The compleat surveyor containing the whole art of surveying of land by the plain table, theodolite, circumferentor, and peractor ... : together with the taking of all manner of heights and distances, either by William Leybourn.

Title

The compleat surveyor containing the whole art of surveying of land by the plain table, theodolite, circumferentor, and peractor ... : together with the taking of all manner of heights and distances, either by William Leybourn.

Author

Leybourn, William, 1626-1716.

Publication

London :: Printed by R. & W. Leybourn, for E. Brewster and G. Sawbridge ...,

1653.

Rights/Permissions

To the extent possible under law, the Text Creation Partnership has waived all copyright and related or neighboring rights to this keyboarded and encoded edition of the work described above, according to the terms of the CC0 1.0 Public Domain Dedication (http://creativecommons.org/publicdomain/zero/1.0/). This waiver does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.

Subject terms

Surveying -- Early works to 1800.

Link to this Item

https://name.umdl.umich.edu/A48331.0001.001 content_copy

Cite this Item

"The compleat surveyor containing the whole art of surveying of land by the plain table, theodolite, circumferentor, and peractor ... : together with the taking of all manner of heights and distances, either by William Leybourn." In the digital collection Early English Books Online 2. https://name.umdl.umich.edu/A48331.0001.001. University of Michigan Library Digital Collections. Accessed June 12, 2025. content_copy

