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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ... - Page 117
by Thomas Gaskin - 1847 - 263 pages
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...Of similar triangles, having the same ratio to one another that the polygons have; and the polygons are to one another in the duplicate ratio of their homologous sides. Let ABCDE, FGHKL be similar polygons, and let AB be the side homologous to the side FG : the polygons...
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How I rose in the world, Volume 1; Volume 14

How - 1868 - 296 pages
...English, Latin, and Greek tongues, and understood (what few lads of my age then understood) , that ' similar triangles are to one another in the duplicate ratio of their homologous sides." In a word, then, I was something of a scholar, and I may well be forgiven if I were a little proud...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION XIX. THEOREM. 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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Report of the commissioners, Volume 6

Schools inquiry commission - Education - 1868 - 532 pages
...inscribed in a circle is equal to the interior and opposite. 7. Describe a circle about a given square. 8. Similar triangles are to one another in the duplicate ratio of their homologous sides. XIX. (Two hours.) Maximum. 1. Translate into French : — Two worthy peasants went together to find...
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Modern Methods in Elementary Geometry

E. M. Reynolds - Geometry - 1868 - 172 pages
...the second. The proof we leave as an exercise for the learner. The proposition that " Similar figures are to one another in the duplicate ratio of their homologous sides " is true of curvilinear figures as well as of rectilinear. Thus two circles are to one another as...
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Nature, Volume 69

Sir Norman Lockyer - Electronic journals - 1904 - 688 pages
...furnished by the liberty which each of these excellent works takes with Euclid's Prop, ig, Bk. vi.- — " similar triangles are to one another in the duplicate ratio of their homologous sides " — mysterious but high-sounding- to countless generations of schoolboys. Here it is, in identical...
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A Treatise on Land Surveying in Theory and Practice ...

John A. Smith - 1869 - 368 pages
...Perpendiculars. 10 22384 to be deducted. Donble areas. 1500 1500 19520 21020 map. As the areas of similar figures are to one another in the duplicate ratio of their homologous sides, we have A : a; IS J : s*. From this proportion we obtain— , jlx* jo /-4V *= , and S=s I — ] ....
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A complete treatise on practical land-surveying

Anthony Nesbit - 1870 - 578 pages
...; then the triangle ABC is to the A triangle ADE as the square of BC to the square of DE. That is, similar triangles are to one another in the duplicate ratio of their homologous sides (Euc. vi. 19 ; Simp, c^ iv. 24; Em. ii. 18). THEOREM XIV. In any triangle ABC, double the square of...
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The Edinburgh university calendar

Edinburgh univ - 1871 - 392 pages
...the part of it without the circle, is equal to the square of the line which touches it. 6. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. Given (b) the base of a triangle, find an expression for the base of a similar triangle whose area...
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How to Prepare for Civil Service Competition, Under the New Regulations

Patrick Weston Joyce - Civil service - 1871 - 170 pages
...twice the rectangle contained by the parts. 2. Deseribe a regular pentagon about a given cirele. 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. If perpendiculars Aa, B&, Cc, be drawn from the angular points of a triangle ALC upon the opposite...
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