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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
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## The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 Seiten
...upon a given straight line similar to one given, and so on. QE r. 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...
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## Calendar of the McGill University, Montreal

McGill University - 1865 - 332 Seiten
...and show that it agrees with Euclid's. 9. Find a third proportional to two given lines. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. If 3 men can mow 7 acres of grass in 5 days of 9 hours each, in how many days of 8 hours...
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## A Rudimentary Treatise on Land and Engineering Surveying, with all the ...

Thomas Baker (Civil engineer) - 1865 - 278 Seiten
...triangle ABC is to the triangle AED as the square of AB is to I lie. square of AE : that is, similar triangles are to one another in the duplicate ratio of their homologous sides. (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of their...
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## The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 Seiten
...described upon a given straight line similar to one given, and so on. QEF PROP. XIX.— THEOBEM. Similar triangles are to one another in the duplicate ratio of their homologous sides. (References— Prop. v. 11, 16, def. 12; vi. 1, 11, 15.) Let ABC, DEF be similar triangles,...
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## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 Seiten
...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 bo to...
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## A collection of elementary test questions in pure and mixed mathematics ...

James Robert Christie - 1866 - 426 Seiten
...with the segmenta of the former will be equal to the square of the radius of the circle. i 3. Similar triangles are to one another in the duplicate ratio of their homologous sides. 4. If two straight lines be at right angles to the same plane, they shall be parallel to one...
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## How I rose in the world, Band 1;Band 14

How - 1868 - 296 Seiten
...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...
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## Report of the commissioners, Band 6

Schools inquiry commission - 1868 - 532 Seiten
...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...
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## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 Seiten
...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...
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## Nature, Band 69

Sir Norman Lockyer - 1904 - 688 Seiten
...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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