Elements of Geometry and Trigonometry: With Practical ApplicationsR.S. Davis & Company, 1869 - 382 pages |
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Page 56
... radii drawn to the extremities of the arc ; as the surface included between the arc AD , and the two radii CA , CD . 160. A SECANT to a circle is a straight line which meets the cir- cumference in two points , and lies partly within and ...
... radii drawn to the extremities of the arc ; as the surface included between the arc AD , and the two radii CA , CD . 160. A SECANT to a circle is a straight line which meets the cir- cumference in two points , and lies partly within and ...
Page 58
... radii , they are equal ( Art . 155 ) ; hence , three equal straight B lines can be drawn from the same point to the same straight line , which is impossible ( Prop . XIV . Cor . 2 , Bk . I. ) . PROPOSITION III . — THEOREM . 173. In the ...
... radii , they are equal ( Art . 155 ) ; hence , three equal straight B lines can be drawn from the same point to the same straight line , which is impossible ( Prop . XIV . Cor . 2 , Bk . I. ) . PROPOSITION III . — THEOREM . 173. In the ...
Page 59
... radii CD , OG are drawn , the triangles ACD , EOG , having the three sides of the one equal to the three sides of the other , each to each , are themselves equal ( Prop . XVIII . Bk . I. ) ; therefore the angle ACD is equal to the angle ...
... radii CD , OG are drawn , the triangles ACD , EOG , having the three sides of the one equal to the three sides of the other , each to each , are themselves equal ( Prop . XVIII . Bk . I. ) ; therefore the angle ACD is equal to the angle ...
Page 60
... radii which make equal angles at the centre intercept equal arcs on the circumference ; and , conversely , if the intercepted ares are equal , the angles made by the radii are also equal . Let ACB and DCE be equal angles made by radii ...
... radii which make equal angles at the centre intercept equal arcs on the circumference ; and , conversely , if the intercepted ares are equal , the angles made by the radii are also equal . Let ACB and DCE be equal angles made by radii ...
Page 61
... radii CA and CB . Then CA and CB , with respect to the perpendicular CE , are equal oblique lines drawn to the chord AB ; 3 E therefore their extremities are at equal distances from the perpendicular ( Prop . XIV . Bk . I. ) ; hence A D ...
... radii CA and CB . Then CA and CB , with respect to the perpendicular CE , are equal oblique lines drawn to the chord AB ; 3 E therefore their extremities are at equal distances from the perpendicular ( Prop . XIV . Bk . I. ) ; hence A D ...
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Common terms and phrases
A B C ABCD adjacent angles altitude angle equal angles ACD base bisect centre chord circle circumference circumscribed cone convex surface cosec Cosine Cotang cylinder diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed frustum gles greater GREENLEAF'S half the sum hence homologous hypothenuse inches included angle inscribed isosceles less Let ABC line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon right angles right-angled triangle rods Scholium secant segment side A B similar slant height solve the triangle sphere spherical polygon spherical triangle Tang tangent triangle ABC triangle equal trigonometric functions TRIGONOMETRY vertex
Popular passages
Page 37 - 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 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Page 95 - Each side of a spherical triangle is less than the sum of the other two sides.
Page 172 - If two planes are perpendicular to each other, a straight line drawn in one of them, perpendicular to their common section, will be perpendicular to the other plane.
Page 121 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 272 - ALSO THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN...
Page 33 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Page 94 - In any quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the straight line that joins the middle points of the diagonals.
Page 102 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.