A Treatise on Special Or Elementary GeometrySheldon, 1872 - 201 pages |
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Page 39
... homologous ( correspond- ing ) sides proportional . * Be careful to distinguish between the vertex , which is a point , and the angle , which is the opening between the lines . 88. Homologous , or Corresponding Sides of similar figures ...
... homologous ( correspond- ing ) sides proportional . * Be careful to distinguish between the vertex , which is a point , and the angle , which is the opening between the lines . 88. Homologous , or Corresponding Sides of similar figures ...
Page 40
... homologous with e , since they are opposite the equal angles B and E. For a like reason a is homologous with d , and c with f . It may also be observed , that the shortest sides in two similar triangles are homologous with each other ...
... homologous with e , since they are opposite the equal angles B and E. For a like reason a is homologous with d , and c with f . It may also be observed , that the shortest sides in two similar triangles are homologous with each other ...
Page 42
... homologous to BC equal to a . I draw an indefinite line , and on it take EF , equal to a . Then at F I make an angle ... homologous sides . In the figure D is made equal to C , and ♬ to A ; whence E = B. DE and BC are homologous sides ...
... homologous to BC equal to a . I draw an indefinite line , and on it take EF , equal to a . Then at F I make an angle ... homologous sides . In the figure D is made equal to C , and ♬ to A ; whence E = B. DE and BC are homologous sides ...
Page 43
... homologous with AB . Now , taking two sides of ABC , as BC and AB , and a side of DEF homologous with one of them , as DE , and finding a fourth proportional Oc , it will be found exactly equal to EF ; so that 1 BC : DE :: AB : EF ...
... homologous with AB . Now , taking two sides of ABC , as BC and AB , and a side of DEF homologous with one of them , as DE , and finding a fourth proportional Oc , it will be found exactly equal to EF ; so that 1 BC : DE :: AB : EF ...
Page 52
... homologous sides . C A D FIG . 92 . B ILL . The meaning of this is , that if ABC and DEF are similar , and any side of ABC is 2 times as great as the homologous side of DEF ( as is the case in the figure , CB being 2FE , CA to 2FD and ...
... homologous sides . C A D FIG . 92 . B ILL . The meaning of this is , that if ABC and DEF are similar , and any side of ABC is 2 times as great as the homologous side of DEF ( as is the case in the figure , CB being 2FE , CA to 2FD and ...
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Common terms and phrases
ABCD adjacent adjacent angles altitude angles equal apothem axis base and altitude bisect centre chord circle whose radius circumference coincide conceive cone cylinder DEM.-If diagonals diameter dicular diedral distance dividers draw drawn edge equal angles equally distant equilateral equivalent exterior angle facial angles fall figure frustum given line given point greater Hence homologous sides inches included angle inscribed inscribed angle intersect isosceles lune measured number of sides oblique lines opposite parallel parallelogram parallelopiped passing pendicular perpen perpendicular plane MN prism Prob Prob.-To produced PROP proportional pyramid Q. E. D. PROPOSITION quadrilateral radii rectangle regular polygon revolve right angled triangle S-ABC secant secant line similar slant height sphere spherical angle spherical triangle square straight line take the direction tangent Theorem.-The area triangle ABC triedral vertex vertices whence
Popular passages
Page 217 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 109 - If the diagonals of a parallelogram are equal, the figure is a rectangle.
Page 72 - Dn the same side of the secant line is equal to two right angles, the two lines are parallel.
Page 33 - ... two, or equal to the difference ? Ex. 5. If you have two triangles with only one side and one angle in the one equal to one Side and one angle in the other, can y^ou apply one as a pattern and make it fit on the other ? Cut out two such triangles and try it. Ex. 6. If you have two triangles with only two sides of one respectively equal to two sides of the other, can you make one fit as a pattern on the other ? Try it. Ex. 7. If you have two triangles with two sides in one equal respectively to...
Page 136 - Theorem — Two triangles are equal when the three sides of the one are respectively equal to the three sides of the other.
Page 125 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the third sides are unequal, and the greater third side belongs to the triangle having the greater included angle.
Page 69 - If two lines are cut by a third, and the sum of the interior angles on the same side of the cutting line is less than two right angles, the lines will meet on that side when sufficiently produced.
Page 2 - LEMMA 4. — A common divisor of two numbers is a divisor of their sum and also of their difference.