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 TablesA. S. Barnes, 1839 - 412 páginas |
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Página 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 28 Therefore 27.6047 is the root nearly . Again ...
... 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 28 Therefore 27.6047 is the root nearly . Again ...
Página 47
... theo . ) GEB = CFH , and AEG = HFD . 2. Also GEBAEF , 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 GEB ( by ...
... theo . ) GEB = CFH , and AEG = HFD . 2. Also GEBAEF , 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 GEB ( by ...
Página 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 ...
Página 49
... theo . 4 ) ; but since AC = CD , being radii of the same circle , it is plain ( by the preceding lemma ) that the angles subtended by them will be also equal , and that their sum is double to either of them , that is , DAC + ADC is ...
... theo . 4 ) ; but since AC = CD , being radii of the same circle , it is plain ( by the preceding lemma ) that the angles subtended by them will be also equal , and that their sum is double to either of them , that is , DAC + ADC is ...
Página 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 ...
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Términos y frases comunes
ABCD acres altitude arch base bearing blank line centre chains and links circle circumferentor column compasses contained Cosine Sine 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 multiplied needle nonius number of degrees object observed opposite parallelogram perches perpendicular plane prob PROBLEM proportion protractor quadrant quotient radius rhombus right angles right line scale of equal screw secant sect sector semicircle side Sine Cotang square root station stationary distance subtract suppose survey taken Tang tangent theo theodolite THEOREM trapezium triangle ABC trigonometry two-pole chains vane vulgar fraction whence
Pasajes populares
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 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 41 - The radius of a circle is a right line drawn from the centre to the circumference.
Página 45 - A lemma is something which is premised, or demonstrated, in order to render what follows more easy. A corollary is a consequent truth derived immediately from some preceding truth or demonstration.
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.
Página 21 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.