## 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 |

### Dentro del libro

Resultados 1-5 de 51

Página iv

There is one treatise, that of Emerson, which is a most copious store-house of

curious and elegant

that the perusal of greater part of the book must, to a mathematical student, be as

...

There is one treatise, that of Emerson, which is a most copious store-house of

curious and elegant

**theorems**: but they are so obscured by a defective notation,that the perusal of greater part of the book must, to a mathematical student, be as

...

Página vi

2. This method is more uniform than the other, as well as more general and

comprehensive. In the geometrical method as it is usually conducted, however

convincing and elegant, the demonstration of one property or

have the ...

2. This method is more uniform than the other, as well as more general and

comprehensive. In the geometrical method as it is usually conducted, however

convincing and elegant, the demonstration of one property or

**theorem**may nothave the ...

Página vii

There are several curious and useful

treatises on trigonometry, which have not yet, to my knowledge, been

demonstrated in any other way; and not a few which I am persuaded do not admit

of any other ...

There are several curious and useful

**theorems**to be found in the analyticaltreatises on trigonometry, which have not yet, to my knowledge, been

demonstrated in any other way; and not a few which I am persuaded do not admit

of any other ...

Página 8

From these and other properties and

demonstrated as we proceed, mathematicians have computed the lengths of the

sines, tangents, secants, and versed sines, to an assumed ra. dius, that

correspond to arcs ...

From these and other properties and

**theorems**, some of which will bedemonstrated as we proceed, mathematicians have computed the lengths of the

sines, tangents, secants, and versed sines, to an assumed ra. dius, that

correspond to arcs ...

Página 15

But, by reason of the parallels DE, LM, we have EN : DN :: bM : bl; which is

evidently the

is to their difference, as the cotangent of half the sum of those two arcs, is to the ...

But, by reason of the parallels DE, LM, we have EN : DN :: bM : bl; which is

evidently the

**theorem**enunciated above. Cor. The sum of the cosines of two arcs,is to their difference, as the cotangent of half the sum of those two arcs, is to the ...

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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.