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

### Inni boken

Resultat 1-5 av 5

Side 26

making an angle DOE , measured by the arch ED ; the plane DOE being

fuppofed perpendicular to the diameter AL , at the center O. Let AB be the

the proposed triangle , BC the perpendicular , AC the hypothenuse , and BAC ( or

DAE ...

making an angle DOE , measured by the arch ED ; the plane DOE being

fuppofed perpendicular to the diameter AL , at the center O. Let AB be the

**base**ofthe proposed triangle , BC the perpendicular , AC the hypothenuse , and BAC ( or

DAE ...

Side 59

Hence it also appears , that the

difference of its two segments ( made by letting fall a perpendicular ) , as the fine

of the angle ( CAD ) at the vertex , to the fine of the difference of the angles at the

...

Hence it also appears , that the

**base**( CD ) of a plane triangle , is to ( Cd ) thedifference of its two segments ( made by letting fall a perpendicular ) , as the fine

of the angle ( CAD ) at the vertex , to the fine of the difference of the angles at the

...

Side 61

As the

fine of half the vertical angle , to the co - fine of balf the difference of the angles at

the

...

As the

**base**of any plane triangle ABC , is to the fum of the two fides , so is thefine of half the vertical angle , to the co - fine of balf the difference of the angles at

the

**base**. In AC , produced , take CD = CB ; join B , D , and draw CE E parallel to...

Side 62

It is B manifest , because CD = CB , that CDB and CBD are equal to one another ,

and that each of them is also equal to half the sum of the angles CBA and A at the

It is B manifest , because CD = CB , that CDB and CBD are equal to one another ,

and that each of them is also equal to half the sum of the angles CBA and A at the

**base**( by Cor . 2. to 10. 1. ) ; therefore ABD , being the excess of the greater ... Side 64

... is to radius , so is the

- proportional , is to the sum of the semi -

, so is the difference of these two , to the perpendicular beight of the triangle .

... is to radius , so is the

**base**AB to a fourth - proportional ; and , as the said fourth- proportional , is to the sum of the semi -

**base**and the line CD biseating the**base**, so is the difference of these two , to the perpendicular beight of the triangle .

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Trigonometry, Plane and Spherical: With the Construction and Application of ... Thomas Simpson Uten tilgangsbegrensning - 1748 |

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 - 1799 |

### Vanlige uttrykk og setninger

added alſo appears arch balf baſe becauſe called caſe chord circle co-f co-fine AC co-tang common complement conſequently Corol COROLLARY determine diameter difference divided drawn equal equal to half evident exceſs extremes fide AC fine fines firſt follows given gives gles greater half the ſum half their difference Hence hyperbolic logarithm hypothenuſe laſt logarithm manifeft meeting method minute moreover Note oppoſite parallel perpendicular plane triangle ABC preceding progreſſion PROP proportion propoſed radius rectangle reſpectively right-angled ſame ſecant ſee ſeries ſhall ſides ſince ſine ſpherical Spherical triangle ABC ſubtracted ſum ſuppoſed tang tangent of half Tbeor Theor THEOREM thereof theſe thoſe unity verſed vertical angle whence