An Introduction to the Theory and Practice of Plane and Spherical Trigonometry, and the Stereographic Projection of the Sphere: Including the Theory of Navigation ...author, 1810 - 420 pages |
From inside the book
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Page xxvii
... formed by the lines ED and DC , and axb expresses the product of the quantity a by the quantity b . Also ab , or ab signifies the same thing . PB + , Divided by , as PB ÷ Cs , or signifies that PB is to be divided by cs . CS AB2 , AB3 ...
... formed by the lines ED and DC , and axb expresses the product of the quantity a by the quantity b . Also ab , or ab signifies the same thing . PB + , Divided by , as PB ÷ Cs , or signifies that PB is to be divided by cs . CS AB2 , AB3 ...
Page 21
... formed : And the intermediate divisions are formed in a similar manner , by taking the loga- rithms of the intermediate numbers , as for example , the loga- rithm of 1 , is 41 , the logarithm of 12 is 79 , of 1 is 114 , & c . These ...
... formed : And the intermediate divisions are formed in a similar manner , by taking the loga- rithms of the intermediate numbers , as for example , the loga- rithm of 1 , is 41 , the logarithm of 12 is 79 , of 1 is 114 , & c . These ...
Page 25
... formed by the lines AB and CB , and that of aBC by the lines aв and CB , & c . ( G ) Every angle of a triangle is measured by an arc of a circle described about the angular point as a centre , thus the arc ac is the measure of the angle ...
... formed by the lines AB and CB , and that of aBC by the lines aв and CB , & c . ( G ) Every angle of a triangle is measured by an arc of a circle described about the angular point as a centre , thus the arc ac is the measure of the angle ...
Page 26
... formed at the point D , on the same side of the line AB , they are altogether equal in measure to two right angles , or 180 ° . PROBLEM I. ( N ) To erect a perpendicular from a given point D in a given line GH , or to make a right angle ...
... formed at the point D , on the same side of the line AB , they are altogether equal in measure to two right angles , or 180 ° . PROBLEM I. ( N ) To erect a perpendicular from a given point D in a given line GH , or to make a right angle ...
Page 34
... formed , but another may be formed similar to it , and that the sides about the equal angles of similar triangles are proportional ; if Ad , ce , Ab , and cb , each represent the radius in the tables , then will AF and CG be the secants ...
... formed , but another may be formed similar to it , and that the sides about the equal angles of similar triangles are proportional ; if Ad , ce , Ab , and cb , each represent the radius in the tables , then will AF and CG be the secants ...
Other editions - View all
An Introduction to the Theory and Practice of Plain and Spherical ... Thomas Keith No preview available - 2017 |
An Introduction to the Theory and Practice of Plain and Spherical ... Thomas Keith No preview available - 2014 |
Common terms and phrases
acute adjacent angle altitude angle CAB Answer apparent altitude azimuth base centre circle co-tangent complement CONSTRUCTION cosec cosine degrees diff draw ecliptic equation Euclid find the angle formulæ given angle given side Given The side greater half the sum Hence horizon hypoth hypothenuse latitude less line of numbers line of sines logarithm logarithmical sine longitude measured meridian miles moon's Nautical Almanac North oblique observed obtuse opposite angle parallax parallel perpendicular Plate pole primitive PROPOSITION quadrant Rad x sine rad² radius right ascension right-angled spherical triangle RULE scale of chords scale of equal SCHOLIUM secant semi-tangents side AC sine A sine sine BC sine of half sine² species spherical angle spherical triangle ABC star star's straight line subtract sun's declination supplement tang tang AC tangent of half three sides Trigonometry versed sine
Popular passages
Page 25 - 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.
Page 136 - Consequently, a line drawn from the vertex of an isosceles triangle to the middle of the base, bisects the vertical angle, and is perpendicular to the base.
Page 6 - And if the given number be a proper vulgar fraction ; subtract the logarithm of the denominator from the logarithm of the numerator, and the remainder will be the logarithm sought ; which, being that of a decimal fraction, must always have a negative index.
Page xxvi - A New Treatise on the Use of the Globes; or, a Philosophical View of the Earth and Heavens : comprehending an Account of the Figure, Magnitude, and Motion of the Earth : with the Natural Changes of its Surface, caused by Floods, Earthquakes, Ac.
Page 32 - The CO-SINE of an arc is the sine of the complement of that arc as L.
Page 31 - The sine, or right sine, of an arc, is the line drawn from one extremity of the arc, perpendicular to the diameter passing through the other extremity. Thus, BF is the sine of the arc AB, or of the arc BDE.
Page 240 - The HORIZON is a great circle which separates the visible half of the heavens from the invisible ; the earth being considered as a point in the centre of the sphere of the fixed stars.
Page 240 - ... ZENITH DISTANCE of any celestial object is the arc of a vertical circle, contained between the centre of that object and the zenith ; or it is what the altitude of the object wants of 90 degrees.
Page 197 - The sum of the two sides of a triangle is to their difference as the tangent of half the sum of the angles at the base is to the tangent of half their difference.
Page 32 - The SECANT of an arc, is a straight line drawn from the center, through one end of the arc, and extended to the tangent which is drawn from the other end.