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 páginas |
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Página 50
... perpendicular CD on the chord AB , it will bisect it in the point D. Let the lines AC and CB be drawn from the centre to the extremities of the chord ; then since CA = CB , the angles CAB = CBA ( by the lemma ) . But the triangles ADC ...
... perpendicular CD on the chord AB , it will bisect it in the point D. Let the lines AC and CB be drawn from the centre to the extremities of the chord ; then since CA = CB , the angles CAB = CBA ( by the lemma ) . But the triangles ADC ...
Página 52
... perpendicular to the hypothenuse BC , join AH , AM , DC , and BG ; in the triangles BDC , ABH , BD = BA , being sides of the same square , and also BC = BH , and the included angles DBC = ABH ( for DBA = CBH being both right , to both ...
... perpendicular to the hypothenuse BC , join AH , AM , DC , and BG ; in the triangles BDC , ABH , BD = BA , being sides of the same square , and also BC = BH , and the included angles DBC = ABH ( for DBA = CBH being both right , to both ...
Página 54
... equal bases AB and DE , are to each other as their altitudes CG and FH . Let BI be perpendicular to AB and equal to CG , in which let KB = FH , and let AI and AK be drawn . That is , The triangle AIB = ACB ( by 54 GEOMETRICAL TRICAL.
... equal bases AB and DE , are to each other as their altitudes CG and FH . Let BI be perpendicular to AB and equal to CG , in which let KB = FH , and let AI and AK be drawn . That is , The triangle AIB = ACB ( by 54 GEOMETRICAL TRICAL.
Página 59
... perpendicular to it ( by def . 10 ) . PROBLEM V. PL . 2. fig . 11 . On a given point A , în a right line EF , to erect a perpendicular . From the point A lay off on each side the equal distances AC , AD ; and from C and D as centres ...
... perpendicular to it ( by def . 10 ) . PROBLEM V. PL . 2. fig . 11 . On a given point A , în a right line EF , to erect a perpendicular . From the point A lay off on each side the equal distances AC , AD ; and from C and D as centres ...
Página 60
... perpendicular required .. Let DA , DE be drawn , the angle ADF = FDE , DA = DE , being radii of the same circle , and DF common ; there- fore ( by theo . 6 ) the angle DFA = DFE , and FA a perpen- dicular . ( By def . 10. ) PROBLEM VIII ...
... perpendicular required .. Let DA , DE be drawn , the angle ADF = FDE , DA = DE , being radii of the same circle , and DF common ; there- fore ( by theo . 6 ) the angle DFA = DFE , and FA a perpen- dicular . ( By def . 10. ) PROBLEM VIII ...
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Términos y frases comunes
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
Pasajes populares
Página 173 - In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal...
Página 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.
Página 163 - RULE. From half the sum of the three sides subtract each side severally.
Página 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.
Página 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.
Página 41 - The radius of a circle is a right line drawn from the centre to the circumference.
Página 52 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Página 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.
Página 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.