Elements of Plane and Spherical Trigonometry |
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Page iv
... theorems : but they are so obscured by a defective notation , that the perusal of greater part of the book must , to a mathematical student , be as perplexing as the solution of a perpetual string of enigmas . It has been my aim to ...
... theorems : but they are so obscured by a defective notation , that the perusal of greater part of the book must , to a mathematical student , be as perplexing as the solution of a perpetual string of enigmas . It has been my aim to ...
Page vi
... theorems . 1. It is more concise , and therefore allows of the in- troduction of a much greater quantity and variety of matter ... theorem may not have the remotest analogy to that which will serve to establish the truth of another . The ...
... theorems . 1. It is more concise , and therefore allows of the in- troduction of a much greater quantity and variety of matter ... theorem may not have the remotest analogy to that which will serve to establish the truth of another . The ...
Page vii
... theorems to be found in the analytical treatises on trigonometry , which have not yet , to my knowledge , been demon- strated in any other way ; and not a few which I am persuaded do not admit of any other kind of proof . 3. This method ...
... theorems to be found in the analytical treatises on trigonometry , which have not yet , to my knowledge , been demon- strated in any other way ; and not a few which I am persuaded do not admit of any other kind of proof . 3. This method ...
Page 8
... theorems , some of which will be demonstrated as we proceed , ma- thematicians have computed the lengths of the sines , tangents , secants , and versed sines , to an assumed ra dius , that correspond to arcs from 1 second of a degree ...
... theorems , some of which will be demonstrated as we proceed , ma- thematicians have computed the lengths of the sines , tangents , secants , and versed sines , to an assumed ra dius , that correspond to arcs from 1 second of a degree ...
Page 15
... theorem enun- ciated above . M E Cor . The sum of the cosines of two arcs , is to their difference , as the cotangent of half the sum of those two arcs , is to the cotangent of half their difference . For , the cosines being the sines ...
... theorem enun- ciated above . M E Cor . The sum of the cosines of two arcs , is to their difference , as the cotangent of half the sum of those two arcs , is to the cotangent of half their difference . For , the cosines being the 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...