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 |
Inni boken
Resultat 1-5 av 38
Side 2
... vertical angle of an oblique angled plane triangle upon the base , or base prolonged , it will at once be manifest that the resolution of triangles generally , may be referred to that of right angled triangles . Thus , as- suming for a ...
... vertical angle of an oblique angled plane triangle upon the base , or base prolonged , it will at once be manifest that the resolution of triangles generally , may be referred to that of right angled triangles . Thus , as- suming for a ...
Side 18
... angles being obtuse will make no difference in the demonstration . Otherwise . From c the vertical angle of the triangle let fall the perpendicular CD upon AB , or AB produced , according as the angles A and B are both acute , or one ...
... angles being obtuse will make no difference in the demonstration . Otherwise . From c the vertical angle of the triangle let fall the perpendicular CD upon AB , or AB produced , according as the angles A and B are both acute , or one ...
Side 19
... vertical angle . From the centre c ( namely , the vertical angle of the triangle ABC ) with the distance of the greater side AC describe the circumference of a circle , meeting AB , CB , produced , in the points E , F , G. Then , it is ...
... vertical angle . From the centre c ( namely , the vertical angle of the triangle ABC ) with the distance of the greater side AC describe the circumference of a circle , meeting AB , CB , produced , in the points E , F , G. Then , it is ...
Side 40
... angles , may be investigated analytically . Let ABC , in the annexed figure , be any plane triangle , c the vertical angle , CD a perpendicular let fall from it upon the base or base produced , and let a , b , and c , denote the sides ...
... angles , may be investigated analytically . Let ABC , in the annexed figure , be any plane triangle , c the vertical angle , CD a perpendicular let fall from it upon the base or base produced , and let a , b , and c , denote the sides ...
Side 63
... vertical staffs , & c . But as these depend solely upon the prin ciple of ... angle included between the other end and the tower , finding them to be 57 ... angles . Thus , suppose in the continuations of the res- pective lines CA , CB ...
... vertical staffs , & c . But as these depend solely upon the prin ciple of ... angle included between the other end and the tower , finding them to be 57 ... angles . Thus , suppose in the continuations of the res- pective lines CA , CB ...
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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.