A Treatise of Practical Surveying, ...

Joseph Crukshank, 1808 - 440 pàgines

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Pàgina 32 - 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.
Pàgina 199 - ... that triangles on the same base and between the same parallels are equal...
Pàgina 94 - 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.
Pàgina 23 - Four quantities are said to be in proportion when the product of the extremes is equal to that of the means : thus if A multiplied by D, be equal to B multiplied by C, then A is said to be to B as C is to D.
Pàgina 95 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Pàgina 37 - ABDE+ACGF the sum of the squares —BKLH-\-KCML, the sum of the two parallelograms or square BCMH; therefore the sum of the squares on AB and AC is equal to the square on BC.
Pàgina 24 - Things that are equal to one and the same thing, are equal to each other. 2. Every whole is greater than its part. % 3. Every whole is equal to all its parts taken together. 4 If to equal things, equal things be added, the whole will be equal. 5. If from equal things, equal things be deducted the remainders will be equal.
Pàgina 36 - XIII. •All parallelograms on the same or equal bases and between the same parallels...
Pàgina 182 - VI. To find the content of a triangular piece of ground, Multiply the base by half the perpendicular, or the perpendicular by half the base ; or take half the product of the base into the perpendicular. The reason hereof is plain, from cor.
Pàgina 35 - Triangles upon equal bases, and between the same parallels, are equal to one another.