The Theory and Practice of Surveying: Containing All the Instructions Requisite for the Skilful Practice of this Art |
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Page 55
... half the parallelogram . Cor . 3. It is hence also plain , that the opposite sides of a parallelogram are equal ; for it has been proved that ABCD being a parallelogram , AB will be CD and AD - BC . THEO . XIII . PL . 1. fig . 31 . All ...
... half the parallelogram . Cor . 3. It is hence also plain , that the opposite sides of a parallelogram are equal ; for it has been proved that ABCD being a parallelogram , AB will be CD and AD - BC . THEO . XIII . PL . 1. fig . 31 . All ...
Page 56
... half of the square ABDE ( by cor . 2. theo . 12. ) and the triangle ABH is half the parallelogram BKLH . The same way it may be proved , that the square ACGF , is equal to the pa- rallelogram KCLM . So ABDE + ACGF the sum of the squares ...
... half of the square ABDE ( by cor . 2. theo . 12. ) and the triangle ABH is half the parallelogram BKLH . The same way it may be proved , that the square ACGF , is equal to the pa- rallelogram KCLM . So ABDE + ACGF the sum of the squares ...
Page 57
... half of 120 degrees , and the three angles will be equal to one another , as well as the three sides : wherefore AB BC AC . 2. E. D. Cor . Hence the radius , from whence the lines on any scale are formed , is the chord of 60 degrees on ...
... half of 120 degrees , and the three angles will be equal to one another , as well as the three sides : wherefore AB BC AC . 2. E. D. Cor . Hence the radius , from whence the lines on any scale are formed , is the chord of 60 degrees on ...
Page 65
... half of DE , describe two arcs to cut each other in some point F ; and the right- line AF , joining the points A and F , will bisect the given angle BẮC . For if DF and FE be drawn , the triangles ADF , AEF , are equilateral to each ...
... half of DE , describe two arcs to cut each other in some point F ; and the right- line AF , joining the points A and F , will bisect the given angle BẮC . For if DF and FE be drawn , the triangles ADF , AEF , are equilateral to each ...
Page 68
... half a right angle ( by lem- ma preceding theo . 7. and cor 2. theo 5. ) whence DAB and BCD will each be a right angle , and ( by def . 44. ) ABCD is a square . SCHOLIUM . By the same method a rectangle or oblong , may be described ...
... half a right angle ( by lem- ma preceding theo . 7. and cor 2. theo 5. ) whence DAB and BCD will each be a right angle , and ( by def . 44. ) ABCD is a square . SCHOLIUM . By the same method a rectangle or oblong , may be described ...
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Common terms and phrases
acres altitude Answer arch azimuth base bearing blank line centre chains and links chord circle circumferentor Co-sec Co-tang column compasses contained decimal difference distance line divided divisions draw east Ecliptic edge feet field-book figures fore four-pole chains geom given number half the sum Horizon glass hypothenuse inches instrument Lat Dep Lat latitude length logarithm measure meridian distance multiplied natural co-sine natural sine needle Nonius number of degrees object observed off-sets opposite parallel parallelogram pegs perches perpendicular plane pole pole star Portmarnock PROB protractor Quadrant quotient radius right angles right line scale of equal SCHOLIUM screw Secant sect Sextant side sights square station stationary distance subtract Sun's survey taken Tang tangent theo theodolite trapezium triangle ABC trigonometry two-pole chains vane versed sine vulgar fraction whence
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 197 - 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.