## Elements of Geometry and Trigonometry |

### From inside the book

Page 208

...

...

**sine**of an arc is the perpendicular let fall from one extremity of the arc , on the diameter which passes through the other extremity . Thus , MP is the**sine**of the arc AM , or of the angle ACM . The tangent of an arc is a line touching ... Page 209

...

...

**sine**of an arc , is the part of the diameter inter- cepted between one extremity of the arc and the foot of the**sine**. Thus , AP is the versed**sine**of the arc AM , or the angle ACM . These four lines MP , AT , CT , AP , are dependent ... Page 210

...

...

**sine**and tangent of an arc B N D ន MT R E A zero , are zero , and the cosine and secant of this same arc , are each equal to the radius . Hence if R represents the radius of the circle , we have " sin 0 = 0 , tang 0 = 0 , cos 0 = R ... Page 211

...

...

**sine**of an arc or of an angle is equal to the**sine**of the supplement of that arc or angle . The arc or angle A has for its supplement 180 ° -A : hence generally , we have sin A sin ( 180 ° -A . ) The same property might also be ... Page 212

...

...

**sine**AP is equal to the radius CA minus CP the cosine AM : that is , ver - sin AM - R - cos AM . Now when the arc AM be- comes AM ' the versed**sine**AP , becomes AP ' , that is equal to R + CP ' . But this expression cannot be derived ...### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book centre chord circ circumference circumscribed common cone convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex