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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The school edition. Euclid's Elements of geometry, the first six books, by R ... - Side 271
av Euclides - 1864
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A treatise of practical mensuration

Anthony Nesbit - 1824 - 434 sider
...both ; then the triangle ABC is to the 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. IV. 24. Em. II. BC THEOREM XIV. In any triangle ABC, double the square of a line...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 sider
...upon a given straight line similar to one given, and so on. Which was to be done. PHOP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homo¡ogout sides. Let ABC, DEF be similar triangles, having the angle В equal to the angle E, and...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...triangles, &c. QED Cor. The same may be demonstrated of parallelograms. PROP. XI. THEOREM. Simi'ar triangles are to one another in the duplicate ratio...having the angle B equal to the angle E, and let AB : BC : : DE : EF, so that BC is homologous to EF ; then the triangle ABC : triangle DEF : : BC2 : EF2....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 320 sider
...so on. Whieh was to be done. PROP. XIX. THEOR. Similar triangles are to one another in the duplieate ratio of their homologous sides. Let ABC, DEF be similar...angle B equal to the angle E, and let AB be to BC, ag DE to EF, so that the side BC is homologous to EF (def. 13. 5.): the triangle ABC hag to the triangle...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 sider
...figure AH has been described similar and similarly situated to the given rectilineal figure CE. QEF PROPOSITION XIX. THEOREM. Similar triangles are to...in the duplicate ratio of their homologous sides. EF, and let BC be the side homologous to EF ; then the triangle ABC has a duplicate ratio to the triangle...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...figure CE. that at c, also the angle ABG equal to that at CDF; hence the remaining angle. AG в is QEF PROPOSITION XIX. THEOREM. Similar triangles are to...in the duplicate ratio of their homologous sides. EF, and let вс be the side homologous to EF ; then the triangle ABC has a duplicate ratio to the...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...already been proved -)- in triangles : t 19. 6. 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 sides, a third f proportional M be taken, AB* has to...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 324 sider
...: and it has already been proved in triangles : therefore, universally, similar rectilinear figures are to one another in the duplicate ratio of their homologous sides. (629) COR. 2. — And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 sider
...CoB. 1. In like manner it may be proved that similar figures of four sides, or of any number of sides, are to one another in the duplicate ratio of their homologous sides; and it has been proved in triangles. Therefore, universally, similar rectilineal figures are to one...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 sider
...with the homologous sides of the figures, are to one another, each to eich, in the same ratio. But similar triangles are to one another in the duplicate ratio of their homologous sides. Therefore the triangles into which the figure А В С DEF is divided, are to the similar triangles...
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