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 15
... of half the difference ; whence the truth of the corollary . PROP . XII . 12. Of any three equidifferent arcs , it will be , as 1 radius , to the cosine of their common difference , General Properties of Lines and Angles . 15.
... of half the difference ; whence the truth of the corollary . PROP . XII . 12. Of any three equidifferent arcs , it will be , as 1 radius , to the cosine of their common difference , General Properties of Lines and Angles . 15.
Página 35
... 7 , = = 7 perp . base 24 1.75 6 = = ' 2916666 = tan 16 ° 15 ′ 37 ′′ , angle at the base ; whence 90 ° 16 ° 15 ′ 37 ′′ 73 ° 44 ′ 23 ′′ , angle at vertex . Or , = perp . base 24 7 = 3.4285714 Right angled Plane Triangles . $ 5.
... 7 , = = 7 perp . base 24 1.75 6 = = ' 2916666 = tan 16 ° 15 ′ 37 ′′ , angle at the base ; whence 90 ° 16 ° 15 ′ 37 ′′ 73 ° 44 ′ 23 ′′ , angle at vertex . Or , = perp . base 24 7 = 3.4285714 Right angled Plane Triangles . $ 5.
Página 41
... whence = sin ( A + B ) sin A COS B + sin B COS A. 14. If in this equation в be regarded as subtractive , then will sin B obviously be subtractive also ; but cos B will not change its sign , because it will still continue to be estimated ...
... whence = sin ( A + B ) sin A COS B + sin B COS A. 14. If in this equation в be regarded as subtractive , then will sin B obviously be subtractive also ; but cos B will not change its sign , because it will still continue to be estimated ...
Página 44
... Whence , cos ( B + A ) = 2 cos a coS B COS ( BA ) . Substituting in these expressions for the sine and co- sine of B + A , the successive values of a , 2a , 3a , & c . instead of B , we shall have , 2 cos A sin A 2 cos A sin 2A - sin A ...
... Whence , cos ( B + A ) = 2 cos a coS B COS ( BA ) . Substituting in these expressions for the sine and co- sine of B + A , the successive values of a , 2a , 3a , & c . instead of B , we shall have , 2 cos A sin A 2 cos A sin 2A - sin A ...
Página 47
... whence sin A + sin B ' sin A ' sin B ' - tan ( A ' + B ' ) .... tan ( A ′ — B ' ) ( T. ) - But , it has been seen ( formula 2 ) that sin A ' a sin B ' " = whence it follows that Sin A ' + sin B ′ a + b sin Asin B ' The preceding ...
... whence sin A + sin B ' sin A ' sin B ' - tan ( A ' + B ' ) .... tan ( A ′ — B ' ) ( T. ) - But , it has been seen ( formula 2 ) that sin A ' a sin B ' " = whence it follows that Sin A ' + sin B ′ a + b sin Asin B ' The preceding ...
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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.