## A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical Applications |

### Dentro del libro

Resultados 1-5 de 5

Página 25

( 1 ) The reason of this deficiency of the sines and

to , is , that if an arc near 90° be found in terms of its sine ; or a very small arc , or

one near 180° , be found in ternis of its

( 1 ) The reason of this deficiency of the sines and

**cosines**, in the cases alludedto , is , that if an arc near 90° be found in terms of its sine ; or a very small arc , or

one near 180° , be found in ternis of its

**cosine**, the variation of these lines is so ... Página 176

As rect . under the

between this sum and the 2 opp . the side sought : square of rad . So is the rect .

under the

ZS ...

As rect . under the

**cosine**of } the sum of the three Zs and the**cosine**of the diff .between this sum and the 2 opp . the side sought : square of rad . So is the rect .

under the

**cosines**of the differences of the same sum and each of the other twoZS ...

Página 278

by the form q , the numerator a may be considered as representing a sine , and

the denominator b a

quadrant in which the arc or angle must be placed : as , for instance , my belongs

to the ...

by the form q , the numerator a may be considered as representing a sine , and

the denominator b a

**cosine**; and the union of the two signs determines thequadrant in which the arc or angle must be placed : as , for instance , my belongs

to the ...

Página 300

Moreover , if we still suppose the arc b successively equal to a , 2 a , 3 a , 4 a , & c

. and proceed in a similar manner with the formula for the

two arcs , given in art . 21 , we shall obtain the following expressions : Cos a =

cos ...

Moreover , if we still suppose the arc b successively equal to a , 2 a , 3 a , 4 a , & c

. and proceed in a similar manner with the formula for the

**cosine**of the sum oftwo arcs , given in art . 21 , we shall obtain the following expressions : Cos a =

cos ...

Página 317

cases , to calculate a few of their terms , to obtain the sine or

required . . 69 . Several other formulæ for expressing the sine ,

functions of the arc , may also be obtained by means of certain imaginary factors

...

cases , to calculate a few of their terms , to obtain the sine or

**cosine**of the arcrequired . . 69 . Several other formulæ for expressing the sine ,

**cosine**, & c . infunctions of the arc , may also be obtained by means of certain imaginary factors

...

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### Otras ediciones - Ver todas

A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle Sin vista previa disponible - 2014 |

A Treatise on Plane and Spherical Trigonometry: With Their Most Useful ... John Bonnycastle Sin vista previa disponible - 2018 |

### Términos y frases comunes

acute added adjacent altitude ambiguous angle apparent base become CALCULATION centre chords circle complement cosec cosine describe diameter diff difference distance draw equal equation Example expressions Extend extent will reach feet former formulæ given given side gives greater greater than 90 half height Hence horizon hypothenuse kind latitude latter less than 90 logarithms longitude manner means measured meridian moon's object oblique observed obtain opposite opposite angle passing perpendicular plane plane triangle points pole PROBLEM projected quadrant radius remaining required to find right ascension right-angled spherical triangle rising RULE scale semitangent setting side side AC sines sphere spherical triangle spherical triangle ABC star substituted supplement tables taken tangents THEOREM Trigonometry true unlike whence

### Pasajes populares

Página xxi - 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 xxiv - ... for the second term, and the greater for the first ; and in either case multiply the second and third terms together, and divide the product by the first for the answer, which will always be of the same denomination as the third term.

Página 295 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Página 329 - The sum of any two sides of a spherical triangle is greater than the third side, and their difference is less than the third side.

Página xxxi - To find the other side: — as the sum of the two given sides is to their difference, so is the tangent of half the sum of their opposite angles to the tangent of half their difference...

Página 3 - 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 xxii - SECANT of an arc, is a straight line drawn from the centre, through one end of the arc, and extended to the tangent which is drawn from the other end.

Página 159 - The AMPLITUDE of any object in the heavens is an arc of the horizon, contained between the centre of the object when rising, or setting, and the east or west points of the horizon. Or, it is...

Página 53 - Having given two sides and an angle opposite to one of them, or two angles and a side opposite to one of them.