Manual of Geometry and Conic Sections: With Applications to Trigonometry and Mensuration |
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Page 29
... parallel , when they cannot meet how far soever both may be prolonged . If two lines are not parallel , they will meet if sufficiently prolonged . PROPOSITION XIX . THEOREM , If two lines are perpendicular BOOK I. 29.
... parallel , when they cannot meet how far soever both may be prolonged . If two lines are not parallel , they will meet if sufficiently prolonged . PROPOSITION XIX . THEOREM , If two lines are perpendicular BOOK I. 29.
Page 30
... parallel to each other . A Let AC and DE be perpendicular to AD . If AC and DE are not parallel , they will meet if sufficiently prolonged , and from that point we shall have two perpendicu- lars to the line AD , which is impossible ( P ...
... parallel to each other . A Let AC and DE be perpendicular to AD . If AC and DE are not parallel , they will meet if sufficiently prolonged , and from that point we shall have two perpendicu- lars to the line AD , which is impossible ( P ...
Page 31
... parallel . Let the lines AC and DE be cut by the secant PQ , making the sum of the angles EQP and QPC equal to two right angles . Through O , the middle point of PQ , draw RS perpendicular to DE . L The angle RPO is the supplement of ...
... parallel . Let the lines AC and DE be cut by the secant PQ , making the sum of the angles EQP and QPC equal to two right angles . Through O , the middle point of PQ , draw RS perpendicular to DE . L The angle RPO is the supplement of ...
Page 32
... parallel , which was to be proved . Cor . From the relations between the angles about P and Q , we infer that AC and DE are parallel : 1o . If the sum of the exterior angles on the same side is equal to two right angles ; 2 ° . If the ...
... parallel , which was to be proved . Cor . From the relations between the angles about P and Q , we infer that AC and DE are parallel : 1o . If the sum of the exterior angles on the same side is equal to two right angles ; 2 ° . If the ...
Page 33
... parallel lines are everywhere equally distant . Let AC and DE be parallel ; from any two points of AC , as P and Q , draw PR and QS perpendicular to DE ; these lines will also be perpendicular to AC , and will therefore be the distances ...
... parallel lines are everywhere equally distant . Let AC and DE be parallel ; from any two points of AC , as P and Q , draw PR and QS perpendicular to DE ; these lines will also be perpendicular to AC , and will therefore be the distances ...
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Common terms and phrases
ACD and PQR ACDE-K altitude angles are equal apothem base and altitude bisectrix bisects centre chord circle OA circumscribed coincide cone conic surface consequently corresponding Cosine Cotang curve denoted diameter distance divide draw ellipse equal to AC equally distant find the area formula frustum given line given point greater hence hyperbola hypothenuse included angle intersect lateral surface less Let ACD logarithm lower base mantissa multiplied number of sides opposite parabola parallelogram parallelopipedon perimeter perpendicular plane KL prolongation PROPOSITION proved pyramid quadrant radii radius rectangle regular inscribed regular polygon right angles right-angled triangle Scho secant segments similar slant height sphere spherical excess spherical triangle square straight line subtracting Tang tangent THEOREM transverse axis triangle ACD triangles are equal triangular prism triedral angle upper base vertex volume
Popular passages
Page 72 - In any proportion, the product of the means is equal to the product of the extremes.
Page 72 - If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.
Page 19 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.
Page 273 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 108 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 1 - O's, points or dots are introduced instead of the 0's through the rest of the line, to catch the eye, and to indicate that from thence the annexed first two figures of the Logarithm in the second column stand in the next lower line. N'.
Page 36 - The sum of the interior angles of a polygon is equal to twice as many right angles as the polygon has sides, less four right angles.
Page 104 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.
Page 36 - ... therefore the sum of the angles of all the triangles is equal to twice as many right angles as the figure has sides. But the sum of all the angles...
Page 70 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.