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

### Inni boken

Resultat 1-5 av 16

Side 4

... or Canon ( see the

Arch EF ( Vid . Def . 3 . and 9. ) ; then , by reason of the Similarity of the Triangles

ABC , AFG , it will be , AB : BC :: AF : FG . 2. E. D. Note , In the Quotations where ...

... or Canon ( see the

**preceding**Figure ) , and FG the Tangent of the Angle A , orArch EF ( Vid . Def . 3 . and 9. ) ; then , by reason of the Similarity of the Triangles

ABC , AFG , it will be , AB : BC :: AF : FG . 2. E. D. Note , In the Quotations where ...

Side 9

3. ) which added to C , an Ang . Cop . and ABC and the Sum subtracted from 180

to one of ' em gives the other Angle ABC . Two Sides The other Let the Angle

ABC be found , by AB , BC and Side AC che

opp .

3. ) which added to C , an Ang . Cop . and ABC and the Sum subtracted from 180

to one of ' em gives the other Angle ABC . Two Sides The other Let the Angle

ABC be found , by AB , BC and Side AC che

**preceding**Case , and then it 3 anopp .

Side 13

From whence , and the

. 1. If the Sine of the Mean , of three equidifferent Arches ( supposing Radius

Unity ) be multiplied by twice the Co - fine of the common Difference , and the

Sine ...

From whence , and the

**preceding**Corollary , we have these two useful Theorems. 1. If the Sine of the Mean , of three equidifferent Arches ( supposing Radius

Unity ) be multiplied by twice the Co - fine of the common Difference , and the

Sine ...

Side 14

IV . To fhew the Manner of constructing the Trigonometrical Canon . First , find the

Sine of an Arch of one Minute , by the

Prop . Prop . 1. which let be denoted by C ; 14 Construction of the Table.

IV . To fhew the Manner of constructing the Trigonometrical Canon . First , find the

Sine of an Arch of one Minute , by the

**preceding**Prop . and then its Co - sine , byProp . Prop . 1. which let be denoted by C ; 14 Construction of the Table.

Side 18

Again , as a second Example , let it be required to find the Sines of all the Arches

, to every Minute , between 59 ° 15 ' and 60 ° ooʻ ; those of the two Extremes

being first found , by the

Again , as a second Example , let it be required to find the Sines of all the Arches

, to every Minute , between 59 ° 15 ' and 60 ° ooʻ ; those of the two Extremes

being first found , by the

**preceding**Method . Method . In this Case , the two ...### Hva folk mener - Skriv en omtale

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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...