## 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

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**scholium**is a remark on one or several preceding propositions , which tends to point out their connection , their use , their restriction , or their extension . X. An hypothesis is a supposition , made in the statement of a proposition ... Page 14

... we shall use the following abbreviations : A. for Axiom , B. for Book , C. for Corollary , D. for Definition , P. for Problem , S. for

... we shall use the following abbreviations : A. for Axiom , B. for Book , C. for Corollary , D. for Definition , P. for Problem , S. for

**Scholium**, T. for Theorem . Cor . III . And as all the angles that 14 GEOMETRY . THEOREMS Of angles. Page 17

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**Scholium**. This proposition must be restricted to the case in which the polygon is convex . A convex polygon may be de- fined to be one , such that no side , by being produced in either direction , can divide the polygon . The polygon ... Page 24

... KG , and since EF and GH are each perpendicular to CD , they must coincide , which proves them equal . = Cor . Two parallels cannot meet , however far they are pro- duced . E

... KG , and since EF and GH are each perpendicular to CD , they must coincide , which proves them equal . = Cor . Two parallels cannot meet , however far they are pro- duced . E

**Scholium**. When two parallels are cut by a 24 GEOMETRY . Page 25

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**Scholium**. When two parallels are cut by a third line , the angles formed receive particular names . WHEN TAKEN SEPARATELY : G B A H D F 1. The four angles AGF , CHE , BGF , and DHE , situated within the parallels , are called interior ...### 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