Elements of Plane and Spherical TrigonometryBaldwin, Cradock, and Joy, 1816 - 244 Seiten |
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Seite v
... of Differential Equa- tions for the variations of triangles , are taken , simply with such alterations as fitted them better for general usefulness , from the Chevalier Delambre's admirable treatise on Astronomy A 3 PREFACE .
... of Differential Equa- tions for the variations of triangles , are taken , simply with such alterations as fitted them better for general usefulness , from the Chevalier Delambre's admirable treatise on Astronomy A 3 PREFACE .
Seite 37
... equa- tions , every other theorem and formula that is likely to be of use , is deduced with great facility by the mere re- duction and transformation of the original equations . This method serves greatly to shorten almost all trigo ...
... equa- tions , every other theorem and formula that is likely to be of use , is deduced with great facility by the mere re- duction and transformation of the original equations . This method serves greatly to shorten almost all trigo ...
Seite 48
... equa- tions A2 + 1 = 0 , and B2 + 10 : so that , though these roots , a = ± √ - 1 , and B = ± √ − 1 , are in- sin B sin2 ( 450 — B ) - ; COS B 5 dications of an absurd supposition , they still serve as 48 Plane Trigonometry .
... equa- tions A2 + 1 = 0 , and B2 + 10 : so that , though these roots , a = ± √ - 1 , and B = ± √ − 1 , are in- sin B sin2 ( 450 — B ) - ; COS B 5 dications of an absurd supposition , they still serve as 48 Plane Trigonometry .
Seite 51
... equa . s ) , there will result , 1 = cot A cot B + cot B cot c + cot a cot c .... ( 5. ) If the sum of A , B , and C , instead of being 180 ° , were 360 ° , the same formulæ would result , as is evident from the consideration , that in ...
... equa . s ) , there will result , 1 = cot A cot B + cot B cot c + cot a cot c .... ( 5. ) If the sum of A , B , and C , instead of being 180 ° , were 360 ° , the same formulæ would result , as is evident from the consideration , that in ...
Seite 52
... equa . o . ) - or , tan A tan c + tan B tan c = 1 tan A tan B ( by mul . ) or , 1 = tan A tan B + tan a tan c + tan в tan C ( by trans . ) and cot a cot в cot ccot A + cot B + cot c .... ( 6. ) . And this formula will obtain , in like ...
... equa . o . ) - or , tan A tan c + tan B tan c = 1 tan A tan B ( by mul . ) or , 1 = tan A tan B + tan a tan c + tan в tan C ( by trans . ) and cot a cot в cot ccot A + cot B + cot c .... ( 6. ) . And this formula will obtain , in like ...
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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
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Seite 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.
Seite 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.
Seite 225 - ... third of the excess of the sum of its three angles above two right angles...
Seite 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.
Seite 30 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Seite 249 - OSTELL'S NEW GENERAL ATLAS; containing distinct Maps of all the principal States and Kingdoms throughout the World...
Seite 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.
Seite 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.
Seite 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.
Seite 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...