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

### Inni boken

Resultat 1-5 av 7

Side 1

In order to which, it is not onl requisite that the Peripheries of

certain Right-lines in, and about, the

assigned Number of equal Parts. - 2. The Periphery of every

to be ...

In order to which, it is not onl requisite that the Peripheries of

**Circles**, but alsocertain Right-lines in, and about, the

**Circle**, be supposed divided into someassigned Number of equal Parts. - 2. The Periphery of every

**Circle**is supposedto be ...

Side 3

The Tangent of an Arch is a Right-line touching the

Arch, produced from thence till it meets a Right-line passing thro' the Center and

the other Extremity. Thus AG is the Tangent of the Arch AB. - Io. The Secant of ...

The Tangent of an Arch is a Right-line touching the

**Circle**in one Extremity of thatArch, produced from thence till it meets a Right-line passing thro' the Center and

the other Extremity. Thus AG is the Tangent of the Arch AB. - Io. The Secant of ...

Side 21

D E FIN IT ION S. I. Great-

passing thro' the Center thereof. 2: The Axis of a Great-

passing thro' the Center, perpendicular to the Plane of the

Points ...

D E FIN IT ION S. I. Great-

**Circle**of a Sphere is a Sečtion of the Sphere by a Planepassing thro' the Center thereof. 2: The Axis of a Great-

**Circle**is a Right-linepassing thro' the Center, perpendicular to the Plane of the

**Circle**: And the twoPoints ...

Side 22

that the Sečtion of two Great-

Diameter of the Sphere ; and consequently, that their Peripheries will always

interse&t each other in two Points at the Distance of a Semicircle, or 18o Degrees

. 2.

that the Sečtion of two Great-

**Circles**(as it passes thro' the Center) will be aDiameter of the Sphere ; and consequently, that their Peripheries will always

interse&t each other in two Points at the Distance of a Semicircle, or 18o Degrees

. 2.

Side 62

Let a

OA, OC and OD be drawn; also let CF, parallel to AB, be drawn, meeting DO,

produced (if need be) in F. It * . is evident that DF will be perpendicular to AB, and

...

Let a

**Circle**be described about the Triangle,and from O, the Center thereof, letOA, OC and OD be drawn; also let CF, parallel to AB, be drawn, meeting DO,

produced (if need be) in F. It * . is evident that DF will be perpendicular to AB, and

...

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Trigonometry: Plane and Spherical; with the Construction and Application of ... Uten tilgangsbegrensning - 1799 |

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

adjacent Angle alſo known Arch Baſe becauſe Caſe Chord Circle Co-fine AC Co-ſ Co-tang common Logarithm conſequently Demonſtration Diameter equal to Half Exceſs find the Sine firſt garithms given gles Great-Circles half the Difference Half the Sum half the vertical hyperbolic Logarithm Hypothenuſe L L A R Y laſt leſs likewiſe manifeſt Number oppoſite Angle pendicular perpendicular plane Triangle ABC poſed Produćt Progreſſion Prop propoſed Propoſition Radius reaſon Rečiangle reſpectively right-angled ſpherical Triangle Right-line Ro L L A R ſaid ſame Secant ſecond ſee ſhall Sides AC ſince Sine BCD ſpherical Triangle ABC ſubtracted ſuppoſed T H E o R E M Tang Tangent of Half Theor Theorem theſe thoſe uſeful 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...