Contents

• frontispiece
• title page
• TO HIS MUCH HONOURED FRIEND EDMƲND WINGATE, of Grayes Inne, Esq
• TO THE READER:
• A GENERAL SURVEY Of the whole WORK.
• notice
• THE COMPLEAT SURVEYOR. The First Book.
  • GEOMETRICALL DEFINITIONS.
    • 1. A Point is that which cannot be divided.
    • 2. A Line is a length without breadth or thicknesse.
    • 3. The ends or bounds of a Line are Points.
    • 4. A Right line is that which lieth equally between his points.
    • 5. A Superficies is that which hath only length and breadth.
    • 6. The extreams of a Superficies are Lines.
    • 7. A plain Superficies is that which lieth equally between his lines.
    • 8. A plain Angle is the inclination or bowing of two lines the one to the other, the one touching the other, & not being directly joyned together.
    • 9. And if the lines which contain the angle be right lines, then is it called a right lined angle.
    • 10. When a right line standing upon a right line maketh the angles on either side equall, then either of those angles is a right angle: and the right line which standeth erected, is called a perpendicular line to that whereon it standeth.
    • 11. An Obtuse angle is that which is greater than a right angle.
    • 12. An Acute angle is lesse than a right angle.
    • 13. A limit or term is the end of every thing.
    • 14. A Figure is that which is contained under one limit or term or many.
    • 15. 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 Cir∣cumference thereof are equall one to the other.
    • 16. A Diameter of a Circle is a right line drawn by the Center thereof, and ending at the Cir∣cumference, on either side dividing the Circle into two equall parts.
    • 17. A Semicircle is a figure contained under the Diameter, and that part of the Circumference cut off by the Diameter.
    • 18. A Section or portion of a Circle, is a Figure contained under a right line, and a part of the circumference, greater or lesse then a semicircle.
    • 19. Right lined figures are such as are contain∣ed under right lines.
    • 20. Three sided figures are such as are contained under three right lines.
    • 21. Four sided figures are such as are contained under four right lines.
    • 22. Many sided figures are such as have more sides than four.
    • 23. All three sided figures are called Triangles.
    • 24. Of four sided Fi∣gures, a Quadrat or Square is that whose sides are equal and his angles right. [As the Figure A.]
    • 25. A Long square is that which hath right an∣gles but unequal sides. [As the Figure B]
    • 26. A Rhombus is a Figure having four equall sides but not right angles. [As the Figure C.]
    • 27. A Rhomboides is a Figure whose opposite sides are equall, and whose opposite angles are also e∣quall, but it hath neither e∣quall sides nor equal angles. [As the Figure D.]
    • 28. All other Figures of four sides (besides these) are called Trapezias.
    • 29. Parallel, or equidistant right lines are such which being in one and the same Superficies and produced infinitely on both sides, do ne∣ver in any part concur.
  • Geometricall Theoremes.
  • GEOMETRICALL PROBLEMES.
    • PROBLEME I. Ʋpon a right line given, how to erect another right line, which shall be perpendicular to the right line given.
    • PROB. II. How to erect a Perpendicular on the end of a right line given.
    • PROB. III. How to let fall a perpendicular, from any point as∣signed, upon a right line given.
    • PROB. IV. How to make an angle equall to an angle given.
    • PROB. V. A right line being given, how to draw another right line which shall be parallel to the former, at any distance required.
    • PROB. VI. To divide a right line given into any number of equall parts.
    • PROB. VII. A right line being given, how to draw another right line parallel thereunto, which shall also passe through a point assigned.
    • PROB. VIII. Having any three points given, which are not situate in a right line, how to finde the center of an arch of a Circle which shall passe directly through the three given points.
    • PROB. IX. Any three right lines being given, so that the two shortest together be longer then the third, to make thereof a Triangle.
    • PROB. X. Having a right line given, how to make a Geome∣tricall Square, whose side shall be equall thereunto.
    • PROB. XI. Two right lines being given, how to finde a third right line which shall be in proportion unto them.
    • PROB. XII. Three right lines being given, to finde a fourth in proportion to them.
    • PROB. XIII. To divide a right line given into two parts, which shall have such proportion one to the other as two given right lines.
    • PROB. XIV. How to divide a Triangle into two parts, according to any proportion assigned, by a line drawn from any angle thereof, and to lay the lesser part towards any side assigned.
    • PROB. XV. The Base of the Triangle being known, to perform the foregoing Probleme by Arithmetick.
    • PROB. XVI. 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 re∣quired.
    • PROB. XVII. How to divide a Triangle given into two parts, ac∣cording to any proportion assigned, by a line drawn from a point limited in any of the sides thereof: and to lay the greater or lesser part towards an angle assigned.
