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" Similar polygons may be divided into the same number of similar triangles, having the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. "
The Cambridge Examiner - Page 121
1884
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 pages
...the given figure, and similarly situated (vi.Def.i). PROP. XIX. THEOR. Similar triangles (ABC, DEF) are to one another in the duplicate ratio of their homologous sides. Let A, D be equal angles, and AB, DE homologous sides of the similar triangles ABC, DEF ; and on AB,...
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A new treatise on mechanics, by the author of A new introduction to the ...

Joseph Denison - Mechanics - 1841 - 210 pages
...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 homologous...
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A new treatise on mechanics, by the author of A new introduction to the ...

Joseph Denison - Mechanics - 1841 - 210 pages
...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 homologous...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...GN. Join BE, AM, GL, FN. And because the polygon ABCDE is similar to the polygon FGHKL, and because similar polygons may be divided into the same number of similar triangles; the triangles ABE, FGL, are similar and equiangular;* and therefore the angle * 20. 6. AEB is equal...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...triangle upon the first to a similar, and similarly described triangle upon the second. PROP. XX. THEOR. Similar polygons may be divided into the same number...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL,...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...triangle upon the first to a similar, and similarly described triangle upon the second. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Draw BE, EC, GL,...
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A course of practical geometry for mechanics

William Pease - Geometry - 1843 - 80 pages
...similar polygon, equal to the sum of the given polygons. For, " universally, similar'rectilineal figures are to one another in the duplicate ratio of their homologous sides." Duplicate ratio is the ratio of the square of one quantity to the square of another. EXAMPLES. 1. Make...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...of A" from K. FRIDAY, Jan. 5. 9. ..llĀ£ 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. 3....
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Report to the Trustees of the Dick Bequest for the Benefit of the ..., Volume 2

Church schools - 1844 - 456 pages
...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. TRIGONOMETRY...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...upon the first to a similar and similarly described triangle upon the second. PROPOSITION XX. THEOREM. Similar polygons may be divided into the same number...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL...
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