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Bøker Bok 110 av 132Similar polygons may be divided into the same number of similar triangles, having...
" Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. "
The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ... - Side 120
av Isaac Sharpless - 1879 - 266 sider
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 sider
...described triangle upon the second. For, BC : BG : : triangle ABC : triangle DEF. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number of similar...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - 518 sider
...the first to a similar, and similarly described triangle upon the second. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number of similar...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volum 5

John Mason Good - 1813
...triangles are to one another in the duplicate ratio of their homologous sides. Prop. XX. Theor. Similar polygons may be divided into the same number of similar...another that the polygons have ; and the polygons hare to one another the duplicate ratio of that which their homo, logons sides have. Prop. XXI. Theor....
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...upon the first to a similar and similarly described triangle upon the second. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number of similar...triangles, having the same ratio to one another that thepolygons have; and the polygons have to one another the duplicate ratio of that which their homologous...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...similar and similarly described triangle upon the second, PROP. XX. THEOR. SIMILAR polygons may he divided into the same number of similar triangles,...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 sider
...the first to a similar, and similarly described triangle upon the second, PROP. XX. THEOR. Similar polygons may be divided into the same number of similar...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL...
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Elements of Geometry

Adrien Marie Legendre - 1819 - 208 sider
...antecedent ABC is to its consequent FGH, or as . .'// is to FG (219). Therefore the surfaces of similar polygons are to each other, as the squares of their homologous sides. 222. Corollary. If three similar figures be constructed whose homologous sides are equal to the three...
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Dictionary of the Mathematical and Physical Sciences, According to the ...

James Mitchell - 1823 - 576 sider
...similar triangles, have their homologous sides proportional. AH similar triangles, rectangles, and polygons, are to each other as the squares of their homologous sides. HORARY Circles, hour lines or circles, marking the hours on globes, dials, &c. HORARY Motion, the motion...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 sider
...first to a similar, and similarly described triangle upon, the second. » PROP, XX. THEOR. Similar polygons may be divided into the same number of similar triangles, having the tame ratio to one another that the polygon« have ; and the polygons have to one another the duplicate...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - 1825 - 224 sider
...antecedent ABC is to its consequent FGH, or as AB is to FG (219). Therefore the surfaces of similar polygons are to each other, as the squares of their homologous sides. • 222. Corollary. If three similar figures be constructed whose homologous sides are equal to the...
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