      • PROP. VI. How to delineate any Observation taken according to the Doctrine of the last Proposition.
      • PROP. VII. How by the Semicircle, to take the Plot of a Field at t Stations, which lieth remote from you, when either by opposition of Enemies you may not, or by some other Impediment you cannot come into the same.
      • PROP. VIII. How to delineate any Observation taken according to the Doctrine of the last Proposition.
      • PROP. IX. How by the Semicircle, to take the Plot of a great Champain-Plain, Wood, or other overgrown Ground, by measuring round about the same, and making Observation at every Angle thereof.
      • PROP. X. How to delineate any Observation taken according unto the Doctrine of the last Proposition.
      • PROP. XI. How to take the Plot of any Field, by the help of the Chain only.
      • PROP. XII. How to delineate any Observation, taken according to the Doctrine of the last Proposition.
    • SECT. III. Of finding the Area or superficial Content of any Field, lying in any Regular or Ir∣regular Form: by reducing the Irregular Fields into Regular Forms.
      • PROP. I. How to find the Area or superficial Content of a Trapezium.
      • PROP. II. To find the Area or superficial Content of a many∣sided Irregular Figure.
      • PROP. III. How to reduce any Number of Perches into Acres, and on the contrary, Acres into Perches.
    • SECT. IV. Of the Use of the Semicircle in taking Al∣titudes, Distances, &c.
      • PROP. I. How by the Semicircle to take an Accessible Alti∣tude.
      • PROP. II. How by the Semicircle to take an Inaccessible Al∣titude, at two Stations.
      • PROP. III. How by the Semicircle to take an Inaccessible Dis∣tance at two Stations.
      • PROP. IV. How to find the Horizontal line of any Hill or Mountain, by the Semicircle.
    • SECT. V. How to find whether Water may be conveyed from a Spring-Head unto any appointed Place.
  • CHAP. X. Of MEASURING, Of Board, Glass, Tiling, Paving, Timber, Stone, and Irregular Solids, such as Geo∣metry can give no Rule for the Measuring thereof.
    • SECT. I. Of the Measuring of Board, Glass, Paving, Tiling, &c.
      • PROP. I. To Measure a Piece of Board, Plank, Glass, &c.
      • PROP. II. To measure Tiling, Flooring, Roofing, and Parti∣tioning-works.
      • PROP. III. To measure Paving, Plaistering, Wainscotting, and Painting-work.
    • SECT. II. Of the Measuring of Timber, Stone, and Irregular Solids.
      • PROP. I. How to Measure any kind of Timber, or Stone, whether Three-square, Four-square, Many-square, Round, or of any other fashion, provided it be streight and equal all along.
      • PROP. II. To measure Round Timber which is Hollow: or a∣ny other Hollow Body.
      • PROP. III. To Measure Tapering Timber, or Stone.
      • PROP. IV. How to find the Solid Content of any Solid Body, in any strange form, such as Geometry can given: no Rule for the measuring thereof.
  • CHAP. XI. Of GAUGING.
    • SECT. I. Of Gauging any Beer, Ale, or Wine-Cask, also any manner of Brewers Tuns.
      • PROP. I. To find the Solid Content in Inches of any Cask.
      • PROP. II. To find the Content of a Vessel in Wine, or Ale Gallons.
      • PROP. III. How to Gauge or Measure Brewers Tuns, &c.
    • SECT. II. Of Gauging or Measuring, and the Moulding of Ships.
      • PROP. I. To Gauge a Ship, thereby to find how many Tuns her burthen is.
      • PROP. II.
  • CHAP. XII. Of DIALLING.
    • SECT. I. Of the Delineation and Projection of sundry most usefull Dials.
      • PROP. I. How to draw the Hour-lines on an Equinoctial Plain.
      • PROP. II. How to draw the Hour-lines on a Polar Plane.
      • PROP. III. How to draw the Hour-lines on a Meridian Plane, which is an East, or West Dial.
      • PROP. IV. How to draw the Hour-lines on a direct South, and North Plane,
      • PROP. V. How to draw the Hour-lines on an Horizontal Plane.
      • PROP. VI. How to draw the Hour-lines, on an Erect declining Plane.
        • A Table of the Names and Latitudes of all the Principal Cities, Towns, and Islands, in and about Great Britain and Ireland.
  • CHAP. XIII. Of FORTIFICATION.
    • SECT. I. Of the Definitions of the Lines, and Angles, belonging to the Principal Ground work of any Regular Fortification.
    • SECT. II. Of General Maxims or Rules observed in Fortifications.
    • SECT. III. Of the Construction and making of the prin∣cipal Ground-line of a Fort, according to the most Modern ways, used by the Ita∣lian, Dutch, French, or English Ingi∣niers.
