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

### Inni boken

Resultat 1-5 av 5

Side 21

If thro ' the Poles A and F of two GreatCircles DF and DA , standing atRight -

angles , two other Great - Circles ACE and FCB be conceived to pass and

thereby

Triangles so ...

If thro ' the Poles A and F of two GreatCircles DF and DA , standing atRight -

angles , two other Great - Circles ACE and FCB be conceived to pass and

thereby

**form**two spherical A Triangles A B C and B FCE , the latter of theTriangles so ...

Side 38

But we must now observe , that there are various

; because it is évident that what has been hitherto said , in respect to the

Properties 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 évident that what has been hitherto said , in respect to the

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

Parts ...

Side 41

But it is further observable that this Series has exactly the same

its Signs ) with that above for the Logarithm of 1 + x ; and that , if both of them be

added together , the Series 2 % + 2 33 2x5 2x7 + & c . thence arising , will be ...

But it is further observable that this Series has exactly the same

**Form**( except inits Signs ) with that above for the Logarithm of 1 + x ; and that , if both of them be

added together , the Series 2 % + 2 33 2x5 2x7 + & c . thence arising , will be ...

Side 44

Thus , in the Brigeon ( or common )

Logarithm of 10 , the Logarithm of any Number will be found , by multiplying 1 (

232 2.45 tiplying the hyperbolic Logarithm of the same 44 The Nature and.

Thus , in the Brigeon ( or common )

**Form**, where an Unit is assumed for theLogarithm of 10 , the Logarithm of any Number will be found , by multiplying 1 (

232 2.45 tiplying the hyperbolic Logarithm of the same 44 The Nature and.

Side 45

232 2.45 tiplying the hyperbolic Logarithm of the same Number by the Fraction ,

434294481 & c . which is the proper Modulus of this

Logarithms of all

it will ...

232 2.45 tiplying the hyperbolic Logarithm of the same Number by the Fraction ,

434294481 & c . which is the proper Modulus of this

**Form**. For , since theLogarithms of all

**Forms**preserve the fame Proportion with respect to each other ,it will ...

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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

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...