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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
The figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 62
by Euclides - 1840
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The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...may be described 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 ...

Mathematics - 1836 - 472 pages
...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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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...more sides may be 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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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...Therefore the triangles ABC, OEF are to each other as the squares on the homologous sides BC, EF. p.. ED PROP. XX. THEOR. Similar polygons may be divided into the same number of similar triangles, which are to each other as the polygons themselves ; and the polygons are to one another as the squares...
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Lectures Against Socialism: Delivered Under the Direction of the Committee ...

London City Mission - Christian socialism - 1840 - 620 pages
...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 alleged,...
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A new supplement to Euclid's Elements of geometry, by the author of 'A new ...

Joseph Denison - Euclid's Elements - 1840 - 96 pages
...square of b$ 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 to the...
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 194 pages
...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, as...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 pages
...similarly situated, to a given rectilineal figure of six, or any number of sides. 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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A new treatise on mechanics, by the author of A new introduction to the ...

Joseph Denison - Mechanics - 1841 - 210 pages
...lines are to each other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) similar triangles are to one another in the duplicate ratio of their homologous sides, therefore, (5 Euclid, 11.) the simi-lar triangles are to one another as the squares of their homologous...
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