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

### Inni boken

Resultat 1-5 av 7

Side 38

Thus , if e be an indefinite small Quantity , the

Number agreeing with any Term i tela of the logarithmic Progresion 1 , ite , 1 + ej

?, I tel , i telt , & c . will be expressed by ne . PROPOSITION I. The byperbolic ...

Thus , if e be an indefinite small Quantity , the

**hyperbolic Logarithm**of the naturalNumber agreeing with any Term i tela of the logarithmic Progresion 1 , ite , 1 + ej

?, I tel , i telt , & c . will be expressed by ne . PROPOSITION I. The byperbolic ...

Side 39

N : But ne is 2.3 ( = L ) the

already specified : Therefore if L ' L3 L4 LS + + & c . = N. 2.3 2. 3.4 2.3.4.5 Q : E. I.

2 2. 3. 4 Lt + 2 PROP . II . To determine the

N : But ne is 2.3 ( = L ) the

**hyperbolic Logarithm**of itel " ( or N ) by what has beenalready specified : Therefore if L ' L3 L4 LS + + & c . = N. 2.3 2. 3.4 2.3.4.5 Q : E. I.

2 2. 3. 4 Lt + 2 PROP . II . To determine the

**hyperbolic Logarithm**( L ) of any ... Side 41

3 3 = ne = the

converge , let the Value of be ever so great ; because x 2 4 1 е e I -m I . I + will be

always less than Unity . But it is further observable that this Series has exactly the

...

3 3 = ne = the

**hyperbolic Logarithm**of Which Series , it is manifest , will alwaysconverge , let the Value of be ever so great ; because x 2 4 1 е e I -m I . I + will be

always less than Unity . But it is further observable that this Series has exactly the

...

Side 42

... x = P - Q : Either of which P + R Values , substituted in the foregoing Series 2 *

+ 233 235 & c . will give the

Example . Let it be proposed to find the

... x = P - Q : Either of which P + R Values , substituted in the foregoing Series 2 *

+ 233 235 & c . will give the

**hyperbolic Logarithm**3 5 of the respective Number .Example . Let it be proposed to find the

**hyperbolic Logarithm**of the Number 2 . Side 43

After the very same Manner the

be determined ; but , as the Series converges , flower and flower , the higher we

go , it is usual , in computing of Tables , to derive the Logarithms we would find ...

After the very same Manner the

**hyperbolic Logarithm**of any . other Number maybe determined ; but , as the Series converges , flower and flower , the higher we

go , it is usual , in computing of Tables , to derive the Logarithms we would find ...

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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...