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" Therefore, universally, similar rectilineal figures 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 ... - Side 180
av Robert Simson - 1806 - 518 sider
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A complete treatise on practical land-surveying

Anthony Nesbit - 1870
...quantity of land by a line parallel to any one of its sides. RULE. — The areas of similar triangles are to one another in the duplicate ratio of their homologous sides ; hence, as the area of the triangle ABC is to the square of the side AC, or BC, so is the area of...
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The Edinburgh university calendar

Edinburgh univ - 1871
...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 - 1871
...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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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 sider
...described, on a given line, similar to a given fig. QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar AS, having L s at A, B, C= s.sa.tD,E,F respectively, so that BC and EF are...
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Euclid's Elements of Geometry

Euclid - 1872 - 261 sider
...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 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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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...duplicate ratio of their homologous sides ; and it has already been proved in triangles (VI. 19) ; therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides. COT. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken (VI. 11), 1....
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Plane and solid geometry, by G.E. Webster and A. Gardiner

George E. Webster - 1874
...equal, then the greatest area is possessed by the figure which has the largest number of sides. (7) Similar rectilineal figures are to one another in the duplicate* ratio of their homologous^ sides. (8) If three straight lines oe proportionals, as the first quantity is to the third quantity, so is...
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Annual Report of the Commissioners ..., Volum 40

1874
...duplicate ratio, and illustrate its meaning as you would to a class. (b.) Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Describe a circle which will pass through a given point, and touch a given circle in a given point....
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Euclidian Geometry

Francis Cuthbertson - 1874 - 349 sider
...ratio of AB to AH. Hence, proceeding as in Proposition VIII., it may be proved that Similar polygons are to one another in the duplicate ratio of their homologous sides. PROPOSITION (r). If four straight lines are proportional, the duplicate ratio of the first two is the...
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