Elements of Plane and Spherical Trigonometry: With Their Applications to Heights and Distances Projections of the Sphere, Dialling, Astronomy, the Solution of Equations, and Geodesic OperationsBaldwin, Cradock, and Joy, 1816 - 244 sider |
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Side 25
... sides and an included angle are given ; they , therefore , constitute a second case . The example marked 3 , has three sides given , but no angle ; this makes a third case : and the remaining variety in which the three angles are given , ...
... sides and an included angle are given ; they , therefore , constitute a second case . The example marked 3 , has three sides given , but no angle ; this makes a third case : and the remaining variety in which the three angles are given , ...
Side 26
... given angle , To its opposite side ; So is the sine of either of the other angles , To its opposite side . If an angle be required , begin the proportion with a - side , and say , As one of the given sides , Is to the sine of its ...
... given angle , To its opposite side ; So is the sine of either of the other angles , To its opposite side . If an angle be required , begin the proportion with a - side , and say , As one of the given sides , Is to the sine of its ...
Side 27
... given two angles equal to 58 ° 7 ′ , and 22 ° 37 ' , respectively , and the side between them 408 yards . Required the remaining angle and sides . Construction . On an indefinite right line , set off , from a convenient diagonal scale ...
... given two angles equal to 58 ° 7 ′ , and 22 ° 37 ' , respectively , and the side between them 408 yards . Required the remaining angle and sides . Construction . On an indefinite right line , set off , from a convenient diagonal scale ...
Side 29
... give AB 117 .... ACB = 282 .... ACB ' : AB ' 2210 .... ABе = 13430 1120 .... ABC = 4510 . Computation . To find the angle B. To sin B Add to each As BC .... 1 17 . . . . . . ..... 2.0681859 To sin ... side CB Solution of its Three Cases . 29.
... give AB 117 .... ACB = 282 .... ACB ' : AB ' 2210 .... ABе = 13430 1120 .... ABC = 4510 . Computation . To find the angle B. To sin B Add to each As BC .... 1 17 . . . . . . ..... 2.0681859 To sin ... side CB Solution of its Three Cases . 29.
Side 30
... side CB has its length between certain limits , that is , be- tween the length of the side AC , and that of the per ... given , the line ABB ' can only be cut in one point . Hence the practical maxim may be thus ex- pressed - when CB is ...
... side CB has its length between certain limits , that is , be- tween the length of the side AC , and that of the per ... given , the line ABB ' can only be cut in one point . Hence the practical maxim may be thus ex- pressed - when CB is ...
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Elements of Plane and Spherical Trigonometry: With Their Applications to ... Olinthus Gregory Uten tilgangsbegrensning - 1816 |
Elements of Plane and Spherical Trigonometry: With Their Applications to ... Olinthus Gregory Uten tilgangsbegrensning - 1816 |
Vanlige uttrykk og setninger
altitude angled spherical triangle axis azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cos² cosec cosine 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 hour line hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian oblique opposite angle parallel perpendicular plane angles plane triangle pole problem prop quadrant radius 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 zenith δα
Populære avsnitt
Side 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.
Side 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.
Side 30 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Side 251 - New General Atlas ; containing distinct Maps of all the principal States and Kingdoms throughout the World...
Side 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.
Side 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.
Side 85 - 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...
Side 19 - ... will be — As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.
Side 70 - Required the horizontal distance of the mountain-top from the nearer station, and its height. Ans. Distance, 24840 yards; height, 1447 yards. 10. From the top of a light-house the angle of depression of a ship at anchor was observed to be 4° 52', from the bottom of the light-house the angle was 4° 2'.
Side 245 - XI- -A Treatise on Astronomy; in which the Elements of the Science are deduced in a natural Order, from the Appearances of the Heavens to an Observer on the Earth ; demonstrated on Mathematical Principles, and explained by an Application to the various Phenomena. By Olinthus Gregory, Teacher of Mathematics, Cambridge, 8vo.