The Principles of Elementary Algebra
The Principles of Elementary Algebra
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2. Similar triangles have their homologous sides pro- portional.
Ex. 1. -y/ab is linear, and denotes the side of the square whose area is equal to that of the rectangle whose sides are a and b, Ex. 2. Vabc is linear, and denotes the edge of the cube whose volume is equal to that of the cuboid of which a, &, c denote direction edges.
Ex. 3. Va^bc is an area. For it is a • Vbc, and Vftc is linear.
Ex. 4. A^bc, being of 4 dimensions, has no geometrical inter- pretation.
GEOMETRICAL INTERPKETATIONS.... 127 Ex. 5. Ah + he is the sum of two areas, and is therefore an area ; but ah -\- c has no geometrical meaning, not being homogeneous.
Ex. 6. The base of an isosceles triangle is h and its altitude is a, to find the perpendicular, ^, from a basal vertex to a side.
Let ABC be the triangle with B as vertex, D the foot of the alti- tude, and AE the required perpendicular.
Then ah = AE • BC, since each expresses double the area of the triangle.
But BDC being right-angled at Z>, BC'2 = BD'^ -{- DC^ = a'^ + ih\ .
What to read after The Principles of Elementary Algebra?
You can find similar books in the "Read Also" column, or choose other free books by N F Nathan Fellowes Dupuis to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
2. Similar triangles have their homologous sides pro- portional.
Ex. 1. -y/ab is linear, and denotes the side of the square whose area is equal to that of the rectangle whose sides are a and b, Ex. 2. Vabc is linear, and denotes the edge of the cube whose volume is equal to that of the cuboid of which a, &, c denote direction edges.
Ex. 3. Va^bc is an area. For it is a • Vbc, and Vftc is linear.
Ex. 4. A^bc, being of 4 dimensions, has no geometrical inter- pretation.
GEOMETRICAL INTERPKETATIONS.... 127 Ex. 5. Ah + he is the sum of two areas, and is therefore an area ; but ah -\- c has no geometrical meaning, not being homogeneous.
Ex. 6. The base of an isosceles triangle is h and its altitude is a, to find the perpendicular, ^, from a basal vertex to a side.
Let ABC be the triangle with B as vertex, D the foot of the alti- tude, and AE the required perpendicular.
Then ah = AE • BC, since each expresses double the area of the triangle.
But BDC being right-angled at Z>, BC'2 = BD'^ -{- DC^ = a'^ + ih\ .
What to read after The Principles of Elementary Algebra?
You can find similar books in the "Read Also" column, or choose other free books by N F Nathan Fellowes Dupuis to read onlineMoreLess
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