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

### Inni boken

Resultat 1-5 av 7

Side 6

Now,

and DE,

Tangents of the foresaid Angles o; (ADB) and DBE (DBC) to the Radius B. D. .

Now,

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

**because**DBF and BDE are Right-angles (by 11.3. and 8. 1.) will beTangents of the foresaid Angles o; (ADB) and DBE (DBC) to the Radius B. D. .

Side 12

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

Moreover mn, being an arithmetical Mean between the Sines BE, DG of the two

Extremes (

to ...

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

Moreover mn, being an arithmetical Mean between the Sines BE, DG of the two

Extremes (

**because**Bm = Dm) is therefore equal to Half their Sum, and Dv equalto ...

Side 38

But we must now observe, that there are various Forms or Species of Logarithms;

of Indices, holds equally true in relation to any Equimultiples, or like Parts, ...

But we must now observe, that there are various Forms or Species of Logarithms;

**because**it is evident that what has been hitherto said, in respect to the Propertiesof Indices, holds equally true in relation to any Equimultiples, or like Parts, ...

Side 41

I —%: Which Series, it is manifest, will always converge, let the Value of be ever

so great ;

observable that this Series has exačtly the same Form (except in its Signs) with

that above ...

I —%: Which Series, it is manifest, will always converge, let the Value of be ever

so great ;

**because**x I - X: will be always less than Unity. But it is furtherobservable that this Series has exačtly the same Form (except in its Signs) with

that above ...

Side 63

From whence it is manifest, that CD will be equal to half the Sum, and AD equal

to half the Difference, of the two Sides of the Triangle. Moreover,

similar Triangles A E H and HCD, it will be, A E”: C D*:: H A* (= HE x HG, by Cor.

to ...

From whence it is manifest, that CD will be equal to half the Sum, and AD equal

to half the Difference, of the two Sides of the Triangle. Moreover,

**because**of thesimilar Triangles A E H and HCD, it will be, A E”: C D*:: H A* (= HE x HG, by Cor.

to ...

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Trigonometry: Plane and Spherical; with the Construction and Application of ... Uten tilgangsbegrensning - 1799 |

Trigonometry, Plane and Spherical;: With the Construction and ..., Volum 2 Thomas Simpson Uten tilgangsbegrensning - 1765 |

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...