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

### Inni boken

Side 11

...

that the Co - tangents of any two different Arches ( represented by P and Q ) are

to one another , inversely as the Tangents of the fame Arches : For , since Tang .

...

**follows**, that the Tangent of Half a Right - angle is equal to the Radius , andthat the Co - tangents of any two different Arches ( represented by P and Q ) are

to one another , inversely as the Tangents of the fame Arches : For , since Tang .

Side 16

... each Number ( which is sufficient to give the Value of an Angle to Seconds ,

and even to Thirds , in most cases ) , then the Opperation may -be as

Multiply the Sum of the Sines of any two adjacent Terms of the Progression 45 ' ,

1 ...

... each Number ( which is sufficient to give the Value of an Angle to Seconds ,

and even to Thirds , in most cases ) , then the Opperation may -be as

**follows**: 1 °Multiply the Sum of the Sines of any two adjacent Terms of the Progression 45 ' ,

1 ...

Side 19

... from whence the Operation will be as

85940641 Sine 59 ° 15 , 0000000730 1 " Prod . 0001486947 86217 1 " Rem . ,

8595551047 Sine 59 ° 16 ' 730 1486217 8548724 Rem . , 8597037264 Sine 59 '

17 730 ...

... from whence the Operation will be as

**follows**: , 00014786947 Excess ,85940641 Sine 59 ° 15 , 0000000730 1 " Prod . 0001486947 86217 1 " Rem . ,

8595551047 Sine 59 ° 16 ' 730 1486217 8548724 Rem . , 8597037264 Sine 59 '

17 730 ...

Side 22

It

Degrees distant from · its Pole ; and that the B A Measure of a spherical Angle

CAD * is an Arch of a Great - Circle intercepted by the two Circles ACB , ADB

forming ...

It

**follows**moreover , that the Periphery of a Great - Circle is every where goDegrees distant from · its Pole ; and that the B A Measure of a spherical Angle

CAD * is an Arch of a Great - Circle intercepted by the two Circles ACB , ADB

forming ...

Side 24

E. D. have COROLLARY I. Hence it

oblique spherical Triangle ADC are to one another , directly , as the Sines of the

opposite Sides . For D B } by the For let BC be perpendicular 24 Spherical ...

E. D. have COROLLARY I. Hence it

**follows**, that the Sines of the Angles of anyoblique spherical Triangle ADC are to one another , directly , as the Sines of the

opposite Sides . For D B } by the For let BC be perpendicular 24 Spherical ...

### Hva folk mener - Skriv en omtale

Vi har ikke funnet noen omtaler på noen av de vanlige stedene.

### Andre utgaver - Vis alle

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...