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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
Elements of Arithmetic, Algebra, and Geometry - Strona 172
autor: George Lees - 1826
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Euclid's Elements of Geometry,: From the Latin Translation of Commandine. To ...

Euclid, John Keill - 1733 - Liczba stron: 393
...Similar "Triangles are in the duplicate Ft ofortion of their homologous Sides. LET ABC, DEF, be fimilar Triangles, having the Angle B equal to the Angle E ; and let AB be to BC as DE is to EF, fo that BC be the Side homologous to £ F. I fay, the Triangle ABC, to the...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - Liczba stron: 466
...given ftraight line fimilar to one given, and fo on. Which was to tx? done. PROP. XIX. THE OR. xiiLAR triangles are to one another in the duplicate ratio of their homologous fides. Let ABC, DEF be fimilar triangles having the angle B equal to the angle E, and let AB be to...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid - 1765 - Liczba stron: 464
...equilateral and equiangular figures are alike deferred upon any right lines. PROP. XIX. THE OR, Similar triangles are to one another in the duplicate ratio of their homologous fides. Let the trianges A B. c, DEF be fimilar, having the angle B equal to the angled ; and let AB...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - Liczba stron: 520
...ftraight line li« milar to one given, and- fo on. Which was to be done. PROP. XIX. THEO R. SIMILAR triangles are to one another in the duplicate ratio of their homologous ftdes. Let ABC, DEF be fimilar triangles having the angle B equal to the angle E, and let AB be to...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - Liczba stron: 520
...given ftraight line ;.milar to one given, and fo ou. Which was to be doue. PROP. XIX. THEO R. SIMILAR triangles are to one another in the duplicate ratio of their homologous fides. Let ABC, DEF be fimilar triangles, having the angle B equal to the angle E, and let AB he to...
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Euclid's Elements of Geometry: From the Latin Translation of Commandine, to ...

John Keill - 1782 - Liczba stron: 399
...Similar Triangles are in the duplicate Proportion of their homologous Sides. LET ABC, DEF, be fimilar Triangles" having the Angle B equal to the Angle E ; and let AB be to BC, as DE is to EF, fo that BC he the Side homologous to E F. I fay, the Triangle ABC, to the...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - 1795 - Liczba stron: 400
...given ftraight line fimilar tct one given, and fo on. Which was to be done. S PROP. XIX. THEO R. IMILAR triangles are to one another in the duplicate ratio of their homologous fides. Let ABC, DEF be fimilar triangles, having the nngle B equal to the angle E, and let AB be to...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - Liczba stron: 351
...fimilar to CDKFE : and fo on. Which was to be done. PROP. BooK V|. PROP. XIX. THEOR. V>rv-vJ IMILAR triangles are to one another in the duplicate ratio of their homologous fides. Let ABC, DEF be fimilar triangles, having the angle B equal to the angle E, and let AB be to...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1806 - Liczba stron: 518
...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 - Liczba stron: 311
...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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