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

### Inni boken

Resultat 1-5 av 27

Side 4

A B D F then ,

AE : ED ( by 5 . 4. ) 2. E. D. Thus , if AC = , 75 , and BC = , 45 ; then it will be , 75 :

945 :: 1 ( Radius ) : the Sine of A = ; 6 ; which , in the Table , answers to 36 ° 52 ' ...

A B D F then ,

**because**of the similar Triangles ACB and AED , it will be AC : BC ::AE : ED ( by 5 . 4. ) 2. E. D. Thus , if AC = , 75 , and BC = , 45 ; then it will be , 75 :

945 :: 1 ( Radius ) : the Sine of A = ; 6 ; which , in the Table , answers to 36 ° 52 ' ...

Side 6

Now ,

BF and DE ,

be Tangents of the forefaid Angles FDB ( ADB ) and DBE ( DBC ) to the Radius B

...

Now ,

**because**of the parallel Lines BF and ED , it will be CF : CD :: BF : DE ; butBF and DE ,

**because**DBF and BDE are Right - angles ( by 11. 3 . and 8. 1. ) willbe Tangents of the forefaid Angles FDB ( ADB ) and DBE ( DBC ) to the Radius B

...

Side 10

... DH its Co - tangent , and CH its Co - fecant . Then ( by 7. 2. ) we have CF = the

Square Root of CE2 - EF ; whence , not only the Co - sine CF , but also the

Versed Sine AF , will А 1 } will be known . Then

Construction ...

... DH its Co - tangent , and CH its Co - fecant . Then ( by 7. 2. ) we have CF = the

Square Root of CE2 - EF ; whence , not only the Co - sine CF , but also the

Versed Sine AF , will А 1 } will be known . Then

**because**of the similar JOConstruction ...

Side 11

Then

1 , CF. FE :: CA : AT ; whence the Tangent is known . 2. CF : CE ( CA ) :: CA : CT ;

whence the Secant is known . 3. EF : CF :: CD : DH ; whence the Co - tangent is ...

Then

**because**of the similar Triangles CFE , CAT , and CDH , it will be ( by 5.4 . )1 , CF. FE :: CA : AT ; whence the Tangent is known . 2. CF : CE ( CA ) :: CA : CT ;

whence the Secant is known . 3. EF : CF :: CD : DH ; whence the Co - tangent is ...

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 (

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 ...### 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 |

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...