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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 167
by Euclides - 1814
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Nature, Volume 69

Sir Norman Lockyer - Electronic journals - 1904
...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
...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
...; 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
...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
...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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The Calendar of Owens college, Manchester

Manchester univ - 1872
...stand. cal angle and the segments into which the line bisecting it divides the base. 4. Similar polygons are to one another in the duplicate ratio of their homologous sides. 5. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...has been already proved for triangles, vi. 19. Therefore, universally, similar rectilinear figures are to one another in the duplicate ratio of their homologous sides. COR. II. If MN be a third proportional to AB and FG, AB has to MN the duplicate ratio of AB to FG,...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 261 pages
...AEDCB) may be divided inl similar triangles, equal in number, and homologous to all. Ana the polygons are to one another in the duplicate ratio of their homologous sides. PART 1. — Because in the triangles FGI and AED, the angles G and E are ' equal, and the sides about...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...proportionals. wherefore 10. ABLHG is similar to CDKEF. In the same manner, a rectilineal figure of six sides may be described upon a given straight line similar to one given, and so on. QEF PROPOSITION 19.— Theorem. Similar triangles are to one another in the duplicate ratio of their...
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Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874
...proportionally, this line shall be parallel to the remaining side of the triangle. 10. Define duplicate ratio. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. Define a plane. State when a straight line is perpendicular to a plane, and when two planes are...
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