## The Theory and Practice of Surveying: Containing All the Instructions Requisite for the Skilful Practice of this Art |

### From inside the book

Page 41

The versed

The versed

**sine**of an arc is that part of the diameter that lies between the right**sine**and the circumference : thus LB is ... The**sine**, tangent , or secant of the complement of any arc , is called the**co**-**sine**,**co**tangent , or**co**... Page 42

... BL the versed

... BL the versed

**sine**, HF the**co**-**sine**, DI the**co**- tangent , and CI the**co**- secant , & c . of the arc BH ; then HL is called the**sine**, BK the tangent , CK the secant , & c . of the angle HCB , whose measure is the arc HB . fig . Page 62

Let DHB be a quadrant of a circle described by the ra .. dius CB ; HB an arc of it , and DH its complement ; HL or FC the

Let DHB be a quadrant of a circle described by the ra .. dius CB ; HB an arc of it , and DH its complement ; HL or FC the

**sine**, FH or CL its**co**-**sine**, BK its tangent , DI its cotangent ; CK its secant , and CI its**co**- secant . Fig . Page 63

The radius is to the tangent of an arc , as the

The radius is to the tangent of an arc , as the

**Co**-**sine**of it is to the**sine**. 3. The**sine**of an arc is to its**co**-**sine**, as the radius to its**co**- tangent ; 4. Or the radius is to the**co**- tangent of an arc , as its**sine**to its**co**... Page 108

is obvious that if the hypothenuse be multiplied by the natural

is obvious that if the hypothenuse be multiplied by the natural

**sine**of either of the acute angles , the product will be the length of the side opposite to that angle ; and multiplied by the natural**co**-**sine**of the same angle ...### What people are saying - Write a review

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### Common terms and phrases

acres altitude angle Answer arch base bearing called centre chains chord circle Co-sec Co-sine Co-tang column compasses contained decimal degrees Dep Lat difference direct Dist distance divided divisions draw drawn east edge equal EXAMPLE extended feet figures fixed four fourth give given glass greater ground half hand height Hence Horizon inches laid land Lat Dep latitude length less logarithm manner marked measure meridian method minutes multiplied natural object observed opposite parallel perches perpendicular plane pole PROB proportion Quadrant quotient radius reduce remainder right angles right line root rule scale Secant sect side sights sine square station Sun's suppose survey taken Tang tangent theo third triangle true whole

### Popular passages

Page 38 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

Page 25 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.

Page 199 - RULE. From half the sum of the three sides subtract each side severally.

Page 106 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Page 27 - The VERSED SINE of an arc is that part of the diameter which is between the sine and the arc. Thus BA is the versed sine of the arc AG.