New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |
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Page 16
... third side BC will coincide with the third side EF ( 26 , Ax . 10 ) . Hence the triangle ABC coincides with triangle DEF , and they are therefore equal ( 26 , Ax . 12 ) . 43. Cor . When , in two triangles , these three parts are equal ...
... third side BC will coincide with the third side EF ( 26 , Ax . 10 ) . Hence the triangle ABC coincides with triangle DEF , and they are therefore equal ( 26 , Ax . 12 ) . 43. Cor . When , in two triangles , these three parts are equal ...
Page 20
... third sides , CF and A C , are equal ( Theo . IV . Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken ' line ( 26 , Ax . 10 ) ; therefore AB , the half of A B F ' , is shorter than AC , the half of ACF ...
... third sides , CF and A C , are equal ( Theo . IV . Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken ' line ( 26 , Ax . 10 ) ; therefore AB , the half of A B F ' , is shorter than AC , the half of ACF ...
Page 21
... third side of that which has the greater angle will be greater than the third side of the other . Let ABC , DEF be two triangles , hav- ing the side A B equal D AA to DE , and A C equal to DF , and the angle A greater than D ; B then ...
... third side of that which has the greater angle will be greater than the third side of the other . Let ABC , DEF be two triangles , hav- ing the side A B equal D AA to DE , and A C equal to DF , and the angle A greater than D ; B then ...
Page 22
... third side of the one greater than the third side of the other , the angle contained by the sides of that which has the greater third side will be greater than the angle contained by the sides of the other . Let ABC , DEF be two ...
... third side of the one greater than the third side of the other , the angle contained by the sides of that which has the greater third side will be greater than the angle contained by the sides of the other . Let ABC , DEF be two ...
Page 28
... third will be found by subtracting that sum from two right angles . 70. Cor . 2. If two angles in one triangle be respectively equal to two angles in another , their third angles will also be equal . 71. Cor . 3. A triangle cannot have ...
... third will be found by subtracting that sum from two right angles . 70. Cor . 2. If two angles in one triangle be respectively equal to two angles in another , their third angles will also be equal . 71. Cor . 3. A triangle cannot have ...
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Common terms and phrases
A B C A B equal ABCD ABCDEF adjacent angles allel alternate angles altitude angle ACD angle BAC antecedent base multiplied bases ABC bisect chord circumference cone consequently convex surface cylinder diagonal diameter divided draw the straight equal and parallel equal angles equal bases equal Theo equiangular equivalent feet formed four right angles frustum given straight line greater Greenleaf's half the sum homologous sides hypothenuse included angle inscribed angle inscribed circle interior angles intersection Let ABC line CD magnitudes mean proportional measured by half meet number of sides opposite parallelogram parallelopipedon perimeter perpendicular polyedron prism quadrilateral radii radius ratio rectangle regular polygon rhombus right angles Theo Scholium secant line side A B side BC slant hight Solid sphere square described tangent THEOREM third triangles ABC triangular triangular prism vertex volume
Popular passages
Page 23 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 29 - 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 83 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar.
Page 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 61 - At a point in a given straight line to make an angle equal to a given angle.
Page 57 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Page 62 - 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 117 - If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel. Let...
Page 100 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Page 88 - Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.