## 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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Resultados 11-15 de 37

Página 58

We shall terminate the present chapter by subjoining three examples. Example I.

Given the

largest angle, by formula (15). Here 4 (a + b + c) – c = 15.5... log = 1°1903317 | (a

...

We shall terminate the present chapter by subjoining three examples. Example I.

Given the

**three sides**of a plane triangle 40, 34, and 25, respectively, to find thelargest angle, by formula (15). Here 4 (a + b + c) – c = 15.5... log = 1°1903317 | (a

...

Página 59

There is a plane triangle whose

series of integer numbers, and whose largest angle is just double the smallest.

Required its

we ...

There is a plane triangle whose

**sides**are**three**consecutive terms in the naturalseries of integer numbers, and whose largest angle is just double the smallest.

Required its

**sides**and angles. That the student may compare the two methods,we ...

Página 76

From a convenient station P, where could be seen

whose distances from each other were known (viz. AB = 800 ... In the triangle

ABD, where all the angles are known, and the

From a convenient station P, where could be seen

**three**objects A, B, and C,whose distances from each other were known (viz. AB = 800 ... In the triangle

ABD, where all the angles are known, and the

**side**AB, n find one of the other**sides**AD. Página 77

Take BAD from BAc, the remainder, DAC is the angle included between two

known

chap. iii. case 2. ... Hence, the

proportions.

Take BAD from BAc, the remainder, DAC is the angle included between two

known

**sides**AD, Ac; from which the angles ADC and ACD may be found, bychap. iii. case 2. ... Hence, the

**three**required distances are found by theseproportions.

Página 79

When the station is out of the triangle made by the objects, but in one of its

produced. 2. When the station is in one of the

formed ...

When the station is out of the triangle made by the objects, but in one of its

**sides**produced. 2. When the station is in one of the

**sides**of the triangle. 3. When the**three**objects lie in a right line. 4. When the station is not within the triangleformed ...

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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.