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 42
... sine of an arc is a perpendicular line let fall from one end thereof , to a diameter drawn to the other end : thus HL is the right sine of the arc HB . The sines on the same diameter increase till they come to the centre , and so become ...
... sine of an arc is a perpendicular line let fall from one end thereof , to a diameter drawn to the other end : thus HL is the right sine of the arc HB . The sines on the same diameter increase till they come to the centre , and so become ...
Σελίδα 43
... sine , tangent , or secant of the complement of any arc is called the co - sine , co - tangent , or co - secant of the arc itself : thus FH is the sine , DI the tangent , and CI the secant of the arc DH : or they are the co - sine , co ...
... sine , tangent , or secant of the complement of any arc is called the co - sine , co - tangent , or co - secant of the arc itself : thus FH is the sine , DI the tangent , and CI the secant of the arc DH : or they are the co - sine , co ...
Σελίδα 50
... sine of an arc is half the chord of twice that arc . For AD is the sine of the arc AF ( by def . 20 ) , AF is half the arc , and AD half the chord AB ( by theo . 8 ) ; therefore the corollary is plain . THEOREM X. PL . 1. fig . 30 . In ...
... sine of an arc is half the chord of twice that arc . For AD is the sine of the arc AF ( by def . 20 ) , AF is half the arc , and AD half the chord AB ( by theo . 8 ) ; therefore the corollary is plain . THEOREM X. PL . 1. fig . 30 . In ...
Σελίδα 51
... 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 of ADB . Q. E. D. THEOREM XI . PL . 1. fig . 22 . If a right line GH cut two other right lines AB , CD , so as to make 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 of ADB . Q. E. D. THEOREM XI . PL . 1. fig . 22 . If a right line GH cut two other right lines AB , CD , so as to make the ...
Σελίδα 53
... sine , tangent , & c . of that arc will be also greater . Therefore , in general , the chord , sine , tangent , & c . of any arc is proportional to the radius of the circle ) ; the same way the chord AB is to the chord ab in the same ...
... sine , tangent , & c . of that arc will be also greater . Therefore , in general , the chord , sine , tangent , & c . of any arc is proportional to the radius of the circle ) ; the same way the chord AB is to the chord ab in the same ...
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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.