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 páginas |
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Página 23
... determined by these or other processes ( some of which will be indicated in the 4th chapter ) , they may be continued thus : sin 30 ° 1 ' = cos l ' sin 30 ° 2 ' = cos 2 ' sin 30 ° 3 ′ cos 3 ' sin 29 ° 59 ′ - sin 29 ° 58 ' sin 29 ° 57 ...
... determined by these or other processes ( some of which will be indicated in the 4th chapter ) , they may be continued thus : sin 30 ° 1 ' = cos l ' sin 30 ° 2 ' = cos 2 ' sin 30 ° 3 ′ cos 3 ' sin 29 ° 59 ′ - sin 29 ° 58 ' sin 29 ° 57 ...
Página 24
... determine the other three ; and the combinations that can be formed out of six quantities , 6.5.4 taken three and three being = or 20 ; it might at 1.2.3 first sight be imagined that 20 distinct rules would be required in this branch of ...
... determine the other three ; and the combinations that can be formed out of six quantities , 6.5.4 taken three and three being = or 20 ; it might at 1.2.3 first sight be imagined that 20 distinct rules would be required in this branch of ...
Página 27
... determines the triangle ; and the sides AC , BC , measured upon the scale of equal parts from which AB was laid down , are found to be 159 and 351 respectively . Computation . Two of the angles being known , their sum 80 ° 44 ' taken ...
... determines the triangle ; and the sides AC , BC , measured upon the scale of equal parts from which AB was laid down , are found to be 159 and 351 respectively . Computation . Two of the angles being known , their sum 80 ° 44 ' taken ...
Página 30
... determine the triangle . Ans . If the angle opposite to the side 50 be acute , then is it = 41 ° 28 ' , the third angle 106 ° 32 ′ , and the remaining side 72.36 . If the angle opposite to side 50 be obtuse , it is 138 ° 32 ′ , and the ...
... determine the triangle . Ans . If the angle opposite to the side 50 be acute , then is it = 41 ° 28 ' , the third angle 106 ° 32 ′ , and the remaining side 72.36 . If the angle opposite to side 50 be obtuse , it is 138 ° 32 ′ , and the ...
Página 34
... , " As the side made radius , " Is to radius ; " So is the other given side , " To the name of that side : which determines the opposite angle . ” 13. When the numbers which measure the sides of the 34 Plane Trigonometry .
... , " As the side made radius , " Is to radius ; " So is the other given side , " To the name of that side : which determines the opposite angle . ” 13. When the numbers which measure the sides of the 34 Plane Trigonometry .
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 30 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Página 251 - New General Atlas ; containing distinct Maps of all the principal States and Kingdoms throughout the World...
Página 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.
Página 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.
Página 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...
Página 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.
Página 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'.
Página 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.