## Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |

### From inside the book

Results 6-10 of 31

Page 46

...

...

**perpen**- dicular ; that is , EF will .equal EG , and the chords will be equally distant from the centre . B F A H C N M E 3 D K Secondly . Suppose the arc AB less than CD . Applying the portion of the figure on the left of HK upon the ... Page 57

...

...

**perpen**- dicular to AB , and prolong it until ED = CE ; then we evidently have AC AD , also BC = BD , and since C was a common point of the circumferences , D will also be a common point . These circumferences will then have two points ... Page 65

...

...

**perpen**- dicular to the radius EB , and the angle ABL M , is measured by half the arc AN'B ( T. X. , C. II . ) . But each angle in the segment ANB is also measured by half the same arc ( T. X. ) . 5 CONSTRUCTION OF POLYGONS . PROBLEM ... Page 70

...

...

**perpen**- dicular to the radii EM and EM ' , and therefore tangent to the circumference ( T. V. ) . Scholium . The case when the given point is in the circum- ference offers no difficulty , since we then draw a radius to the given point ... Page 83

...

...

**perpen**- dicular to AD . The two tri- angles ABE , ACF are similar , B since they are equiangular ; hence E ' F FI B X D C D ' E AB : AC :: BE : CF. But the two triangles BDE , CFD are also similar , and give BE : CF :: BD : CD ...### Other editions - View all

### Common terms and phrases

a+b+c ACē altitude angles equal apothem bisect centre chord circ circumference cone consequently corresponding cosec Cosine Cotang cylinder decimal denote described diameter dicular distance divided draw drawn equation equivalent exterior angles feet figure formed frustum give given line greater half hence homologous sides hypotenuse inscribed circle intersection logarithm measure middle point multiplied number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right-angled triangle Scholium secant sector similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang tangent THEOREM three sides triangle ABC triangular prism vertex volume