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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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A new treatise on mechanics, by the author of A new introduction to the ...

Joseph Denison - Mechanics - 1841 - 184 pages
...lines are 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 homologous...
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A new treatise on mechanics, by the author of A new introduction to the ...

Joseph Denison - Mechanics - 1841 - 184 pages
...lines are 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 homologous...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 351 pages
...sides, and it has already been proved* in triangles: therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to AB, FG, two of the homologous * 11. 6. sides, a third* proportional M be taken, AB...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...proportionals, they are similar to one another ; and in the same manner a rectilineal figure of six or more sides may be 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...proportionals, they are similar to one another ; and in the same manner a rectilineal figure of six, or more, sides may be described upon a given straight line similar to one given, and so on. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of the homologous sides....
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A course of practical geometry for mechanics

William Pease - Geometry - 1843 - 68 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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Report to the Trustees of the Dick Bequest for the Benefit of the ..., Volume 2

Church schools - 1844
...that their 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. TRIGONOMETRY...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844
...and u the distance of A" from K. FRIDAY, Jan. 5. 9. ..llú 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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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...proportionals, they are similar to one another : and in the same manner a rectilineal figure of six or more sides may be described upon a given 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...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...angles proportionals, they are similar to one another. 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 XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their...
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