## Elements of Geometry and Trigonometry |

### From inside the book

Results 6-10 of 74

Page 214

...

...

**tang**( an arc ) = -**tang**( its supplement ) cot ( an arc ) = - cot ( its supplement ) . It is no less evident , that if one or several circumfe- rences were added to any arc AM , it would still termi- nae exactly at the point M , and ... Page 216

...

...

**tang**A : CP : CM :: CA : CT ; or cos A : R :: R : sec A : - PM : CP :: CD : DS ; or sin A : cos A :: R : cot A = PM : CM :: CD : CS ; or sin A : R :: R : cosec A : R sin A cos A R2 Cós A R cos A sin A R2 sin A which are the four ... Page 217

...

...

**tang**90 ° = R2 Ο an expression which designates an infinite quantity ; for , the quotient of radius divided by a very small quantity , is very great , and increases as the divisor diminishes ; hence , the quo- tient of the radius ... Page 218

Adrien Marie Legendre Charles Davies. Hence cot A : cot B :

Adrien Marie Legendre Charles Davies. Hence cot A : cot B :

**tang**B :**tang**A ; that is , the cotan- gents of two arcs are reciprocally proportional to their tangents . The formula cot Axtang A = R2 might be deduced imme- diately , by ... Page 221

...

...

**tang**p R = R cot p - cot P R = R**tang**p : sin P R - cos P formulas which are often employed in trigonometrical calcula- tions for reducing two terms to a single one . XXIV . From the first four formulas of Art XXIII . and the first of ...### 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