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

### Inni boken

Resultat 1-5 av 5

Side 69

13) : : Co-tang. EFI : Tang. Q3 and as Radius : Co-tang. #C) :: AG : AE :: 2AG (AC

– BC): 2AE (AB). Q. E. D. PR o P. XX. ... AB ::

2.) therefore

13) : : Co-tang. EFI : Tang. Q3 and as Radius : Co-tang. #C) :: AG : AE :: 2AG (AC

– BC): 2AE (AB). Q. E. D. PR o P. XX. ... AB ::

**Co**-**s**. F B BC :**Co**-**s**. AC (by - Theor.2.) therefore

**Co**-**s**. AB x**Co**-**s**. B C = Rad. x**Co**-**s**. A C ; but the former of these is ... Side 70

Radius +

. But the Radius may be considered as the Sine of an Arch of 90°, or the Co-fine

of ...

**Co**-**s**. B C ::**Co**-**s**. A B :**Co**-**s**. A C (by Theor. 2.), it will be (by Comp. and Div.)Radius +

**Co**-**s**. BC : Rad. —**Co**-**s**. BC ::**Co**-**s**. AB+**Co**-**s**. AC :**Co**-**s**, AB –**Co**-**s**. AC. But the Radius may be considered as the Sine of an Arch of 90°, or the Co-fine

of ...

Side 73

4 and Equality); therefore

of the Base of any spherical friangle ABC,

4 and Equality); therefore

**is**T. DE-- T. BC : T. DE – T. BC::**S**. AD+**S**. AB :**S**. AD —**S**. AB; whence (by Prop. ... The Produć of the Square of Radius and the**Co**-oneof the Base of any spherical friangle ABC,

**is**equal to the Produć of the Sines of ... Side 74

With the Construction and Application of Logarithms Thomas Simpson.

Rad. (::

by multiplying Means and Extremes, we have Co-f. A Box Radius = S. C B •e.

With the Construction and Application of Logarithms Thomas Simpson.

**Co**-**s**. CB :Rad. (::

**Co**-**s**. BD:**Co**-**s**, CD)::**Co**-**s**. AB :**Co**-**s**: AC (by Corol, to Theor. 2.) whence,by multiplying Means and Extremes, we have Co-f. A Box Radius = S. C B •e.

Side 75

It appears from the last Prop. that

S. BC x

then we shall have

It appears from the last Prop. that

**Co**-**s**: ABx Ris =**Co**-**s**. AC x**Co**-**s**. BC + S. AC xS. BC x

**Co s**. C. R > in which, for**Co**-**s**. C let its Equal R — V be substituted, andthen we shall have

**Co**-**s**. A B x R =**Co**-**s**. A C x**Co**-**s**. F B C + S. AC x S. BC – A S.### Hva folk mener - Skriv en omtale

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

### Vanlige uttrykk og setninger

adjacent Angle alſo known Arch Baſe becauſe Caſe Chord Circle Co-fine AC Co-ſ Co-tang common Logarithm conſequently Demonſtration Diameter equal to Half Exceſs find the Sine firſt garithms given gles Great-Circles half the Difference Half the Sum half the vertical hyperbolic Logarithm Hypothenuſe L L A R Y laſt leſs likewiſe manifeſt Number oppoſite Angle pendicular perpendicular plane Triangle ABC poſed Produćt Progreſſion Prop propoſed Propoſition Radius reaſon Rečiangle reſpectively right-angled ſpherical Triangle Right-line Ro L L A R ſaid ſame Secant ſecond ſee ſhall Sides AC ſince Sine BCD ſpherical Triangle ABC ſubtracted ſuppoſed T H E o R E M Tang Tangent of Half Theor Theorem theſe thoſe uſeful verſed Sine vertical Angle whence whoſe

### 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...