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

### Inni boken

Resultat 1-5 av 21

Side 2

Any Part AB of H K the Periphery of the Circle is called I ( В Arch , and is said to

be the Measure of the Angle ACB at the

Note , The Degrees ... The

...

Any Part AB of H K the Periphery of the Circle is called I ( В Arch , and is said to

be the Measure of the Angle ACB at the

**F**Center , which it subА с tends . D } 1Note , The Degrees ... The

**Co**- fine of an Arch is the 8. The 2 Plane Trigonometry...

Side 23

Hence it is also

Triangles ABC and FCE , are both Right ... and as Radius to the

Angle at the Base , so is the Tangent of the Hypothenuse to the Tangent of the

Base .

Hence it is also

**F**manifest , that the Angles B and E , of the ComplementalTriangles ABC and FCE , are both Right ... and as Radius to the

**Co**- fine of theAngle at the Base , so is the Tangent of the Hypothenuse to the Tangent of the

Base .

Side 26

D B Radius : Sine

CB :

rightangled spherical Triangles ABC , CBD have the fame Perpendicular DBC ...

D B Radius : Sine

**F**:: Sine CF : Sine CE ; that is , Radius :**Co**- sine BA ::**Co**- fineCB :

**Co**fine AC ( see Cor . 4. p . 23. ) 2. E. D. COROLL ARY . B Hence , if tworightangled spherical Triangles ABC , CBD have the fame Perpendicular DBC ...

Side 27

Case 1. it will be , Radius : Sine C :: Sine CF : Sine EF ; that is , Radius : Sine C ::

Perpendicular . For , supposing CEF

line ...

Case 1. it will be , Radius : Sine C :: Sine CF : Sine EF ; that is , Radius : Sine C ::

**Co**- fine BC :**Co**- sine A. 2. E. D. COROLLARY . 1 Hence ... Tangent of thePerpendicular . For , supposing CEF

**F**as before , it will be , as Radius : E**Co**-line ...

Side 29

... B В let the Arch BC be equally divided in D , so that CD may be half the DifH

GA PO ference , and AD half the Sum , of ... In any spherical Triangle ABC it will

be , as the

...

... B В let the Arch BC be equally divided in D , so that CD may be half the DifH

**F**GA PO ference , and AD half the Sum , of ... In any spherical Triangle ABC it will

be , as the

**Co**- tangent of Helf the Sum of the two Sides is to the Tangent of Half...

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

### Vanlige uttrykk og setninger

added alſo appears Arch Bafe balf Baſe becauſe Caſe Center Chord Circle Co-f Co-fine Co-ſine AC Co-tang common conſequently COROLLARY Demonſtration determine Diameter Difference drawn equal equal to Half evident Exceſs Extremes fame firſt follows Form gent given gives gles greater half the Difference Half the Sum Hence hyperbolic Logarithm Hypothenuſe Index laſt Logarithm manifeſt meeting Method Minute Moreover Note Number oppoſite parallel perpendicular plane Triangle ABC preceding Product Progreſſion PROP Proportion propoſed Radius Rectangle Remainder reſpectively right-angled ſame Secant ſecond ſee Series ſhall Sides ſince Sine Sine ACD Solution ſuppoſed Table Tang Tangent of Half Tbeor Terms Theor THEOREM thereof theſe thoſe Unity Value 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...