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 2
... a right angled triangle , equal to unity , for example , com- puting the bases and perpendiculars of all possible right angled triangles having the assigned hypothenuse , and arranging them 2 Definitions and Principles .
... a right angled triangle , equal to unity , for example , com- puting the bases and perpendiculars of all possible right angled triangles having the assigned hypothenuse , and arranging them 2 Definitions and Principles .
Página 25
... 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 , but no side , would make a fourth case , were it not ( see chap . i . 6 ) that for want ...
... 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 , but no side , would make a fourth case , were it not ( see chap . i . 6 ) that for want ...
Página 27
... example , at the extremities of the base , c at the vertex , then , according to the nature of the problem , write down the requisite proportion in four distinct lines , with the letters of reference to each term , and the given numbers ...
... example , at the extremities of the base , c at the vertex , then , according to the nature of the problem , write down the requisite proportion in four distinct lines , with the letters of reference to each term , and the given numbers ...
Página 28
... Example II . 216 ; CB 5. In a plane triangle ABC are given AC 117 ; the angle a = 22 ° 37 ' ; to find the rest . Construction . Draw an indefinite right line ABB ' , from an assumed point a in which draw a line 28 Plane Trigonometry .
... Example II . 216 ; CB 5. In a plane triangle ABC are given AC 117 ; the angle a = 22 ° 37 ' ; to find the rest . Construction . Draw an indefinite right line ABB ' , from an assumed point a in which draw a line 28 Plane Trigonometry .
Página 31
... Example II . 9. The two sides of a triangle are 40 and 32 , and the included angle 90 ° , required the other angles and side . In this example the operation may be considerably shortened by working without , instead of with , the loga ...
... Example II . 9. The two sides of a triangle are 40 and 32 , and the included angle 90 ° , required the other angles and side . In this example the operation may be considerably shortened by working without , instead of with , the loga ...
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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.