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

Joseph Denison - 1841 - 184 sider
...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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...Wherefore similar polygons, &c. QED COR. 1. In like manner it may be proved that similar figures of four, or of any number of sides, are one to another in the...in the duplicate ratio of their homologous sides. NB Squares are similar figures, and therefore they are to one another in the duplicate ratio of their...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...to another in the duplicate ratio of their homologous sides, and the same has already been proved of triangles : therefore, universally, similar rectilineal...2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (def. 11. 5.) to M the duplicate ratio of that which AB has to...
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A course of practical geometry for mechanics

William Pease - 1843 - 68 sider
...a 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 ..., Volum 2

1844
...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 ..., Volum 1

1844
...of A" from K. FRIDAY, Jan. 5. 9. ..ll£ 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's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...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. COH. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, (vi. 11.) AB...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...however, of performing this and many other problems, the student PROP. XIX. THEOR. — Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angles B and E equal, and AB : BC : : DE : EF, so that...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 sider
...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 sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 sider
...to another in the duplicate ratio of their homologous sides, and the same has already been proved of triangles : therefore, universally, similar rectilineal...2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (def. 11. 5.) to M the duplicate ratio of that which AB has to...
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