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 Books Bücher Similar triangles are to one another in the duplicate ratio of their homologous sides. The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Seite 167
von Robert Simson - 1762 - 466 Seiten
Vollansicht - Über dieses Buch ## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 Seiten
...given straight line similar to 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. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to...
Vollansicht - Über dieses Buch ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 488 Seiten
...triangles are to one another in the duplicate ratio of their homologous sides. . Let ABC, DEF -be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as A DEtoEF,sothat the side BC is homologous to E Fa ; the triangle ABC has to the triangle DEF, the duplicate...
Vollansicht - Über dieses Buch ## The Element of Geometry

John Playfair - 1836 - 148 Seiten
...given straight line similar to 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. Let ABC, DEF be similar triangles having the angle B equal to the angle E, and let AB be to...
Vollansicht - Über dieses Buch ## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 488 Seiten
...extremes be equal to the square of the mean, the three straight lines are proportionals. XIX. Similar triangles are to one another in the duplicate ratio of their homologous sides. Сок. From this it is manifest, that if three straight lines be proportionals, as the first...
Vollansicht - Über dieses Buch ## Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 290 Seiten
...described upon a given straight line similar to one given ; and so on. PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF, he similar triangles, having the angle B equal to the angle E, and let AB be to...
Vollansicht - Über dieses Buch ## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 Seiten
...on a given straight line, similar to one given : which was to be done. * PROP. XIX. THEOR. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angles B and E equal, and AB : BC : : DE : EF,...
Vollansicht - Über dieses Buch ## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1838 - 434 Seiten
...triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BD, as DE to EF, so that the side BC is homologous to EF (12. def. 5.) ; the triangle ABC has to the...
Vollansicht - Über dieses Buch ## The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 Seiten
...rectilineal figure similar to a given rectilineal figure, and similarly situated. PROP. XIX. THEOR. 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,...
Vollansicht - Über dieses Buch ## Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 Seiten
...but ABC : CAG : : AB : AG (vi. Prop. i) ; and therefore ABC : DEF : : AB : AG, that is to say, the triangles are to one another in the duplicate ratio of their homologous sides AB, DE (v. Def. ii). COR. — Hence it is manifest that if three straight lines be proportional,...
Vollansicht - Über dieses Buch ## A new supplement to Euclid's Elements of geometry, by the author of 'A new ...

Joseph Denison - 1840 - 96 Seiten
...is to the homologous side de ; or as the square of ac is to the homologous side ae. Because similar triangles are to one another in the duplicate ratio of their homologous sides (6 Euclid, 19), the triangle ate is to the triangle abe in the duplicate ratio of the side ab...
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