## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-3 of 35

Page 128

...

...

**give**( Book IV . Prop . XIV . ) , PC2 + PB2 = 2PQ2 + 2QC2 . The triangle BAC will in like manner**give**, AC2 + AB2-2AQ2 + 2QC2 . Taking the first equation from the second , and observing that the triangles APC , APB , which are both ...Page 156

...

...

**give**: sol . AG sol . AZ :: AB × AD × AE : AO × AM × AX . Hence any two rectangular parallelopipedons are to each other , & c . Scholium . We are consequently authorized to assume , as the measure of a rectangular parallelopipedon , the ...Page 224

...

...

**give**AT CA :: CD : DS , or tang A : R :: R : cot A : XIX . The sines and cosines of two arcs , a and b , being given , it is required to find the sine and cosine of the sum or difference of these arcs . From Let the radius AC = R , the ...### Contents

BOOK | 7 |

Problems relating to the First and Third Books 57 | 57 |

BOOK IV | 68 |

14 other sections not shown

### Other editions - View all

### Common terms and phrases

adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone consequently convex surface cosine Cotang cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE PROBLEM Prop proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar sine slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line TABLE OF LOGARITHMIC tang tangent THEOREM triangle ABC triangular prism vertex