A Treatise on Surveying: Containing the Theory and Practice : to which is Prefixed a Perspicuous System of Plane Trigonometry : the Whole Clearly Demonstrated and Illustrated by a Large Number of Appropriate Examples, Particularlry Adapted to the Use of SchoolsJohn Richardson, 1817 - 206 páginas |
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Página 47
... preceding example ; or otherwise thus , Draw the line AB of any length , and draw AC mak- ing the angle A = 53 ° 8 ' ; make AC = 480 by a scale of equal parts , and from C draw CB perpendicular to AB , then ABC is the triangle required ...
... preceding example ; or otherwise thus , Draw the line AB of any length , and draw AC mak- ing the angle A = 53 ° 8 ' ; make AC = 480 by a scale of equal parts , and from C draw CB perpendicular to AB , then ABC is the triangle required ...
Página 48
... given angle , To the sine of the angle opposite the other given side . * Add the angle thus found to the given angle , This is evident from the demonstration of the rule in the preceding case . 48 PLANE TRIGONOMETRY .
... given angle , To the sine of the angle opposite the other given side . * Add the angle thus found to the given angle , This is evident from the demonstration of the rule in the preceding case . 48 PLANE TRIGONOMETRY .
Página 51
... preceding example ; only AB , being shorter than BC , the arc ab cuts AC in two points on the same side of BC ; hence the angle A may be either acute or obtuse . The side re- quired has also two values as AC and AC . By Calculation . As ...
... preceding example ; only AB , being shorter than BC , the arc ab cuts AC in two points on the same side of BC ; hence the angle A may be either acute or obtuse . The side re- quired has also two values as AC and AC . By Calculation . As ...
Página 56
... preceding demonstration and ( 165 ) , AF : AE :: AG ; AB ; hence when the perpendicular falls without the triangle , the base , is to the sum of the sides , as the difference of the sides , is to the sum of the segments of the base . A ...
... preceding demonstration and ( 165 ) , AF : AE :: AG ; AB ; hence when the perpendicular falls without the triangle , the base , is to the sum of the sides , as the difference of the sides , is to the sum of the segments of the base . A ...
Página 61
... preceding rules solve all the cases of plane trian- gles , both right - angled and oblique . There are however other rules , suited to right - angled triangles , which are sometimes more convenient than the general ones . Pre- vious to ...
... preceding rules solve all the cases of plane trian- gles , both right - angled and oblique . There are however other rules , suited to right - angled triangles , which are sometimes more convenient than the general ones . Pre- vious to ...
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Términos y frases comunes
ABCD ABFD acres adjacent adjacent angles angle opposite angles ABC base bearing and distance breadth Calculation centre Co-secant Secant Co-sine Co-tang column decimal DegDeg Dist DEMONSTRATION diff difference of latitude divide division line draw east equal EXAMPLES feet field-notes figures find the angle find the area four-pole chains fourth term given angle given area given bearing given number given side John Gummere LatDegDeg LatDegDegDeg Dist LatDegDegDegDeg Dist latitude and departure length logarithm M.
M. Sine measured meridian distance natural number off-sets parallel parallelogram perches PROBLEM quired quotient radius rectangle remainder Required the area right angles right line right-angled triangle ROBERT ADRAIN RULE semiperimeter side AB side AC square root station stationary line subtract tance Tang Tangent tract of land trapezium triangle ABC trigonometry
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Página 2 - An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the times therein mentioned." And also to the act, entitled " An Act supplementary to an Act, entitled, " An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the time therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and...
Página 2 - District, has deposited in this office the title of a book, the right whereof he claims as proprietor, in the words following, to wit : " THE CHILD'S BOTANY," In conformity to the act of the Congress of the United States, entitled, " An act for the encouragement of learning by securing the copies of maps, charts, and books to the authors and proprietors of such copies, during the times therein mentioned...
Página 35 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Página 44 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Página 52 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 26 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Página 79 - A maypole, whose top was broken off by a blast of wind, struck the ground at 15 feet distance from the foot of the pole: what was the height of the whole maypole, supposing the broken piece to measure 39 feet in length ? Ans.
Página 29 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 86 - PROBLEM I. To find the area of a parallelogram; whether it be a square, a rectangle, a rhombus, or a rhomboides. RULE.* Multiply the length by the perpendicular height, and the product will be the area.
Página 36 - Sine, or Right Sine, of an arc, is the line drawn from one extremity of the arc, perpendicular to the diameter which passes through the other extremity. Thus, BF is the sine of the arc AB, or of the supplemental arc BDE.