## Trigonometry: Plane and Spherical; with the Construction and Application of Logarithms. By Thomas Simpson, F.R.S. |

### Inni boken

Resultat 1-5 av 5

Side 8

In any plane triangle , it will be , as the sum of any two sides is to their difference ,

so is the tangent of

their difference . T C For , let ABC be the triangle , and AB and AC the А. two ...

In any plane triangle , it will be , as the sum of any two sides is to their difference ,

so is the tangent of

**half the sum**of the two opposite angles , to the tangent of balftheir difference . T C For , let ABC be the triangle , and AB and AC the А. two ...

Side 11

Two sides The other As sum of AB and äc : their AC , AB and angles C dih : tang .

of

diff . ( by Theor : V . ) which added to , and subtracted from , the half furn , gives ...

Two sides The other As sum of AB and äc : their AC , AB and angles C dih : tang .

of

**half the sum**of the included and ABC ABC and C : tang of half their 14 angle Adiff . ( by Theor : V . ) which added to , and subtracted from , the half furn , gives ...

Side 30

... the tangent of balf the sum of those arches to the tangent of balf their difference

: and , as the sum of the co - fines is to their difference , so is the co - tangent of

.

... the tangent of balf the sum of those arches to the tangent of balf their difference

: and , as the sum of the co - fines is to their difference , so is the co - tangent of

**half the sum**of the arches to the tangent of half the difference of the Jame arches.

Side 61

and , consequently ,

Moreover , seeing DCB is = the

9. 1. ) it is evident that BCF ( or DCF ) is equal to

as ECF is ...

and , consequently ,

**half**D + CBD the vertical angle ACB = ( by 9. 1. ) D.Moreover , seeing DCB is = the

**sum**of the .. angles A and CBA , at the base ( by9. 1. ) it is evident that BCF ( or DCF ) is equal to

**half**that**sum**; and , therefore ,as ECF is ...

Side 62

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

, and that each of them is also equal to

the base ( by Cor . 2. to io , 1. ) ; therefore ABD , being the excess of the greater ...

It is LA 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 atthe base ( by Cor . 2. to io , 1. ) ; therefore ABD , being the excess of the greater ...

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### 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 demonſtrated determine diameter difference divided drawn Edition equal equal to half evident exceſs extremes fame fides fine fines firſt follows given gives gles great-circles greater half the difference half the ſum Hence hyperbolic logarithm hypothenuſe known laſt logarithm manifeſt meeting method minute Moreover natural Note oppoſite parallel perpendicular plane triangle ABC preceding PROP proportion propoſed radius reſpectively ſame ſecant ſee ſeries ſhall ſides ſince ſine ſum ſuppoſed tang tangent of half Tbeor Theor THEOREM thereof theſe thoſe unity verſed vertical angle whence