Elements of Plane and Spherical Trigonometry |
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Page 9
... PROP . I. 1. THE chord of any arc is a mean proportional be- tween the versed sine of that arc and the diameter of the circle . * The nature and use of logarithms being fully explained in Dr. Hutton's valuable work , and , indeed , in ...
... PROP . I. 1. THE chord of any arc is a mean proportional be- tween the versed sine of that arc and the diameter of the circle . * The nature and use of logarithms being fully explained in Dr. Hutton's valuable work , and , indeed , in ...
Page 10
... PROP . II . L B N H CD 2. As radius : cosine of any arc :: twice the sine of that arc the sine of double the arc . In the preceding figure CH is the cosine of the arc BN , AB is twice the sine BH of that arc , and BD is the sinc of AB ...
... PROP . II . L B N H CD 2. As radius : cosine of any arc :: twice the sine of that arc the sine of double the arc . In the preceding figure CH is the cosine of the arc BN , AB is twice the sine BH of that arc , and BD is the sinc of AB ...
Page 11
... PROP . V. 5. The chord of 60 ° is equal to the radius of the cir- cle ; the versed sine , and cosine of 60 ° are each equal to half the radius ; and the secant of 60 ° is equal to double the radius . Let AB be an arc of 60 ° , AB its ...
... PROP . V. 5. The chord of 60 ° is equal to the radius of the cir- cle ; the versed sine , and cosine of 60 ° are each equal to half the radius ; and the secant of 60 ° is equal to double the radius . Let AB be an arc of 60 ° , AB its ...
Page 12
... prop . 1 , of this chapter . For 4AH * AB2 AL . AD = 2AC . AD . Whence AH2 = AC . AD . Also , 4CH2 = LB2 = AL . LD = 2AC . LD . Whence CH2 = AC . LD . PROP . VIII . 8. The rectangle under the radius and the sine of the sum or of the ...
... prop . 1 , of this chapter . For 4AH * AB2 AL . AD = 2AC . AD . Whence AH2 = AC . AD . Also , 4CH2 = LB2 = AL . LD = 2AC . LD . Whence CH2 = AC . LD . PROP . VIII . 8. The rectangle under the radius and the sine of the sum or of the ...
Page 13
... prop . 2 of this chapter . PROP . IX . 9. The rectangle under the radius and the cosine of the sum or the difference of two arcs , is equal to the difference or the sum of the rectangles under their res- pective cosines and sines ...
... prop . 2 of this chapter . PROP . IX . 9. The rectangle under the radius and the cosine of the sum or the difference of two arcs , is equal to the difference or the sum of the rectangles under their res- pective cosines and sines ...
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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...