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" ... figures are to one another in the duplicate ratio of their homologous sides. "
Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ... - Página 129
por Euclides - 1840
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Instructions Given in the Drawing School Established by the Dublin Society ...

Joseph Fenn - 1769 - 536 páginas
...fimilarly fituated. Z>. i. B.6 • • Which was to be done. PR OP OS IT ION XIX. THEOREM XIII. IMILAR triangles (ABC, DEF) are to one another in the duplicate ratio of their homologous fides (CB, FE or AC, DF, &c). Hypothefis. • Thefis. 7be triangles ABC, DEF artßmilar. The Д ABC...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 546 páginas
...sides, and it has already been proved in triangles. Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to AB, FG, two of the homologous sides, a h 10. iU t'. third proportional M be taken,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 páginas
...COR. 1. In like manner it may be proved that similar four sided figures, or of any number of sides, are to one another in the duplicate ratio of their homologous sides ; and it has already been proved in triangles. Therefore, universally, similar rectilineal figures...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volumen5

John Mason Good - 1813 - 714 páginas
...similar, and similarly situated to a given rectilineal figure. Prop. XIX. Tbeor. 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 of similar triangles, having...
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The Eclectic review. vol. 1-New [8th], Volumen1

1814 - 760 páginas
...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 - 588 páginas
...sides, and it has already been proved in triangles. Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to AB, FG, two of the homologous sides, k 10 Def. 5. a third proportional M be taken,...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 páginas
...straight line similar Co one given, and so on. Which was to be done. ^ PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. D Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC,...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 páginas
...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 - 476 páginas
...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 - 1046 páginas
...sides, and it has already been proved in triangles Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has ( 10....
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