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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 Cambridge Examiner - Сторінка 123
1884
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 стор.
...described triangle upon the second. For, BC : BG : : triangle ABC : triangle DEF. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number...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 стор.
...triangle 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...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 ..., Том 5

John Mason Good - 1813
...Similar 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...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
...triangle 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...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 Eclectic review. vol. 1-New [8th]

1814
...have met it before. The demonstration of the 19tb Prop, of Euclid's 6th book, ie " Similar triangles are to one another in the duplicate ratio of their homologous sides," requires the previous or the syn hro nous establishment of Props, vi. 11, v. 16, v. 11, vi. 15., and...
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## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 стор.
...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 стор.
...triangle 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...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 geometry [Euclid book 1-3] in general terms, with ..., Частина 3

Euclides - 1821
...proportionality of the sides about 'the «£^.s composing them. 52 PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. Assume on the greater base from either extremity a third proportional to that base and the homologous...
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## A Treatise on Practical Mensuration in Eight Parts ...

Anthony Nesbit - 1824 - 434 стор.
...triangle ABC is to the triangle ADE, as the square of BC to the square of DE. That is, similar triangles are to one another in the duplicate ratio of their homologous sides. (Euc. VI. 19. Simp. IV. 24. Em. II. BC THEOREM XIV. In any triangle ABC, double the square of a line...
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## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 стор.
...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 tame ratio to one another that the polygon« have ; and the polygons have to one another the duplicate...
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