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Llibres Llibres 31 - 40 de 175 sobre 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. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Pągina 167
per Robert Simson - 1762 - 466 pągines
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1836 - 471 pągines
...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...
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The Element of Geometry

John Playfair - 1836 - 114 pągines
...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...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 pągines
...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...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 pągines
...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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 390 pągines
...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,...
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The Elements of Euclid

Euclid - 1838 - 416 pągines
...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...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...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,...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...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,...
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A new supplement to Euclid's Elements of geometry, by the author of 'A new ...

Joseph Denison - 1840
...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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Lectures against socialism

London city mission - 1840
...argument nor testimony would suit the determination of such a case. If I want to determine whether similar triangles are to one another in the duplicate ratio of their homologous sides; the proper evidence will be to examine, by the powers of the mind, into the proofs which are...
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