The Theory and Practice of Surveying: Containing All the Instructions Requisite for the Skilful Practice of this Art. With a New Set of Accurate Mathematical TablesHarper, 1832 - 348 σελίδες |
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Σελίδα 27
... Theo- retical and Practical . " - ED . * This rule is found in Hutton's Mathematics . There have been differ- ent rules given for extracting the cube root , among which this , and another rule given in Pike's Arithmetic ( by ...
... Theo- retical and Practical . " - ED . * This rule is found in Hutton's Mathematics . There have been differ- ent rules given for extracting the cube root , among which this , and another rule given in Pike's Arithmetic ( by ...
Σελίδα 47
... theo . ) GEB = CFH , and AEG = HFD . 2. Also GEB = AEF , and CFH = EFD ; but GEB = CFH ( by part 1. of this theo . ) , therefore AEF = EFD . The same way we prove FEB = EFC . 3. AEF = EFD ( by the last part of this theo . ) ; but AEF ...
... theo . ) GEB = CFH , and AEG = HFD . 2. Also GEB = AEF , and CFH = EFD ; but GEB = CFH ( by part 1. of this theo . ) , therefore AEF = EFD . The same way we prove FEB = EFC . 3. AEF = EFD ( by the last part of this theo . ) ; but AEF ...
Σελίδα 48
... theo . 1 ) ; there- fore the three angles A + B + ACB = two right angles . Q. E. D. Cor . 1. Hence if one angle of a triangle be known , the sum of the other two is also known ; for since the three angles of every triangle contain two ...
... theo . 1 ) ; there- fore the three angles A + B + ACB = two right angles . Q. E. D. Cor . 1. Hence if one angle of a triangle be known , the sum of the other two is also known ; for since the three angles of every triangle contain two ...
Σελίδα 50
... theo . 5 ) ; then have we AC , CD , and the angle ACD in one triangle severally equal to CB , CD , and the angle BCD in the other ; therefore ( by theo . 6 ) AD = DB . Q. E. D. Cor . Hence it follows , that any line bisecting a chord at ...
... theo . 5 ) ; then have we AC , CD , and the angle ACD in one triangle severally equal to CB , CD , and the angle BCD in the other ; therefore ( by theo . 6 ) AD = DB . Q. E. D. Cor . Hence it follows , that any line bisecting a chord at ...
Σελίδα 51
... theo . 7 ) , viz . the arc BK is the measure of the angle BAD ; therefore ( by cor . to the last ) BE , the half of BD , is the sine of BAD : in the same way may be proved that half of AD is the sine of ABD , and the half of AB the sine ...
... theo . 7 ) , viz . the arc BK is the measure of the angle BAD ; therefore ( by cor . to the last ) BE , the half of BD , is the sine of BAD : in the same way may be proved that half of AD is the sine of ABD , and the half of AB the sine ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD acres altitude arch azimuth base bearing blank line centre chains and links circle circumferentor co-sine column compasses contained cube root decimal diagonal diameter difference of latitude divided divisions divisor draw east ecliptic edge EXAMPLE feet field-book figure four-pole chains geometrical series given angle given number half the sum height Hence horizon glass hypothenuse inches instrument length logarithm manner measure meridian distance method multiplied needle nonius number of degrees object observed offsets opposite parallelogram perches perpendicular plane prob PROBLEM proportion protractor quadrant quotient radius rhombus right angles right line scale of equal SCHOLIUM screw secant sect sector semicircle side square root station stationary distance subtract suppose survey taken tangent theo theodolite THEOREM third trapezium triangle ABC trigonometry two-pole chains vane vulgar fraction whence
Δημοφιλή αποσπάσματα
Σελίδα 173 - In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal...
Σελίδα 49 - 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.
Σελίδα 163 - RULE. From half the sum of the three sides subtract each side severally.
Σελίδα 41 - 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.
Σελίδα 97 - 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.
Σελίδα 41 - The radius of a circle is a right line drawn from the centre to the circumference.
Σελίδα 52 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 24 - The square of the sum of two numbers is equal to the square of the first number plus twice the product of the first and second number plus the square of the second number.
Σελίδα 35 - DIVISION BY LOGARITHMS. RULE. From the logarithm of the dividend subtract the logarithm of the divisor, and the number answering to the remainder will be the quotient required.