    • PROB. XVIII. To perform the foregoing Probleme Arithmetically.
    • PROB. XIX. How to divide a Triangle, whose area or content is known, into two parts, by a line drawn from a point limited in any side thereof, according to any number of Acres, Roods and Perches.
    • PROB. XX. How to divide a Triangle according to any propor∣tion given, by a line drawn parallel to one of the sides.
    • PROB. XXI. To perform the foregoing Probleme Arithmetically.
    • PROB. XXII. To divide a Triangle of any known quantity, into two parts, by a line drawn parallel to one of the sides, according to any number of Acres, Roods, and Perches.
    • PROB. XXIII. From a line given, to cut off any parts required.
    • PROB. XXIV. To finde a mean proportionall between two lines given.
    • PROB. XXV. How to divide a line in power according to any proportion given.
    • PROB. XXVI. How to inlarge a line in power, according to any proportion assigned.
    • PROB. XXVII. To inlarge or diminish a Plot given, according to any proportion required.
    • PROB. XXVIII. How to make a Triangle which shall contain any number of Acres, Roods and Perches, and whose base shall be equal to any (possible) number given.
    • PROB. XXIX. How to reduce a Trapezia into a Triangle, by a line drawn from any angle thereof.
    • PROB. XXX. How to reduce a Trapezia into a Triangle, by lines drawn from any point in any of the sides thereof.
    • PROB. XXXI. How to reduce an irregular Plot of five sides into a Triangle.
    • PROB. XXXII. A Trapezia being given, how from any angle there∣of of to divide the same into two parts being in pro∣portion one to the other as two given right lines, and to set the part cut off towards an assigned side.
    • PROB. XXXIII. A Trapezia being given, how, from a point limited in any side thereof, to draw a line which shall di∣vide the same into two parts in proportion as two given lines.
    • PROB. XXXIV. A Trapezia being given, how to divide the same into two parts in proportion as two lines given, and so that the line of partition may be parallel to any side thereof.
    • PROB. XXXV. The figure of a Plot being given, how to divide the same into two parts, being in proportion one to the other as two given lines are, with a line drawn from an angle assigned.
    • PROB. XXXVI. How to divide a Triangle into any number of equall parts, by lines drawn from a point given in any side thereof.
    • PROB. XXXVII. How to divide an irregular Plot of six sides, into two parts, according to any assigned proportion, by a right line drawn from a point limited in any of the sides thereof.
    • PROB. XXXVIII. How to divide an irregular Plot according to any proportion, by a line drawn from any angle thereof.
• THE COMPLEAT SURVEYOR. The Second Book.
  • CHAP. I. Of Instruments in generall.
  • CHAP. II. Of the Theodolite, the description thereof, and the detection of an errour frequently committed in the making thereof, with the manner how to correct the same.
  • CHAP. III. The description of the Circumferentor.
  • CHAP. IV. A Description of the Plain Table, how it hath been formerly made, and how it is now altered, it being the most absolute Instrument of any other for a Surveyor to use, in that it performeth what∣soever may be done either by the Theodolite, Circumferentor, or any other Instrument, with the same ease and exactnesse.
  • CHAP. V. Of Chains, the severall sorts thereof.
    • Of Mr. RATHBORNS Chain.
    • Of Mr. GUNTERS Chain.
    • Cautions to be observed in the use of any Chain.
    • How to reduce any number of Chains and Links, into Feet.
  • CHAP. VI. Of the Protractor.
  • CHAP. VII. Of Scales.
  • CHAP. VIII. Of a Field-Book.
  • CHAP. IX. Of Instruments for Reducing of Plots.
• THE COMPLEAT SURVEYOR. The Third Book.
  • CHAP. I. The Elplanation and Ʋse of the Table of SINES.
    • PROP. I. Any Degree and Minute being given, to finde the Sine thereof.
    • PROP. II. Any Sine being given, to finde the number of de∣grees and minutes thereunto belonging.
    • table
  • CHAP. II. The Explanation and Ʋse of the Table of LOGARITHMS.
    • PROP. I. A number being given, to finde the Logarithme thereof.
    • PROP. II. A Logarithme being given, how to finde the ab∣solute number thereunto belonging.
    • table
  • CHAP. III. The use of the Tables of Sines and Logarithms in the resolving of Plain Triangles.
  • CHAP. IV. Containing the doctrine of the dimension of right lined Triangles, whether right angled or oblique angled, and the severall Cases threin resolved, both by Tables, and Lines of Artificiall 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 finde the Per∣pendicular.
        • A generall Rule.
        • How to perform the same work, by the lines of Sines and Numbers.
      • CASE II. The Base, and the angle at the Base being given, to finde the Hypothenusall.
        • By the lines of Sines and Numbers.
      • CASE III. The Hypothenusall, and angle at the Base being given, to finde the Perpendicular.
        • By the lines of Sines and Numbers.
      • CASE IV, The Hypothenusall, and angle at the Base being given, to finde the Base
        • By the lines of Sines and Numbers.
