Author:  Leybourn, William, 16261716. 
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. 
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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. Leybourn, William, 16261716. London: Printed by R. & W. Leybourn, for E. Brewster and G. Sawbridge ..., 1653. 
Subject terms:  Surveying  Early works to 1800. 
URL:  http://name.umdl.umich.edu/A48331.0001.001 
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 M^{r}. RATHBORNS Chain.
Of M^{r}. 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 FieldBook.
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 inaccessible 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 inaccessible 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
Commonfields 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 Woodlands 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 Fieldbook.
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
