The Principles of Elementary Algebra
The Principles of Elementary Algebra
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In our eReader you can find the full English version of the book. Read The Principles of Elementary Algebra Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book 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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