Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry and Mensuration. Accompanied with All the Necessary Logarithmic and Trigonometric Tables |
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Page 12
... 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 ...
... 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
... * In the references 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 . side . 14 GEOMETRY . THEOREMS Of angles.
... * In the references 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 . side . 14 GEOMETRY . THEOREMS Of angles.
Page 15
... Scholium . Since a straight line has two different directions , exactly opposite each other , it is sometimes considered as making with itself an angle equal to two right angles . THEOREМ П. If through the vertex of any angle , lines ...
... Scholium . Since a straight line has two different directions , exactly opposite each other , it is sometimes considered as making with itself an angle equal to two right angles . THEOREМ П. If through the vertex of any angle , lines ...
Page 17
... 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 ...
... 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 22
... from the extremities of this line . Scholium . The most distant extremity A of this line will be on the side of the perpendicular opposite the point G. Cor . I. Any point equidistant from the extremities of 22 GEOMETRY .
... from the extremities of this line . Scholium . The most distant extremity A of this line will be on the side of the perpendicular opposite the point G. Cor . I. Any point equidistant from the extremities of 22 GEOMETRY .
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Common terms and phrases
ABē ABCD altitude angles equal apothem base bisecting centre chord circle circumference circumscribed circle circumscribed polygon cone consequently corresponding cosec Cosine Cotang cubic cylinder decimal denote diameter dicular distance divided draw drawn equally distant equation exterior angles feet figure frustum GEOMETRY given angle given line gives greater half hence homologous hypotenuse inches included angle intersection logarithm measure middle point multiplied number of sides opposite parallel parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedral angle polyedron prism PROBLEM proportion pyramid quadrant quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle Scholium secant similar similar triangles Sine slant height solid sphere spherical triangle square straight line subtract suppose surface Tang Tangent THEOREM three sides triangle ABC volume