|Author:||Love, John, fl. 1688.|
|Title:||Geodæsia, or, The art of surveying and measuring of land made easie by plain and practical rules, how to survey, protract, cast up, reduce or divide any piece of land whatsoever : with new tables for the ease of the surveyor in reducing the measures of land : moreover, a more facile and sure way of surveying by the chain, than has hitherto been taught : as also, how to lay-out new lands in America, or elsewhere : and how to make a perfect map of a river's mouth or harbour : with several other things never yet publish'd in our language / by John Love ...|
|Publication info:||Ann Arbor, Michigan: University of Michigan, Digital Library Production Service
2011 December (TCP phase 2)
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Geodæsia, or, The art of surveying and measuring of land made easie by plain and practical rules, how to survey, protract, cast up, reduce or divide any piece of land whatsoever : with new tables for the ease of the surveyor in reducing the measures of land : moreover, a more facile and sure way of surveying by the chain, than has hitherto been taught : as also, how to lay-out new lands in America, or elsewhere : and how to make a perfect map of a river's mouth or harbour : with several other things never yet publish'd in our language / by John Love ...
Love, John, fl. 1688.
London: Printed for John Taylor ..., 1688.
Signatures *B2, *E2-3, and *F3-4 are stained with print missing; signature *G bound and photographed between pages 194-195, in filmed copy. Pages 196-end photographed from British Library copy and inserted at end.
Reproduction of original in Bodleian Library.
Surveying -- Early works to 1800.
THE PREFACE TO THE READER.
A Catalogue of Books Printed for and Sold by John Taylor at the Ship in S. Paul's Church-Yard.
GEODAESIA: OR, THE ART OF Measuring Land, &c.
How to Extract the Square Root.
Of four Sided Figures there are these Sorts:
PROB. I. How to make a Line Perpendicular to a Line Given.
PROB. ii. How to raise a Perpendicular upon the End of a Line.
Another way to do the same, I think more easie, though indeed almost the same.
PROB. iii. How from a Point assigned, to let fall a Per∣pendicular upon a Line given.
PROB. iv. How to divide a Line into any Number of Equal Parts.
PROB. v. How to make an Angle Equal to any other Angle given.
PROB. vi. How to make Lines Parallel to each other.
PROB. vii. How to make a Line Parallel to another Line, which must also pass through a Point assigned.
PROB. viii. How to make a Triangle, three Lines being given you.
PROB. ix. How to make a Triangle equal to a Triangle given, and every way in the same Proportion.
PROB. x. How to make a Square Figure.
PROB. xi. How to make a Parallelogram, or long Square.
PROB. xii. How to make a Rhombus.
PROB. xiii. How to divide a Circle into any number of Equal Parts, not exceeding ten, or other∣wise how to make the Figures called, Pen∣tagon, Hexagon, Haptagon, Octo∣gon, &c.
To make a Pentagon or Five-sided Figure.
To make a Hexagon or Six-sided Figure.
To make a Heptagon, or Figure of Seven, equal Sides and Angles.
To make an Octogon, commonly called an Eight-square Figure.
To make a Nonagon.
To make a Decagon.
PROB. xiv. Three Points being given: How to make a Circle, whose Circumference shall pass through the three given Points, provided the three Points are not in a streight Line.
PROB. xv. How to make an Ellipsis, or Oval several ways.
PROB. xvi. How to divide a given Line into two Equal Parts, which may be in such Proportion to each other, as two given Lines.
Example by Arithmetick.
PROB. xvii. Three Lines being given, to find a Fourth in Proportion to them.
The Explanation of the Table.
The Use of this Table.
And first of the Chain.
Of Instruments for the taking of an Angle in the Field.
To take the Quantity of an Angle.
To take the Quantity of the same Angle by the Semicircle.
How to take the same Angle by the Circumferentor.
How with the Semicircle to take the Quantity of an Angle in the Field by the Needle.
Of the Field-Book.
Of the Scale.
How to lay down an Angle by the Line of Chords.
How to make a Regular Polygon, or a Figure of 5, 6, 7, 8, or more Sides, by the Line of Chords.
To make a Triangle in a Circle by the Line of Chords.
How to make a Line of Chords.
Of the Protractor.
How to lay down an Angle with the Protractor.
How to take the Plot of a Field at one Station in any place thereof, from whence you may see all the Angles by the Semicircle.
How to Protract the Former Observations taken.
How to take the Plot of the same Field at one Station by the Plain Table.
How to take the Plot of the same Field at one Station by the Semi-circle, either with the help of the Needle and Limb both together, or by the help of the Needle only.
How by the Semi-circle to take the Plot of a Field, at one Station, in any Angle thereof, from whence the other Angles may be seen.
To Protract the former Observations.
How to take the Plot of a Field at two Sta∣tions, provided from either Station you may see every Angle, and measuring only the Stationary Distance.
Stationary Distance 20 Chains, 00 Links.
How to Protract or lay down upon Paper these foregoing Observations.
How to take the Plot of a Field at two Stati∣ons, when the Field is so Irregular, that from one Station you cannot see all the Angles.
How to take the Plot of a Field at one Station in an Angle (so that from that Angle you may see all the other Angles) by measuring round about the said Field.
How to take the Plot of the foregoing Field, by measuring one Line only, and taking Ob∣servations at every Angle.
How to take the Plot of a Large Field or Wood, by measuring round the same, and taking Observations at every Angle thereof, by the Semicircle.
