Elements of Plane and Spherical TrigonometryBaldwin, Cradock, and Joy, 1816 - 244 Seiten |
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Seite 121
... azimuth of that body ; the distance of the same circle from the east or west points is the ampli- tude . 25. In order to represent on a plane the celestial sphere with all its circles great and small , the ancients invented two kinds of ...
... azimuth of that body ; the distance of the same circle from the east or west points is the ampli- tude . 25. In order to represent on a plane the celestial sphere with all its circles great and small , the ancients invented two kinds of ...
Seite 124
... to the horizon , QE will be to the radius QR the cosine of the azimuth , and EL per- pendicular to the horizon will be the sine of the alti- tude . To determine this from the projection , draw 124 Projections of the Sphere .
... to the horizon , QE will be to the radius QR the cosine of the azimuth , and EL per- pendicular to the horizon will be the sine of the alti- tude . To determine this from the projection , draw 124 Projections of the Sphere .
Seite 158
... azimuth , measured also by the arc VR . Then the formula we may first employ in the present investi- gation , is equa . 2 of chap . vi . which suited to the case before us , is ...... ( 1 * ) , ( 1. ) cos zs = cos PS COS PZ + sin ps sin ...
... azimuth , measured also by the arc VR . Then the formula we may first employ in the present investi- gation , is equa . 2 of chap . vi . which suited to the case before us , is ...... ( 1 * ) , ( 1. ) cos zs = cos PS COS PZ + sin ps sin ...
Seite 159
... azimuth in that case may be determined . 8. When the body s is in the horizon , or s and v co- incide , we have zs = 90 ° , or cos n = 0 ; hence 0 sin d sin + cos d cos l cos P , sin d sin l or , cos P- = - tan d tan l .. cos d cos l ...
... azimuth in that case may be determined . 8. When the body s is in the horizon , or s and v co- incide , we have zs = 90 ° , or cos n = 0 ; hence 0 sin d sin + cos d cos l cos P , sin d sin l or , cos P- = - tan d tan l .. cos d cos l ...
Seite 161
... azimuth at rising and setting ? The sun's declination on the proposed day at noon , is 16 ° 0 ′ 46 ′′ north ; and the formulæ to be employed are the 5th and 6th . For the first , viz . COS P tan d tan l , we have , i log tand .. 16 ° 0 ...
... azimuth at rising and setting ? The sun's declination on the proposed day at noon , is 16 ° 0 ′ 46 ′′ north ; and the formulæ to be employed are the 5th and 6th . For the first , viz . COS P tan d tan l , we have , i log tand .. 16 ° 0 ...
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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...