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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 ... - Pągina 167
per Robert Simson - 1762 - 466 pągines
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## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841
...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...
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## A new treatise on mechanics, by the author of A new introduction to the ...

Joseph Denison - 1841
...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...
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## A new treatise on mechanics, by the author of A new introduction to the ...

Joseph Denison - 1841
...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 similar triangles are to one another as the squares of their...
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## Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...described upon a given straight line similar to one given, and so on. QEF PROP. XIX. THEOR. SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. ABC has to the triangle DEF the duplicate ratio of that which вc has to EF. Take BG a third...
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## Report to the Trustees of the Dick Bequest for the Benefit of the ..., Volum 2

1844
...common chord will be bisected at right angles by a straight line joining their centres. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. 5. About the centre of a given circle describe another circle, equal in area to half the former....
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## The British Annals of Education for ...: Being The Scholastic ..., Volum 1

1844
...the distance of A" from K. FRIDAY, Jan. 5. 9. ..ll£ SENIOR MODERATOR AND JUNIOR EXAMINER. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Every solid angle is contained by plane angles which are together less than four right angles....
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## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 pągines
...straight line similar to one given, and so on. Which was to be done. PROPOSITION 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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## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...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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## The first six and the eleventh and twelfth books of Euclid's Elements; with ...

James Thomson - 1845 - 358 pągines
...methods, however, of performing this and many other problems, the student 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, the parts read in the University of Cambridge [book ...

Euclides - 1846
...similarly situated, to a given rectilineal figure of six sides ; &c. QEF PROP. XIX. THEOB. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle at B equal to the angle at E, and let AB...
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