ADVERTISEMENT.

Lordships Surveyed,

and Maps drawn

of the fame. Timber Measured and Valued, with other Artificers Work; and Dialling in all its Parts, Performed by Edward Laurence.

He is to be heard of when in London at Mr Senex's at the Globe in Salisbury-Court.

or

N. B. In Winter, and at fuch Times as he is not Surveying, Gen. tlemen may have their Sons Daughters Taught Accompts after a Natural, Easy and Concise Method, with the Use of the Globes and Maps, and all other useful Parts of the Mathematicks.

THE

Young Surveyor's

GUIDE.

I

Practical Geometry.

Design in this part to lay down the first Principles of Geometry; and to do it methodically, to begin with Definitions, and the Explication of the most ordinary Terms: To which I shall add some Maxims, wherein Natural Reason does instruct us; and then proceed to Geometrical Problems; and such Propofitions as I find convenient for this Tract, fo that a Man may be able to give a de

monftrable Account of what he does.

1

Geometrical Definitions.

IA Point is that which is confidered as having no manner of Dimensions: And as being indivisible in every refpect, the Ends or Extremities of Lines are Points.

2 Fig.1 A Line has Length, but noBreadth, nor Thickness; of which there are two forts, viz, right or streight, and curve or crooked; as AB is a fireight Line, BC a crooked Line.

3. Fig. 2. An Angle is the meeting of two Lines in a Point; provided the two Lines so meeting, do not make one streight Line: As in the Lines AB and AC meeting together in the Point A, make an Angle BAC, which is measur'd by an Arch of a Circle DE, described from the angular Point A as a Center, and intercepted between the Lines AC, and AB, which form it an Angle, is faid to be equal to, greater or less than another, according as the Arch which measures it, contains as many, more, or fewer of the equal Parts into which that Circumference is supposed to be divided.

Of which right-lined Angles there are three forts, viz. Right Angled, Acute, and Obtufe: when a Line falleth perpendicularly upon another, it maketh two right Angles, that is, neither leaneth to one fide or the other.

Example.

Fig. 3. Let CAB be a right Line, DA perpendicular to it, that is to say, neither leaning towards B or C, but exactly upright, then are both the Angles at A, viz. DAB and DAC right Angles, and contain in each just 90 Degrees, or the 4th part of a Circle; but if the Line DA had not been Perpendicular, but had leaned towards B, then had DAC been an Obtufe Angle, or greater then a right Angle; and DAB, an Acute Angle; or less then a Right Angle. 4. A Figure is that which is comprehended under one, or more Lines.

5. All Figures contained under three Sides,' are called Triangles, which Euclid divides, with respect either to their Angles or Sides.

6. Fig. 4. An Equilateral Triangle is that which hath its three Sides equal, as the Triangle ABC.

7. Fig. 5. Anifofceles Triangle, is that which hath two Sides equal: As if the two Sides AB and AC be equal, the Triangle ABG is Iscosceles.

8. Fig. 6. AScelenum, is a Triangle having all the three Sides unequal, as GHI

9. Fig. 7. A Rectangled Triangle, is that which hath one right Angle, as DEF,

10. Fig.8. An Ambligone, or obtufe Angled Triangle, is that which hath one Obtufe Angle, Has IGH.

B2

Fig

11. Fig. 9. An Oxygone, or Acute Angled Triangle, is that whose Angles are all Acute, as ABC.

12. Fig 10. ASquare confists of four equal Sides, and four right Angles, as AB. 12. A Parallelogram is a Figure that ha'h its two oppofite Sides B parallel. 14. Fig. 11. An OblongRectangle, having, its oppofite Sides equal, and its Angles right, as CB, is called a long Square or Parallelogram.

15. Fig. 12. A Rhombus, is that whose Sides are all equal, but not right Angled, as B. 16. Fig. 13. ARhomboides, is that whose op. posite Sides and Angles are equal among themselves; but not right Angled, as D.

17. Fig. 14. Parallel Lines are such as being in the fame Plain will never meet, keeping still the fame distance one from the other; as AB and CD

18. Fig. 15. All other four fided Figures are called Trapezia: Other Figures that are contained under 5, 6, 7, or more Sides, I call Irregular, Polygones, as Fis an Irregular Figure, and G is a Trapezia.

Note, Such as are made by the Circumference of a Circle divided into any Number of equal parts, are regular Figures; having all their Sides and Angles equal, and are called from the Number of Angles they contain, as a Pentagone, Hexagone, Heptagone, Otagone, &c. Which fignifies a Figure of 5, 6, 7 or 8 Angles or Sides, whose