## 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 Operations |

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Página 80

Such is the case with the triangle that would be formed on a celestial or terrestrial

globe, by the horizon, the brazen

zenith, and passing through the east or west point. 6. Two arcs or angles, ...

Such is the case with the triangle that would be formed on a celestial or terrestrial

globe, by the horizon, the brazen

**meridian**, and a quadrant of altitude, fixed at thezenith, and passing through the east or west point. 6. Two arcs or angles, ...

Página 118

A secondary to the equator drawn through any place on the earth, and passing

through the poles, is called the

upon the surface of the earth, is its distance from the equator measured on an arc

...

A secondary to the equator drawn through any place on the earth, and passing

through the poles, is called the

**meridian**of that place. 7. The latitude of any placeupon the surface of the earth, is its distance from the equator measured on an arc

...

Página 120

The distance of the sun, or of any of the heavenly bodies, from the equator,

measured on an arc of the

according as the body is situated north or south of the equator. 15. Secondaries

to the ...

The distance of the sun, or of any of the heavenly bodies, from the equator,

measured on an arc of the

**meridian**, is called the declination ; north or south,according as the body is situated north or south of the equator. 15. Secondaries

to the ...

Página 121

That vertical circle which intersects the

called the prime vertical: the points where it cuts the horizon are the east and

west points; at the distance of 90° from each of these on the horizon are the north

and ...

That vertical circle which intersects the

**meridian**of any place at right angles, iscalled the prime vertical: the points where it cuts the horizon are the east and

west points; at the distance of 90° from each of these on the horizon are the north

and ...

Página 123

AB being the projection of a certain parallel, suppose that the star which in its

apparent motion describes that parallel, has its inferior transit of the

. The point B which is its place on the sphere, is also its place then in the

projection.

AB being the projection of a certain parallel, suppose that the star which in its

apparent motion describes that parallel, has its inferior transit of the

**meridian**at B. The point B which is its place on the sphere, is also its place then in the

projection.

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Elements of Plane and Spherical Trigonometry: With Their Applications to ... Olinthus Gregory Sin vista previa disponible - 2018 |

### Términos y frases comunes

altitude angled spherical triangle azimuth base becomes bisect centre chap chord circle circle of latitude computation consequently cosc cosec cosine cosº cotangent declination deduced determine dial diameter difference distance draw earth ecliptic equa equal equation Example find the rest formulae given side half Hence horizon hour angle hypoth hypothenuse intersecting latitude logarithmic longitude measured meridian obliq oblique opposite angle parallel perpendicular plane angles plane triangle pole problem projection prop quadrant radius rectangle right angled spherical right angled triangle right ascension right line secant secº sin A sin sine sines and cosines solid angle sphere spherical excess spherical trigonometry star substyle sun’s supposed surface tangent theorem three angles three sides tion triangle ABC values versed sine versin vertical angle whence zenith

### 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.