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 20
... THEOREM IX . If two straight lines have two points common they will coin- cide throughout their whole extent . If A and B are points common to two straight lines , they will coincide between A and B ( A. XIII . ) . F E A B D If possible ...
... THEOREM IX . If two straight lines have two points common they will coin- cide throughout their whole extent . If A and B are points common to two straight lines , they will coincide between A and B ( A. XIII . ) . F E A B D If possible ...
Page 21
... THEOREM XII . If from a point without a line , a perpendicular be drawn , and several oblique lines : I. The perpendicular will be shorter than any oblique line . II . Any two oblique lines which terminate at equal distances from the ...
... THEOREM XII . If from a point without a line , a perpendicular be drawn , and several oblique lines : I. The perpendicular will be shorter than any oblique line . II . Any two oblique lines which terminate at equal distances from the ...
Page 23
... THEOREM XIV . If a line be drawn bisecting a given angle , that is , dividing it into two equal angles : I. Any point in this bisecting line will be equidistant from the sides of the angle . II . Any point without this bisecting line ...
... THEOREM XIV . If a line be drawn bisecting a given angle , that is , dividing it into two equal angles : I. Any point in this bisecting line will be equidistant from the sides of the angle . II . Any point without this bisecting line ...
Page 24
... THEOREM XV . When two lines are perpendicular to the same line , they are parallel . If the lines AB and CD are perpendic- G ular to GH they will be parallel . E A B For , since they are perpendicular to GH , we have the angles BEG and ...
... THEOREM XV . When two lines are perpendicular to the same line , they are parallel . If the lines AB and CD are perpendic- G ular to GH they will be parallel . E A B For , since they are perpendicular to GH , we have the angles BEG and ...
Page 26
... Theorem itself , hence AB and CD are parallel . Secondly . Suppose AGI = GHD . We have AGH = EGB ( T. I. ) , consequently EGB = GHD ; that is , the lines AB and CD have the same direction , and are therefore parallel . Thirdly . Suppose ...
... Theorem itself , hence AB and CD are parallel . Secondly . Suppose AGI = GHD . We have AGH = EGB ( T. I. ) , consequently EGB = GHD ; that is , the lines AB and CD have the same direction , and are therefore parallel . Thirdly . Suppose ...
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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