## 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 82

For the

together less than four right angles; therefore, the sides a, b, c, which measure

those plane angles are together less than a circle. 16. Let the tetraedron oasc be

...

For the

**solid angle**at o is contained by three plane angles, which (Euc. xi. 21) aretogether less than four right angles; therefore, the sides a, b, c, which measure

those plane angles are together less than a circle. 16. Let the tetraedron oasc be

...

Página 104

Therefore, putting P for the sum of all the angles of the polygon, n for their

number, and v for the sum of all the vertical ... A

that which is made by the meeting of more than two plane angles, which are not

in the ...

Therefore, putting P for the sum of all the angles of the polygon, n for their

number, and v for the sum of all the vertical ... A

**solid angle**is defined by Euclid,that which is made by the meeting of more than two plane angles, which are not

in the ...

Página 105

According to this definition,

surfaces which comprise them, as plane angles do to the lines by which they are

included: so that, as in the latter, it is not the magnitude of the lines, but their

mutual ...

According to this definition,

**solid angles**bear just the same relation to thesurfaces which comprise them, as plane angles do to the lines by which they are

included: so that, as in the latter, it is not the magnitude of the lines, but their

mutual ...

Página 106

scribed, and that those planes are produced till they cut the surface of the sphere;

then will the surface of the spherical triangle, included between those planes, be

a proper measure of the

scribed, and that those planes are produced till they cut the surface of the sphere;

then will the surface of the spherical triangle, included between those planes, be

a proper measure of the

**solid angle**made by the planes at their common point ... Página 107

ner as angles determined by planes are measured by the triangles or polygons,

they mark out upon the same, or an equal sphere. In all cases, the maximum limit

of

ner as angles determined by planes are measured by the triangles or polygons,

they mark out upon the same, or an equal sphere. In all cases, the maximum limit

of

**solid angles**, will be the plane towards which the various planes determining ...### Comentarios de la gente - Escribir un comentario

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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.