ADVERTISEMENT.

of the same. Timber Measured

. and Valued, with other Artificers Work; and Dialling in all its Parts, Perforined by Edward Laurence.

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

N. B. In Winter, and at such Times as he is not Surveying, Gen. tlemen may have their Sons or 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

Young Surveyor's GUIDE.

Pradical Geometry.

I

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 fall add some Maxims, wherein Natural Reason does instruct us ; and then proceed 1o Geometrical Probleins ; and such Propositions as I find convenient for this Tract, so that a Man may be able to give a de. inonftrable Account of what he does.

1

Geometrical Definitions. I A Poirt is that which is considered as having no manner of Dimensions: And as being indivisible in every respect, the Ends or Extremities of Lines are Points.

2 Fig. 1 A Line has Length, but noBreadth, nor Thickness ; of which there are two sorts, 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 said 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 side 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 it the Line DA had not been Perpendicular, but had leaned towards B, then had DAC been an Obruse 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.

s. All Figures containedịunder 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. AnlsoscelesTriangle is that which hath two Sides equal: As if the two Sides AB and AC be equal, the Triangle ABC is Iscosceles.

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

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

10. Fig.8. An Ambligone, or obtufe Angled Triangle, is that which hath one Obture Angle, H as IGH.

B 2

Fir

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

12. Fig 10. ASquare consists of four equal Sides, and four right Angles, as AB.

13. A Parallelogram is a Figure that ha'h its two oppolite Sides B parallel.

14.Fig.11. An Oblong Rectangle, having, its opposite Sides equal, and its Angles right, as CB, is called a long Square or Parallelogram.

15. Fig. 1 2. A Rhombus,is that whore Sides are all qual, but not right Angled, as B.

16. Fig.13. A Rhomboides,is that whose opposite sides and Angles are equal among ihemselves; but not right angled, as D.

17. Fig. 1c. ParallelLines are such as being in the same Plain will never meet, keeping still the same 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 F is an Irregular Figure, and G is a Trapezia.

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