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" Now, since the areas of similar polygons are to each other as the squares of their homologous sides... "
First lessons in Plane Geometry. Together with an application of them to the ... - Page 129
by Francis Joseph Grund - 1830 - 12 pages
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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - Arithmetic - 1856 - 392 pages
...squares, and parallelograms are to each other as the product of their bases by their altitudes. (t.) The areas of similar polygons are to each other as the squares of their like dimensions. (.) The circumference of a circle equals very nearly 3.1416* times its...
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The Common-school Arithmetic: a Practical Treatise on the Science of Numbers

Dana Pond Colburn - 1858 - 290 pages
...the triangle MRN, figure 1, is to the area of ACB, figure 2, as MN times RS is to AB times A C. (u.) The areas of similar polygons are to each other as the squares of their like dimensions. ILLUSTRATION. — If the two triangles ABC and EFG are similar, the area...
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Arithmetic and Its Applications: Designed as a Text Book for Common Schools ...

Dana Pond Colburn - 1860 - 390 pages
...squares, and parallelograms are to each other as the product of their bases by their altitudes. (/.) The areas of similar polygons are to each other as the squares of thcir like dimensions. (.) The circumference of a circle equals very nearly 3.1416* times its...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 472 pages
...similar, (Dcf. 16, B. II). Hence the theorem; a plane passed through a pyramid, etc. Cor, 1. Since the areas of similar polygons are to each other as the squares of their homologous sides, (TU. 22, B. H), we have area abode : area ABCDE : ab 2 : AB3. But, ab :...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 514 pages
...one antecedent А В С is to its consequent FGH (Prop. XI. Bk. П.), or as A B2 is to F Ga ; hence the areas of similar polygons are to each other as the squares described on their homologous sides. 278. Cor. 1. The perimeters of similar polygons are also to each...
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Military Schools and Courses of Instruction in the Science and Art of War ...

Henry Barnard - Military education - 1862 - 399 pages
...triangle and on the hypothenuse are to each other as the adjacent segments and entire hypothenuse. The areas of similar polygons are to each other as the squares of the homologous sides of the polygons. Notions on surveying for content (arpentage}.—Method of...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 520 pages
...any one antecedent ABC is to its consequent FGH (Prop. XI. Bk. II.), or as A Ba is to F Ga ; hence the areas of similar polygons are to each other as the squares described on their homologous sides. 278. Cor. 1. The perimeters of similar polygons are also to each...
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The American Journal of Education, Volume 12

Education - 1862 - 752 pages
...triangle and on the hypothenuse are to each other as the adjacent segments and entire hypothenuse. "The areas of similar polygons are to each other as the squares of the homologous sides of the polygons. Notions on surveying for content (arpentnye). — Method of...
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Military Schools and Courses of Instruction in the Science and Art ..., Part 1

Henry Barnard - Military education - 1862 - 412 pages
...triangle and on the hynothenuHe are to each other as the adjacent segments ana entire hypothenuse. The areas of similar polygons are to each other as the squares of the homologous sides of the polygons. Notions on surveying for content (arpeniage).—Method of...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...perimeters of similar polygons are also to each other as their corresponding diagonals. 279. Cor. 2. The areas of similar polygons are to each other as the squares described on their corresponding diagonals. PROPOSITION XXXII. — THEOREM . 280. A chord in a circle...
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