Elements of Plane and Spherical Trigonometry |
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Page 4
... said to be one of 90 degrees . 11. The complement of an arc is its difference from a quadrant ; and the complement of an angle is its differ- ence from a right angle . 12. The supplement of an arc is its difference from Plane Trigonometry .
... said to be one of 90 degrees . 11. The complement of an arc is its difference from a quadrant ; and the complement of an angle is its differ- ence from a right angle . 12. The supplement of an arc is its difference from Plane Trigonometry .
Page 6
... quadrant , the arc is less than its corresponding tangent ; and of any arc whatever , the chord is less than the arc , and the sine less than the chord . For , in the preceding diagram , the circular sector CAB is less than the triangle ...
... quadrant , the arc is less than its corresponding tangent ; and of any arc whatever , the chord is less than the arc , and the sine less than the chord . For , in the preceding diagram , the circular sector CAB is less than the triangle ...
Page 7
... quadrant AE , and then the sine is in its maximum state , being equal to radius , thence called the sine total ; the versed sine is also then equal to the radius ; and the secant and tangent becom- ing incapable of mutually limiting ...
... quadrant AE , and then the sine is in its maximum state , being equal to radius , thence called the sine total ; the versed sine is also then equal to the radius ; and the secant and tangent becom- ing incapable of mutually limiting ...
Page 8
... quadrant , computed to the radius 1 , and expressed de- cimally . On the right hand pages are placed in suc- cession the corresponding logarithms of the numbers that denote the several sines , tangents , & c . on the res- pective ...
... quadrant , computed to the radius 1 , and expressed de- cimally . On the right hand pages are placed in suc- cession the corresponding logarithms of the numbers that denote the several sines , tangents , & c . on the res- pective ...
Page 13
... BD , but their sum AD is less than a quadrant . But the properties enunciated in these two propositions are equally true , let the magnitudes of the arcs , of their sum , and their difference 2 General Properties of Lines and Angles . 19.
... BD , but their sum AD is less than a quadrant . But the properties enunciated in these two propositions are equally true , let the magnitudes of the arcs , of their sum , and their difference 2 General Properties of Lines and Angles . 19.
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Common terms and phrases
altitude angled spherical triangle axis azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulæ given side h cos h half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius rectangle right angled spherical right angled triangle right ascension right line secant sin a sin sin² sine solid angle sphere spherical excess spherical trigonometry star substyle sun's supposed surface tan² tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence yards zenith
Popular passages
Page 4 - 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 248 - SCIENTIFIC DIALOGUES ; intended for the Instruction and Entertainment of Young People ; in which the first principles of Natural and Experimental Philosophy are fully explained, by the Rev.
Page 225 - ... third of the excess of the sum of its three angles above two right angles...
Page 19 - In any plane triangle, as twice the rectangle under any two sides is to the difference of the sum of the squares of those two sides and the square of the base, so is the radius to the cosine of the angle contained by the two sides.
Page 30 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Page 249 - OSTELL'S NEW GENERAL ATLAS; containing distinct Maps of all the principal States and Kingdoms throughout the World...
Page 34 - Call any one of the sides radius, and write upon it the word radius ; observe whether the other sides become sines, tangents, or secants, and write those words upon them accordingly. Call the word written upon each side the name of each side ; then say, As the name of the given side, Is to the given side ; So is the name of the required side, To the required side.
Page 69 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower was 33° 45' ; required the height of the tower.
Page 18 - AC, (Fig. 25.) is to their difference ; as the tangent of half the sum of the angles ACB and ABC, to the tangent of half their difference.
Page 83 - A cos 6 = cos a cos c + sin a sin c cos B cos c = cos a cos 6 + sin a sin 6 cos C Law of Cosines for Angles cos A = — cos B...