## Trigonometry, Plane and Spherical: With the Construction and Application of Logarithms |

### Inni boken

Resultat 1-5 av 20

Side 6

it is plain that ADB is

propos'd . Moreover , since ABC = ABD ( ADB ) + DBC , and C = ADBDBC ( by 10

. 1. ) it is plain that ABC - Cis = 2 DBC ; or that DBC is

...

it is plain that ADB is

**equal to Half**the Sum of the Angles opposite to the Sides .propos'd . Moreover , since ABC = ABD ( ADB ) + DBC , and C = ADBDBC ( by 10

. 1. ) it is plain that ABC - Cis = 2 DBC ; or that DBC is

**equal to Half**the Difference...

Side 7

2 2 2 2 Hence , in two Triangles ABC and ABC , having two Sides

each , it will be ( by EquaAbC + ACb ... And as Radius to the Tangent of the

Excess of this Angle above 45 ° , so is the Tangent of

required ...

2 2 2 2 Hence , in two Triangles ABC and ABC , having two Sides

**equal**, each toeach , it will be ( by EquaAbC + ACb ... And as Radius to the Tangent of the

Excess of this Angle above 45 ° , so is the Tangent of

**Half**the Sum of therequired ...

Side 11

... the Tangent of

tangents of any two different Arches ( represented by P and Q ) are to one

another , inversely as the Tangents of the fame Arches : For , since Tang . P x Co

- tang .

... the Tangent of

**Half**a Right - angle is**equal**to the Radius , and that the Co -tangents of any two different Arches ( represented by P and Q ) are to one

another , inversely as the Tangents of the fame Arches : For , since Tang . P x Co

- tang .

Side 12

and therefore B m ( or D m ) will be the Sine of BC ( or DC ) , and Om its Co - sine

: Moreover mn , being an arithmetical Mean between the Sines B E , DG of the

two Extremes ( because Bm = Dm ) is therefore

and therefore B m ( or D m ) will be the Sine of BC ( or DC ) , and Om its Co - sine

: Moreover mn , being an arithmetical Mean between the Sines B E , DG of the

two Extremes ( because Bm = Dm ) is therefore

**equal to Half**their Sum , and Dy ... Side 15

... which is given ( by p . 138 and 139 of the Elements ) = İN 2 + W3 = ,

965925826 , & c . ( = the Supplement Chord of 30 % ) and the Sine of 18 ° , which

is = * VI- = 7309017 , 1309017 , & c . (

Secants .

... which is given ( by p . 138 and 139 of the Elements ) = İN 2 + W3 = ,

965925826 , & c . ( = the Supplement Chord of 30 % ) and the Sine of 18 ° , which

is = * VI- = 7309017 , 1309017 , & c . (

**equal to Half**the of Sines , Tangents andSecants .

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Trigonometry, Plane and Spherical;: With the Construction and Application of ... Thomas Simpson Uten tilgangsbegrensning - 1765 |

Trigonometry, Plane and Spherical: With the Construction and Application of ... Thomas Simpson Uten tilgangsbegrensning - 1799 |

### Vanlige uttrykk og setninger

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### Populære avsnitt

Side 1 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees; and each degree into 60 minutes, each minute into 60 seconds, and so on.

Side 3 - Canon, is a table showing the length of the sine, tangent, and secant, to every degree and minute of the quadrant, with respect to the radius, which is expressed by unity or 1, with any number of ciphers.

Side 6 - In every plane triangle, it will be, as the sum of any two sides is to their difference...

Side 41 - The sum of the logarithms of any two numbers is equal to the logarithm of their product. Therefore, the addition of logarithms corresponds to the multiplication of their numbers.

Side 13 - If the sine of the mean of three equidifferent arcs' dius being unity) be multiplied into twice the cosine of the common difference, and the sine of either extreme be deducted from the product, the remainder will be the sine of the other extreme. (B.) The sine of any arc above 60°, is equal to the sine of another arc as much below 60°, together with the sine of its excess above 60°. Remark. From this latter proposition, the sines below 60° being known, those of arcs above 60° are determinable...

Side 31 - ... is the tangent of half the vertical angle to the tangent of the angle which the perpendicular CD makes with the line CF, bisecting the vertical angle.

Side 73 - BD, is to their Difference ; fo is the Tangent of half the Sum of the Angles BDC and BCD, to the Tangent of half their Difference.

Side 28 - As the sum of the sines of two unequal arches is to their difference, so is the tangent of half the sum of those arches to the tangent of half their difference : and as the sum...

Side 68 - In any right lined triangle, having two unequal sides ; as the less of those sides is to the greater, so is radius to the tangent of an angle ; and as radius is to the tangent of the excess of...