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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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## Considerations on the Suggestions of the University Commissioners with ...

Henry Latham - 1857 - 390 Seiten
...7. Give Dcf. 5, Book V. of Euclid, and shew whether the areas 3, 4, 7, 8 are proportionals. Similar triangles are to one another in the duplicate ratio of their homologous sides. Shew how to inscribe a rectangle DEFG in a triangle ABC, so that the angles D, E may be in the...
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## Some account of the origin and objects of the new Oxford examinations for ...

sir Thomas Dyke Acland (11th bart.) - 1858 - 270 Seiten
...algebraical expression for the mean proportional between two given quantities ? 19. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 20. Show that, if an equilateral triangle be inscribed in a circle, the square of its side is...
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## A Treatise on Practical Mensuration

Anthony Nesbit - 1859 - 494 Seiten
...the triangle ABC is to the 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. B VI. 19. Simp. IV. 24. Em. II. 18.) THEOREM XIV. In any triangle the double of the square...
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## Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 672 Seiten
...speed does each man walk \ Voluntary Portion. 1. Define in Euclid's manner duplicate ratio. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Define parallel straight lines. If two straight lines be parallel, the straight line drawn...
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## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 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, D.EFbe similar triangles, having the angle B equal to the angle E, and let AB be to...
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## REPORT OF THE DIRECTOR OF PUBLIC INSTRUCTION, BOMBAY, FOR THE YEAR 1858-59.

EDUCATION SOCIETY'S PRESS, CULLA - 1860 - 608 Seiten
...the fourth ? The sides about the equal angles of equiangular triangles are proportionals. 12. Similar triangles are to one another in the duplicate ratio of their homologous sides. LOGIC. I.—LOWER STANDARD. What ii the use of words ? Explain First and Second Intention. 2....
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## Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ...

Euclides - 1861 - 464 Seiten
...Plans, Maps, and Geometrical Drawings of every kind. PROP. 19. — THEOR. (Very important.) Similar triangles are to one another in the duplicate ratio of their homologous sides ; ie, as the squares of their like sides. CON. 11, VI. DEM. Def. 12, V.— 16, V. If four Ms...
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## Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 Seiten
...than a semicircle is greater than a right angle. 10 DIRECT COMMISSIONS. VOLUNTAKY PORTION. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Describe a rectilineal figure which shall be similar to one given rectilineal figure and...
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## Papers Read at the Royal Institute of British Architects

1863 - 302 Seiten
...equal parts how a rule of three sum may be solved geometrically. 9. Proposition 19. Theorem. Similar triangles are to one another in the duplicate ratio of their homologous sides. J 0. If the superficial content of a triangle which has a base of 40 feet is 800 feet, what...
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## Wisconsin Journal of Education, Band 7

1863 - 406 Seiten
...9=42 or £ the triangle ABC. I should mention 2 to draw ox parallel to BG. Now we know that similar triangles are to one another in the duplicate ratio of their homologous sides . • . BGC : oxC::BGa : ox', or 47.04 : 42::11.2" : 112 the square root of which is 10.583+=ox,...
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