      • CASE V. The Perpendicular, and angle at the Base being given, to finde the Hypothenusall.
        • By the lines of Sines and Numbers.
      • CASE VI. The Hypothenusall and Perpendicular being given, to finde the angle at the Base.
        • By the lines of Sines and Numbers.
    • Of Oblique angled plain Triangles.
      • CASE VII. Having two angles, and a side opposite to one of them given, to finde the side opposite to the other.
        • By the lines of Sines and Numbers.
        • By the lines of Sines and Numbers.
      • CASE VIII. Two sides and an angle opposite to one of them being given, to finde the angle opposite to the other.
        • By the lines of Sines and Numbers.
      • CASE IX. Having two sides, and the angle contained by them given, to finde either of the other angles.
        • By the lines of Tangents and Numbers.
      • CASE X. The three sides of a right lined plain Triangle being given, how to finde the Area, or the su∣perficiall content thereof.
• THE COMPLEAT SURVEYOR. The Fourth Book.
  • CHAP. I. Of the use of the Scale.
    • 1. Any length being measured by your Chain, how to lay down the same distance upon paper.
    • 2. A right line being given, to finde how many Chains and Links are therein con∣tained, according to any Scale assigned.
    • 3. How to lay down upon paper, an angle containing any number of degrees and minutes, by the Line of Chords.
    • 4. Any angle being given, to finde what number of degrees and minutes are contained therein.
  • CHAP. II. Of the use of the Protractor.
    • 1. To lay down upon paper an angle of any quantity.
    • 2. Any angle being given, to finde the quantity thereof by the Protractor.
  • CHAP. III. Of the Plain Table, how to set the parts thereof together, and make it fit for the field.
  • CHAP. IV. How to measure the quantity of any angle in the field, by the Plain Table, Theodolite, and Circumferentor: and also to observe an angle of Altitude.
    • 1. How to observe an angle in the Field by the Plain Table.
    • 2. How to finde the quantity of an angle in the field by the Theodolite.
    • 3. How to finde the quantity of any angle in the field, by the Circumferentor.
    • 4. How to set the Index and Labell Horizontall upon the Staffe.
    • 5. How to observe an angle of Altitude.
  • CHAP. V. How to take an inaccessible Distance at two sta∣tions by the three forementioned Instruments, and first, by the Plain Table.
  • CHAP. VI. How to take an inaccessible distance at two stations by the Theodolite.
  • CHAP. VII. How to take an in-accessible distance at two stations by the Circumferentor.
  • CHAP. VIII. How to protract or lay down a Distance taken, ac∣cording to the directions of the two last Chapters, upon paper, by help of your Protractor or line of Chords.
  • CHAP. IX. How to take the altitude of any Tower, Tree, Stee∣ple, or the like (being accessible) by the Labell and Tangent line.
  • CHAP. X. How to protract or lay down upon paper, the obser∣vation made in the last Chapter.
  • CHAP. XI. How to take an in-accessible Altitude, by the Labell and Tangent line.
  • CHAP. XII. How to Protract the observation taken in the last Chapter.
  • CHAP. XIII. How to take the distance of divers places one from another, according to their true scituation, in plano, and to make (as it were) a Map there∣of, by the Plain Table.
  • CHAP. XIV. How to perform the work of the last Chapter by the Theodolite.
  • CHAP. XV. How to protract the former Observations upon pa∣per, and to make a Scale to measure any of the Distances.
  • CHAP. XVI. How to take the true plot of a field at one station taken within the same field, so that from thence you may see all the angles of the same field, by the Plain Table.
  • CHAP. XVII. How to take the plot of a field at one station taken in the middle thereof by the Theodolite.
  • CHAP. XVIII. How to take the plot of a Field at one station taken in the middle thereof by the Circumferentor.
  • CHAP. XIX. How to protract any observations taken according to the directions in the last Chapter.
  • CHAP. XX. How to take the plot of a Field at one station taken in any angle thereof, from whence all the other angles may be seen, by the Plain Table.
  • CHAP. XXI. How to take the plot of a Field at one station taken in any angle thereof by the Theodolite.
  • CHAP. XXII. How to take the Plot of a field at one station taken in any angle thereof, from which all the rest may be seen, by the Circumferentor.
  • CHAP. XXIII. How to Protract any observation taken according to the Doctrine of the two last Chapters.
  • CHAP. XXIV. How to take the Plot of a Field at two stations taken in any parts thereof, by measuring from either of the stations to the visible angles, by the Plain Table.
  • CHAP. XXV. How to take the true Plot of a Field at two sta∣tions taken in any parts thereof, from whence the angles may be seen by the Theodolite.
  • CHAP. XXVI. How to take the Plot of a Field at two stations taken in any parts thereof, by the Circumfe∣rentor.
  • CHAP. XXVII. How to protract any observations taken according to the directions of the two last Chapters.
  • CHAP. XXVIII. How to take the Plot of a field at two stations taken in the middle thereof, from either of which all the angles in the field may be seen, with the mea∣suring of one line only, by the Plain Table.
