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

### Inni boken

Resultat 1-5 av 5

Side 10

is

Right one): For then another Right-line Ba, equal to BA, may be drawn from B to a

Point in the Base, somewhere between C and the Perpendicular BD, and ...

is

**less**. than the given Side BC, adjacent to it (except the Angle found is exactly aRight one): For then another Right-line Ba, equal to BA, may be drawn from B to a

Point in the Base, somewhere between C and the Perpendicular BD, and ...

Side 16

This, if you desire no more than the 4 or 5 first Places of each (which is exact

enough where nothing

effected by barely taking the proportional Parts of the Differences. But if a greater

Degree ...

This, if you desire no more than the 4 or 5 first Places of each (which is exact

enough where nothing

**less**than Degrees and Minutes is regarded), may beeffected by barely taking the proportional Parts of the Differences. But if a greater

Degree ...

Side 40

... may be) x will be always

Term of the logarithmic Progression agreeing with the proposed Number, or,

which is the same, let 1-Hel" = —”– : Then (by taking the Root on both Sides) I-X:

- 3.

... may be) x will be always

**less**than Unity: Moreover, let 1+2" (as before) be theTerm of the logarithmic Progression agreeing with the proposed Number, or,

which is the same, let 1-Hel" = —”– : Then (by taking the Root on both Sides) I-X:

- 3.

Side 41

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

so great ; because x I - X: will be always

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 47

Let A, B and C denote any three Numbers in arithmetical Progression, not

than Ioooo each, whereof the common Difference is Ioo. 2. From twice the

Logarithm of B, subtract the Sum of the Logarithms of A and C, and let the

Remainder be ...

Let A, B and C denote any three Numbers in arithmetical Progression, not

**less**than Ioooo each, whereof the common Difference is Ioo. 2. From twice the

Logarithm of B, subtract the Sum of the Logarithms of A and C, and let the

Remainder be ...

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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

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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...