## 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 3

In order to which , it is not only requisite , that the peripheries of circles , but also

certain right - lines in , and about , the circle , be supposed

assigned number of equal parts . 2. The periphery of every circle is supposed to

be ...

In order to which , it is not only requisite , that the peripheries of circles , but also

certain right - lines in , and about , the circle , be supposed

**divided**into fomeassigned number of equal parts . 2. The periphery of every circle is supposed to

be ...

Side 5

... which is supposed unity , and conceived to be

decimal parts . By the help of this table , and the doctrine of fimilar triangles , the

whole business of trigonometry is performed ; which I shall now proceed to fhew .

... which is supposed unity , and conceived to be

**divided**into 10000 , or more ,decimal parts . By the help of this table , and the doctrine of fimilar triangles , the

whole business of trigonometry is performed ; which I shall now proceed to fhew .

Side 31

I D For , let AB and K AC be the two proposed arches , and I ler BG and CH be

their fines , and OG S and OH their cofines : imoreover , B В let the arch BC be

equally

half ...

I D For , let AB and K AC be the two proposed arches , and I ler BG and CH be

their fines , and OG S and OH their cofines : imoreover , B В let the arch BC be

equally

**divided**in D , fo that CD may 1 11 GA be half the dif . ference , and ADhalf ...

Side 38

That , the difference of the indices of any two terms of the progrenzo is equal ti the

index of the quotient of one of them

of or a . Which is only a . the converse of the preceding article , 3 : That , 3.

That , the difference of the indices of any two terms of the progrenzo is equal ti the

index of the quotient of one of them

**divided**by ihe other . Thus 53 is = the indexof or a . Which is only a . the converse of the preceding article , 3 : That , 3.

Side 56

... that the fine of R the double of any arch , is equal to twice the rečtangle of the

fine and co - fine of the single arch ,

equal to the difference . of the squares of the fine and co - fine of the single arch ,

also ...

... that the fine of R the double of any arch , is equal to twice the rečtangle of the

fine and co - fine of the single arch ,

**divided**by radius ; and that its co - fine isequal to the difference . of the squares of the fine and co - fine of the single arch ,

also ...

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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