Elements of Geometry, Part 1Harper & Brothers, 1896 - Geometry |
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Page 158
... square of the bisector of their included angle plus the product of the segments of the third side formed by the ... construct two straight lines having given their sum and ratio . 362. Exercise . Having given the lesser segment of a straight ...
... square of the bisector of their included angle plus the product of the segments of the third side formed by the ... construct two straight lines having given their sum and ratio . 362. Exercise . Having given the lesser segment of a straight ...
Page 159
... square in a given triangle . P A M E A B DN C F Hint . On the altitude AD construct the square ADFE and draw BE cutting the side AC at M. From M draw MN and MP parallel to EF and AE respectively . Prove these lines equal and sides of ...
... square in a given triangle . P A M E A B DN C F Hint . On the altitude AD construct the square ADFE and draw BE cutting the side AC at M. From M draw MN and MP parallel to EF and AE respectively . Prove these lines equal and sides of ...
Page 185
... CONSTRUCT a square equivalent to P + 2 . Construct a right angle A and on its sides lay off AB and AC equal respectively to the sides of Q and P. Join BC . Construct the square X having its side equal to BC . X is the required square ...
... CONSTRUCT a square equivalent to P + 2 . Construct a right angle A and on its sides lay off AB and AC equal respectively to the sides of Q and P. Join BC . Construct the square X having its side equal to BC . X is the required square ...
Page 187
... construct a line whose length is equal to any square root . Thus suppose we wish to construct a line equal to √3 inches . Lay off a , b , c , one inch each ; then AD = √3 inches . 410. ConstrUCTION . To construct a triangle equivalent ...
... construct a line whose length is equal to any square root . Thus suppose we wish to construct a line equal to √3 inches . Lay off a , b , c , one inch each ; then AD = √3 inches . 410. ConstrUCTION . To construct a triangle equivalent ...
Page 188
... construct a square which shall have a given ratio to a given square . a m n D a X E F A m B n C n GIVEN - a the side of a given square and the given ratio . m 12 TO CONSTRUCT - a square which shall have the ratio to the given m Draw the ...
... construct a square which shall have a given ratio to a given square . a m n D a X E F A m B n C n GIVEN - a the side of a given square and the given ratio . m 12 TO CONSTRUCT - a square which shall have the ratio to the given m Draw the ...
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Common terms and phrases
ABCD adjacent angles altitude angles are equal angles of parallel apothem assigned quantity bisecting centre chord circumference circumscribed circle coincide decagon diagonals diameter distance divided Draw equal circles equilateral triangle Exercise exterior angle figure Find the area GEOMETRY given circle given line given point given straight line GIVEN TO PROVE given triangle GIVEN-the Hence homologous sides hypotenuse included angle intersection isosceles triangle length line parallel lines are parallel locus mean proportional measured by arc middle points number of sides opposite sides parallel axiom parallel to BC parallelogram perimeter PLANE GEOMETRY Q. E. D. PROPOSITION quadrilateral radii ratio of similitude rectangle regular inscribed regular polygon right angles right triangle segment similar polygons straight line joining tangent THEOREM third side third straight line triangle ABC triangle whose sides triangles are equal unequal vertex vertices
Popular passages
Page 248 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Page 215 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii or as the squares of their apothems.
Page 63 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC. In BC take any point D, and join AD; and at the point A, in the straight line AD, make (I.
Page 49 - If, from a point within a triangle, two straight lines are drawn to the extremities of either side, their sum will be less than the sum of the other two sides of the triangle.
Page 148 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Page 47 - ... the third side of the first is greater than the third side of the second.
Page 149 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Page 47 - If two triangles have two sides of one equal respectively to two sides of the other...
Page 100 - At a given point in a straight line to erect a perpendicular to that line. Let AB be the straight line, and let c D be a given point in it.
Page 140 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.