Schultze and Sevenoak's Plane and Solid Geometry |
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Page 151
... proportional between the first and the last terms , and the last term is said to be the third proportional to the first and the second terms . Thus , in the proportion , a : b = b : c , b is the mean proportional be- tween a and c , and ...
... proportional between the first and the last terms , and the last term is said to be the third proportional to the first and the second terms . Thus , in the proportion , a : b = b : c , b is the mean proportional be- tween a and c , and ...
Page 152
... proportional to Ex . 762. Find the third proportional to ( c ) x : 72 : 21 , ( d ) a : m = x : n . ( b ) 2 , 1 , and 3 , ( c ) m , n , and p . ( a ) 9 and 12 , ( b ) 14 and 21 , ( c ) 1 and a . PROPOSITION II . THEOREM 279. If the ...
... proportional to Ex . 762. Find the third proportional to ( c ) x : 72 : 21 , ( d ) a : m = x : n . ( b ) 2 , 1 , and 3 , ( c ) m , n , and p . ( a ) 9 and 12 , ( b ) 14 and 21 , ( c ) 1 and a . PROPOSITION II . THEOREM 279. If the ...
Page 153
... proportional between two quantities is equal to the square root of their product . Given To prove Proof . a : b = b : c . b = Vac . a : b = b : c . .. b2 = ac . Extracting the square root of both members b = √ac . Ex . 767. Find the ...
... proportional between two quantities is equal to the square root of their product . Given To prove Proof . a : b = b : c . b = Vac . a : b = b : c . .. b2 = ac . Extracting the square root of both members b = √ac . Ex . 767. Find the ...
Page 159
... Thus AB is divided internally , A'B ' externally . The segments of AB are AC and BC . The segments of A'B ' are A'C ' and B'C ' . A Α ' B ' PROPORTIONAL LINES PROPOSITION XIII . THEOREM * 293. A line PROPORTION . 159 SIMILAR POLYGONS.
... Thus AB is divided internally , A'B ' externally . The segments of AB are AC and BC . The segments of A'B ' are A'C ' and B'C ' . A Α ' B ' PROPORTIONAL LINES PROPOSITION XIII . THEOREM * 293. A line PROPORTION . 159 SIMILAR POLYGONS.
Page 160
Arthur Schultze, Frank Louis Sevenoak. PROPORTIONAL LINES PROPOSITION XIII . THEOREM * 293. A line parallel to one side of a triangle divides the other two sides proportionally . E Given in △ ABC , DE parallel to BC . To prove AD : DB ...
Arthur Schultze, Frank Louis Sevenoak. PROPORTIONAL LINES PROPOSITION XIII . THEOREM * 293. A line parallel to one side of a triangle divides the other two sides proportionally . E Given in △ ABC , DE parallel to BC . To prove AD : DB ...
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Common terms and phrases
altitude angle equal angle formed angles are equal annexed diagram bisect bisector chord circumference circumscribed congruent cylinder diagonals diagram for Prop diameter dihedral angles divide draw drawn equiangular polygon equilateral triangle equivalent exterior angle face angles Find the area Find the radius Find the volume frustum given circle given line given point given triangle Hence HINT homologous hypotenuse inscribed intersecting isosceles triangle lateral area lateral edge line joining locus median parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle polyhedron prism PROPOSITION prove Proof pyramid Q. E. D. Ex quadrilateral radii ratio rectangle reflex angle regular polygon respectively equal rhombus right angles right triangle segments sphere spherical polygon spherical triangle square straight line surface tangent THEOREM trapezoid triangle ABC triangle are equal trihedral vertex angle vertices
Popular passages
Page 222 - Two triangles having 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.
Page 208 - The area of a rectangle is equal to the product of its base and altitude.
Page 183 - If two chords intersect in a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 160 - A line parallel to one side of a triangle divides the other two sides proportionally.
Page 82 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.
Page 70 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 188 - Pythagorean theorem, which states that the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse.
Page 409 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...
Page 333 - The sum of any two face angles of a trihedral angle is greater than the third face angle.
Page 193 - 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.