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

### Inni boken

Resultat 1-5 av 10

Side 23

... as Radius is to the Sine of the Angle at the Base , fo is the Sine of the Hypot

benuse to the Sine of the Perpendicular ; and as Radius to the Co - fine of the

Angle at the Base , so is the Tangent of the

Base .

... as Radius is to the Sine of the Angle at the Base , fo is the Sine of the Hypot

benuse to the Sine of the Perpendicular ; and as Radius to the Co - fine of the

Angle at the Base , so is the Tangent of the

**Hypothenuse**to the Tangent of theBase .

Side 24

making an Angle DOE , measured by the Arch ED ; the Plane DOE being

supposed perpendicular to the Diameter AL , at the Center O. Let A B be the

Base of the proposed Triangle , BC the Perpendicular , AC the

and BAC ( or ...

making an Angle DOE , measured by the Arch ED ; the Plane DOE being

supposed perpendicular to the Diameter AL , at the Center O. Let A B be the

Base of the proposed Triangle , BC the Perpendicular , AC the

**Hypothenuse**,and BAC ( or ...

Side 25

... in right - angled spherical Triangles ABC , DBC , having one Leg BC common ,

the Tangents of the

one Leg , so is the Co - fine of the other Leg to the Co - line of the

... in right - angled spherical Triangles ABC , DBC , having one Leg BC common ,

the Tangents of the

**Hypothenuses**are to each ... as Radius is to the Co - fine ofone Leg , so is the Co - fine of the other Leg to the Co - line of the

**Hypothenuse**. Side 26

B Hence , if two rightangled spherical Triangles ABC , CBD have the fame

Perpendicular DBC , the Co - fines of their

directly , as the Co - fines of their Bafes . For Rad . : Co - fin . BC :: Co - sin . AB :

Co - sin ...

B Hence , if two rightangled spherical Triangles ABC , CBD have the fame

Perpendicular DBC , the Co - fines of their

**Hypothenuses**will be to each other ,directly , as the Co - fines of their Bafes . For Rad . : Co - fin . BC :: Co - sin . AB :

Co - sin ...

Side 28

A. THE OR EM V. In any right - angled Spherical Triangle it will be , as Radius is

to the Co - line of the

tangent of the other Angle . For ( CEF being as in the last ) it will be , as Radius ...

A. THE OR EM V. In any right - angled Spherical Triangle it will be , as Radius is

to the Co - line of the

**Hypothenuse**, so is the Tangent of either Angle to the Co -tangent of the other Angle . For ( CEF being as in the last ) it will be , as Radius ...

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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...