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 5
... parallel to it let AT be drawn T and limited by CT : let GB and EM be drawn parallel to AA ' , B ' E ' the latter being limited by cr or CT produced . Then BE is the complement of BA , and angle BCE the comple- ment of angle BCA ; BEA ...
... parallel to it let AT be drawn T and limited by CT : let GB and EM be drawn parallel to AA ' , B ' E ' the latter being limited by cr or CT produced . Then BE is the complement of BA , and angle BCE the comple- ment of angle BCA ; BEA ...
Página 10
... arc , till the prolongation Ts becomes equal to cr the secant , and join cs , intersecting the quadrantal arc AE in D. Then , because TSTC , angle TCS TSC TCE , by reason of the parallels Ts , ce . Hence BD DE and 10 Plane Trigonometry .
... arc , till the prolongation Ts becomes equal to cr the secant , and join cs , intersecting the quadrantal arc AE in D. Then , because TSTC , angle TCS TSC TCE , by reason of the parallels Ts , ce . Hence BD DE and 10 Plane Trigonometry .
Página 11
... parallels Ts , ce . Hence BD DE and As tan AB + Sec AB comp . Ab , tan AD = tan ( AB + Comp AB ) . PROP . V. 5. The chord of 60 ° is equal to the radius of the cir- cle ; the versed sine , and cosine of 60 ° are each equal to half the ...
... parallels Ts , ce . Hence BD DE and As tan AB + Sec AB comp . Ab , tan AD = tan ( AB + Comp AB ) . PROP . V. 5. The chord of 60 ° is equal to the radius of the cir- cle ; the versed sine , and cosine of 60 ° are each equal to half the ...
Página 14
... parallel to Bs , or perpendicular to the radius GB . B R A R T D D Then , because of the similar triangles TAC , THR , we shall have , TC : CA :: TR : RH , whence TC . RH = CA. TR , TC : TA :: TR : TH , whence TC . TH TA . TR . Each of ...
... parallel to Bs , or perpendicular to the radius GB . B R A R T D D Then , because of the similar triangles TAC , THR , we shall have , TC : CA :: TR : RH , whence TC . RH = CA. TR , TC : TA :: TR : TH , whence TC . TH TA . TR . Each of ...
Página 15
... parallel G K 18 M E - BG to DE . Then , it is evident that NEKE + BG , is the sum of the sines of AE and AB , and ND ... parallels DE , LM , we have EN : DN :: bм : 6L ; which is evidently the theorem enun- ciated above . - Cor . The sum ...
... parallel G K 18 M E - BG to DE . Then , it is evident that NEKE + BG , is the sum of the sines of AE and AB , and ND ... parallels DE , LM , we have EN : DN :: bм : 6L ; which is evidently the theorem enun- ciated above . - Cor . The sum ...
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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.