  • CHAP. XXIX. How to take the Plot of a field at two stations taken in any part thereof, from either of which all the angles in the field may be seen, and measuring on∣ly the stationarie distance, by the Theodolite or Circumferentor.
  • CHAP. XXX. How to protract any observations taken according to the directions of the last Chapter.
  • CHAP. XXXI. How to take the Plot of a Wood, Park, or other large Champion plain by the Plain Table, by measuring round about the same, and making ob∣servation at every angle,
  • CHAP. XXXII. How to take the Plot of a Wood, Park, or other large Champion plain, by going about the same, and making observation at every angle thereof, by the Theodolite.
  • CHAP. XXXIII. How to protract or lay down any observations taken according to the doctrine of the last Chapter.
  • CHAP. XXXIV. How to know whether you have taken the angles of a Field truly in going round about the same with the Theodolite, as in Chap. 33, whereby you may know whether your Plot will close or not the sides being truly measured.
  • CHAP. XXXV. How to take the Plot of any Wood, Park, or other large Champion plain, by going about the same, and making observation at every angle thereof, by the Circumferentor.
  • CHAP. XXXVI. How to protract any observations taken by the Circumferentor, according to the doctrine of the last Chapter.
  • CHAP. XXXVII. How to take the Plot of any Park, Forrest, Chase, Wood, ot other large Champion plain, by the Index and Needle, together with the degrees on the frame of the Table, most commodiously supplying the use of the Peractor.
  • CHAP. XXXVIII. How to protract any observation taken as in the last Chapter.
  • CHAP. XXXIX. How to finde how many Acres, Roods and Perches, are contained in any piece of Land, the plot there∣of being first taken by any Instrument.
    • Of the Geometricall Square.
    • Of the long Square.
    • Of the Triangle.
    • Of the Trapezia.
    • Of irregular Figures, how to reduce them into Triangles or Trapezias, and to cast up the content thereof.
    • Of the Circle.
    • The Circumference of a Circle being given, to finde the Diameter.
  • CHAP. XL. Of the manner of casting up the content of any piece of Land in Acres, Roods and Perches, by Master Rathborns Chain.
  • CHAP. XLI. How to reduce any number of Perches into Roods and Acres, or any number of Acres and Roods into Perches.
    • section
    • To reduce Acres into Perches.
  • CHAP. XLII. How to cast up the content of any piece of Land in Acres, Roods and Perches, by Master Gunters Chain.
    • section
    • Another Example.
    • The use of the Scale of Reduction.
    • Another Example.
  • CHAP. XLIII. Containing divers compendious rules, for the ready casting up of the content of any plain superficies, and other necessary conclusions incident to Sur∣veying, by the line of Numbers.
    • 1. The length and breadth of a right angled Paral∣lelogram or long Square being given in Perches, to finde the content thereof in Perches.
    • 2. The length and breadth of a long Square being given in Perches, to finde the content in Acres.
    • 3. The length and breadth of a Parallelogram be∣ing given in Chains, to finde the content in Acres.
    • 4. Having the Base and perpendicular of a Tri∣angle given in Perches, to finde the content in Acres.
    • 5. The Base and perpendicular of a Triangle being given in Chains, to finde the content in Acres.
    • 6. The Area or superficiall content of any piece of Land being given according to one kinde of Perch, to finde the content thereof accoading to cnother kinde of Perch.
    • 7. Having the length of the Furlong, to finde the breadth of the Acre.
  • CHAP. XLIV. How to reduce one kinde of measure into another, as Statute measure to Customarie measure.
  • CHAP. XLV. How to lay out severall Furlongs in Common-fields unto divers Tenants.
  • CHAP. XLXI. To finde the horizontall line of any hill or mountain.
    • section
    • Another way.
  • CHAP. XLVII. How to plot Mountanous and uneven grounds, with the best way to finde the content thereof.
  • CHAP. XLVIII. How to take the Plot of a whole Mannor, or of divers parsels of Land lying together, whether Wood-lands or Champion plains, by the Plain Table.
  • CHAP. XLIX. How to take the plot of a whole Mannor, or of di∣vers severals whether Woodland or Champion plains, by the Theodolite, Circumferentor, or Peractor.
  • CHAP. L. How to protract or draw the plot of a whole Man∣nor, or of divers inclosures, the observations of the severall angles, lines and bounders being noted in your Field-book.
  • CHAP. LI. The figure of any plot being given, how to inlarge or diminish the same according to any assigned proportion.
  • CHAP, LII. How to draw a perfect draught of a whole Mannor, and to furnish it with all necessary varieties, also to trick and beautifie the same: in which, (as in a Map) the Lord of the Mannor may at any time (by inspection only) see the symetry, scituation and content of any parcell of his Land.
  • CHAP. LIII. How to finde whether water way be conveyed from a Spring head, to any appointed place.
    • section
    • Another way.
• conclusion