## Elements of Geometry and Trigonometry |

### From inside the book

Results 1-5 of 24

Page 96

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**angle**B - E ; these tri-**angles**are therefore similar , and they give the proportion AB CE : AD : AC ; and hence AB ...**solid**, for a reason that shall be seen afterwards . Its value is easily con- ceived , by imagining that the ... Page 126

... angle or mutual inclination of two planes is the quan- tity , greater or less , by which they separate from each other ; this angle is measured by the angle contained between two lines , one in each plane , and both ...

... angle or mutual inclination of two planes is the quan- tity , greater or less , by which they separate from each other ; this angle is measured by the angle contained between two lines , one in each plane , and both ...

**Solid Angles**, Page 138

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**solid angle**is formed by three plane angles , the sum of any two of these angles will be greater than the third . The proposition requires demonstra- tion only when the plane angle , which is compared to the sum of the other two , is ... Page 139

... angle ASD < ASC ( Book I. Prop . IX . Sch . ) . Adding BSD = BSC , we shall have ASD + BSD or ASB < ASC + BSC . PROPOSITION XX . THEOREM . The sum of the plane angles which form a

... angle ASD < ASC ( Book I. Prop . IX . Sch . ) . Adding BSD = BSC , we shall have ASD + BSD or ASB < ASC + BSC . PROPOSITION XX . THEOREM . The sum of the plane angles which form a

**solid angle**is always less than four right angles . Cut the ... Page 140

Adrien Marie Legendre Charles Davies. Let the angle ASC = DTF , the angle ASB DTE , and the an- gle BSC - ETF ; then ...

Adrien Marie Legendre Charles Davies. Let the angle ASC = DTF , the angle ASB DTE , and the an- gle BSC - ETF ; then ...

**solid angles**are contained by three plane angles , respectively equal to each other , and if 140 GEOMETRY .### 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