Elements of Geometry and Trigonometry: With Practical ApplicationsR.S. Davis & Company, 1869 - 382 pages |
From inside the book
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Page 29
... hypothenuse and a side of the one equal to the hypothenuse and a side of the other , each to each , the triangles are equal . Let the two right - an- A gled triangles ABC , DEF , have the hypothenuse A C equal to D F , and the side AB ...
... hypothenuse and a side of the one equal to the hypothenuse and a side of the other , each to each , the triangles are equal . Let the two right - an- A gled triangles ABC , DEF , have the hypothenuse A C equal to D F , and the side AB ...
Page 63
... hypothenuses CA , CD are equal ; and the side A F , the half of A B , is equal to the side D G , the half of DE ; therefore the triangles are equal , and CF is equal to CG ( Prop . XIX . Bk . I. ) ; hence the two equal chords AB , DE ...
... hypothenuses CA , CD are equal ; and the side A F , the half of A B , is equal to the side D G , the half of DE ; therefore the triangles are equal , and CF is equal to CG ( Prop . XIX . Bk . I. ) ; hence the two equal chords AB , DE ...
Page 87
... hypothenuse of a right - angled triangle is equivalent to the sum of the squares described on the other two sides . Let ABC be a right - angled triangle , having the right angle at A ; then the square described H on the hypothenuse BC ...
... hypothenuse of a right - angled triangle is equivalent to the sum of the squares described on the other two sides . Let ABC be a right - angled triangle , having the right angle at A ; then the square described H on the hypothenuse BC ...
Page 88
... hypothenuse , is equivalent to the sum of the squares A BHL , ACIK , described on the two other sides ; that is , B ... hypothenuse diminished by the square of the other side ; thus , A B is equivalent to B C2 ― A C2 . 239. Cor . 2. The ...
... hypothenuse , is equivalent to the sum of the squares A BHL , ACIK , described on the two other sides ; that is , B ... hypothenuse diminished by the square of the other side ; thus , A B is equivalent to B C2 ― A C2 . 239. Cor . 2. The ...
Page 89
... hypothenuse , the squares of the sides about the right angle will be to each other as the adjacent segments of the hypothenuse . For the rec- tangles BDEF , DCGE , having the same altitude , are to each other as their bases , BD , CD ...
... hypothenuse , the squares of the sides about the right angle will be to each other as the adjacent segments of the hypothenuse . For the rec- tangles BDEF , DCGE , having the same altitude , are to each other as their bases , BD , CD ...
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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'.