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Książki Książki 2130 z 192 na temat Similar triangles are to one another in the duplicate ratio of their homologous sides..
" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
Reports on Elementary schools - Strona 766
autor: Her MAjesty' Inspectors of schools - 1850
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - Liczba stron: 324
...: and it has already been proved in triangles : therefore, universally, similar rectilinear figures are to one another in the duplicate ratio of their homologous sides. (629) COR. 2. — And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB...
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Elements of geometry: Being chiefly a selection from Playfair's geometry

John Playfair - 1829 - Liczba stron: 186
...other as the rectangles contained by the sides about the equal angles. .• PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be two similar triangles, having the angles at A and D equal; and let AC : AB : : DF :...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - Liczba stron: 272
...will be be reciprocally proportional ; 39, being cited instead of 35. Therefore, &c. PROP. 42. (Eue. vi. 19.) Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, and let the sides В С, EF be homologous ; the triangle ABC shall...
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University of Cambridge - 1830
...in origin and intensity. SATURDAY MORNING .... 9 to 11. First, Second, Third and Fourth Classes. 1. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 2. If two straight lines meeting one another, be parallel to two straight lines which meet one another,...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Euclid, Robert Simson - 1835 - Liczba stron: 513
...upon a 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 BC, as...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...reciprocally proportional; ЗУ. being citc'd instead of 35. Therefore, &c. • PROP. 42. (Eue. vi. 10.) Similar triangles are to one another in the duplicate ratio of their homologous sides. LetABC.DEF be similar triangles, and let the sides В С, EF be homologous ; the triangle ABC shall...
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The Element of Geometry

John Playfair - 1836 - Liczba stron: 114
...upon a 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 BC, as...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - Liczba stron: 472
...by the 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 is to...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - Liczba stron: 240
...be 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 BC, as...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - Liczba stron: 390
...described 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, so that...
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