      • I. Of the Italian Fortifications.
      • PROP. I. To fortifie a Hexagon according to this Author's Proportion.
      • II. Of the French Fortifications.
      • PROP. II. To fortifie a Hexagon according to the Proportion of De la Mont.
      • PROP. III. To fortifie a Hexagon according to Manesson Mallet's Proportion.
        • III. Of the Dutch Fortifications.
      • PROP. IV. To fortifie a Hexagon according to the Emperour's Proportion.
        • IV. Of the English Fortifications.
      • PROP. V. How to fortifie a Hexagon according to Count Pagan's Proportion.
      • PROP. VI. To fortifie a Hexagon according to the way prescri∣bed by His Majesty Carolus II.
      • PROP. VII. By the Semicircle to lay down on the Ground, any of the former Fortifications.
    • SECT. IV. Of the Dimensions, and Measures of the Rampires, Parapets, Mote, Coridor, or Covert-way, and its Esplanade, or Breast∣work.
      • PROP. VIII. How to lay down the Profile of the Work, according to this Table.
    • SECT. V. Of the Dimensions and Construction of Pla forms, Caveleers and Cazemats in t Flanks.
    • SECT. VI. Of the Dimensions, and Constructions of those Out-Works, called Ravelins, Horn, Crown∣works, &c.
    • SECT. VII. Of some Maxims or Rules necessary to be known in Irregular Fortification.
    • SECT. VIII. Of the Dimensions and Construction of small Forts, or Scones, which are built for the Defence of some Pass, River, or other place.
      • PROP. IX. To fortifie a Triangle, with Demi-Bastions.
      • PROP. X. To fortifie a Square with Demi-Bastions.
      • PROP. XI. To fortifie a Parallelogram with Demi-Bastions, and Tong.
      • PROP. XII. To fortifie a Star Redoubt of 4, 5, or 6 Points
      • PROP. XIII. To Delineate a Plain Redoubt
  • CHAP. XIV. Of Military Orders, or the Embat∣telling and Encamping of Souldiers.
    • SECT. I. Of the Embattelling and Ordering of Soul∣diers.
      • PROP. I. To Order any number of Souldiers into a Square Battail of Men.
      • PROP. II. To Order any number of Souldiers into a Double Battail.
      • PROP. III. To Order any number of Souldiers into a Battail of the Grand Front.
      • PROP. IV. Any number of Men, together with their distance in Rank and File, being propounded, to Order them into a Square Battail of Ground.
      • PROP. V. Any number of Souldiers propounded, to Order them in Rank and File, according to the reason of any two Numbers given.
    • SECT. II. Of Castermetation, or Quartering and En∣camping of Souldiers.
  • CHAP. XV. Of GUNNERY.
    • SECT. I. Of the Names of the Principal Members of a Piece of Ordnance.
    • SECT. II. Of the Dimension of our Usal English Can∣non, and other Ordnance, &c.
      • PROP. I. How to know the different Fortification of a Piece of Ordnance.
      • PROP. II. How to know how much Powder is fit for proof, and what for service, for any Piece of Ordnance.
      • PROP. III. To know what Bullet is fit to be used in any Piece of Ordnance.
      • PROP. IV. By knowing the proportion of Metals one to another, and by knowing the Weight of one Ball, to know what any other shall weigh.
    • SECT. III. Of the Qualification of an able Gunner, and necessary Operations before shooting, and in shooting.
      • PROP. I. How to Tertiate, Quadrate, and to Dispart a Piece of Ordinance.
      • PROP. II. To know how far any Piece of Ordnance will shoot, &c.
        • The Use of the Table of Randoms.
    • SECT. IV. Of Shooting in Mortar-Pieces.
      • PROP. I. To make Fuses for Bombs, &c.
        • table
      • PROP. II.
      • PROP. III. Finding that a Mortar of 300, being elevated 54°, sends his Bomb 760 88/100 Paces, what Degree of Elevation must that Mortar have, to shoot the Bomb 555 Paces?
• plate
• A TABLE OF Logarithm Numbers, From One to Ten Thousand: Whereby the LOGARITHM OF ANY NUMBER Under Four Hundred Thousand may be readily discovered.
• A TABLE OF PROPORTIONAL PARTS, WHEREBY The Intermediate Logarithms of all Numbers, AND The Numbers of all Logarithms from 10000 to 100000 may more readily be found out by the foregoing Table of Loga∣rithms.
• A TABLE OF ARTIFICIAL SINES AND TANGENTS To every DEGREE and MINUTE OF THE QUADRANT.
• Some Books sold by W. Freeman at the Ar∣tichoke next St. Dunstan's Church in Fleet-street.
• A Catalogue of Books.