When you have Surveyed after this manner, how to know before you go out of the Field whether you have wrought true or not.
Directions how to Measure Parallel to a Hedge (when you cannot go in the Hedge it self,) and also in such case, how to take your Angles.
How to take the Plot of a Field or Wood, by observing near every Angle, and measuring the Distance between the Marks of Obser∣vation, by taking, in every Line, two Off-sets to the Hedge.
This way of Surveying is much easier done (though I cannot say truer) by taking only a great Square in the Field; from the Sides of which, the Off-sets are taken.
How by the help of the Needle to take the Plot of a large Wood by going round the same, and making use of that Division of the Card that is numbred with four 90s or Quadrants.
Example of the foregoing Figure.
How by the Chain only, to take an Angle in the Field.
How by the Chain only to Survey a Field by going round the same.
The common way taught by Surveyors, for tak∣ing the Plot of the foregoing Field.
How to take the Plot of a Field at one Sta∣tion, near the Middle thereof, by the Chain only.
How to plot the former Observations.
Of the Square, and Parallelogram.
To find the Content of a Trapezia.
How to find the Content of an Irregular Plot, consisting of many Sides and Angles.
How to find the Content of a Circle, or any Portion thereof.
By the Diameter only to find the Content.
How to measure the Superficial Content of the Section of a Circle.
How to find the Content of a Segment of a Circle without knowing the Diameter.
How to find the Superficial Content of an Oval.
How to find the Superficial Content of Regular Polygons; as Pentagons, Hexagons, Hep∣tagons, &c.
A certain quantity of Acres being given, how to lay out the same in a Square Figure.
How to lay out any given Quantity of Acres in a Parallelogram; whereof one Side is given.
How to lay out a Parallelogram that shall be 4, 5, 6, or 7, &c. times longer than it is broad.
How to make a Triangle that shall contain any number of Acres, being confined to a certain Base.
How to find the Length of the Diameter of a Circle which shall contain any number of Acres required.
How to Reduce a large Plot of Land or Map into a lesser compass, according to any given Proportion; or e contra, how to Enlarge one.
How to change Customary-Measure into Sta∣tute, and the contrary.
Knowing the Content of a piece of Land, to find out what Scale it was plotted by.
To Survey a Mannor observe these following Rules.
How to take the Draught of a County or Country.
How to divide a Triangle several ways.
How to divide a Triangular Piece of Land in∣to any Number of Equal or Ʋnequal Parts, by Lines proceeding from any Point assigned in any Side thereof.
How to divide a Triangular Piece of Land, ac∣cording to any Proportion given, by a Line Parallel to one of the Sides.
Of dividing Four-Sided Figures or Trapeziaes.
How to reduce a Trapezia into a Triangle, by Lines drawn from any Angle thereof.
How to reduce a Trapezia into a Triangle, by Lines drawn from a Point assigned in any Side thereof.
How to reduce an Irregular Five-Sided Figure into a Triangle, and to divide the same.
If in dividing the Plot of a Field there be Outward Angles, you may change them after the following manner.
How to Divide an Irregular Plot of any number of Sides, according to any given Proportion, by a streight Line through it.
An easie way of Dividing Lands.
How to Divide a Circle according to any Pro∣portion, by a Line Concentrick with the first.
The use of the Tables of Sines and Tangents.
How to find the Cosine or Sine Complement; the Cotangent or Tangent Complement of any given Degrees and Minutes.
Any Sine or Tangent, Co-sine or Co-tangent being given, to find the Degrees and Mi∣nutes belonging thereto.
Certain Theorems for the better understanding Right-Lined Triangles.
CASE i. In Right-Angled Triangles, the Base being given, and the Acute Angle at the Base; how to find the Hypothenusal Line, and the Perpendicular.
How to find the Perpendicular.
CASE ii. The Perpendicular and Angle ACB being given to find the Base and Hypothenusal.
For the Hypothenusal.
CASE iii. The Hypothenusal, and either of the Acute Angles given, to find the Base and Perpen∣dicular.
CASE iv. The Hypothenusal and Base being given, to find the two Acute Angles, viz. ACB, and CAB.
CASE v. The Hypothenusal and Perpendicular being gi∣ven, to find the Angles and Base.
CASE vi. Of Oblique Angled Plain Triangles.
CASE vii. Two Angles being given, and a Side opposite to one of them, to find the other opposite Side.
CASE viii. Two Sides of a Triangle being given, with the Angle contained by them, to find either of the other Angles.
CASE ix. Three Sides of an Oblique Triangle being gi∣ven, to find the Angles.
CASE x. The three Sides of an Oblique Triangle being given, how to find the Superficial Content without knowing the Perpendicular.
How to take the Heighth of a Tower, Steeple, Tree, or any such thing.
How to take the Heighth of a Tower, &c. when you cannot come nigh the Foot thereof.
How to take the Heighth of a Tower, &c. when the Ground either riseth or falls.
How to take the Horizontal-line of a Hill.
How to take the Shoals of a Rivers Mouth, and Plot the same.
How to know whether Water may be made to run from a Spring-head to any appointed Place.
A TABLE OF THE Northing or Southing, Easting or Westing of every Degree from the Meridian, according to the Num∣ber of Chains run upon any De∣gree.
THE USE OF THE Foregoing Table,
A TABLE OF Sines & Tangents To every Fifty Minute OF THE QUADRANT.
A TABLE OF Logarithm Numbers.