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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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...straight line similar to one given, and so on. Which was to be done. 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 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 - 1819 - 333 sider
...the same has already been proved of triangles : therefore, universally similar rectilineal figuree are to one another in the duplicate ratio of their...sides. COR. 2. And if to AB, FG, two of the homologous sidei, a third proportional M be taken, AB has (def. 11. 5.) to M the duplicate ratio of that which...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 sider
...straight line similar Co one given, and so on. Which was to be done. ^ PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. D Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC,...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821
...proportionality of the sides about 'the «£^.s composing them. 52 PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. Assume on the greater base from either extremity a third proportional to that base and the homologous...
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A treatise of practical mensuration

Anthony Nesbit - 1824 - 434 sider
...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
...Coa. 1. In like manner, it may Le proved, that p-milar four sided figures, or of any number of suies, are one to another in the duplicate ratio of their...2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has ( 10. de', i.) to II the duplicate ratio ofthat which AB has...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 sider
...duplicate ratio of their homologous sides ; and it has been already proved in triangles. Wherefore universally similar rectilineal figures are to one...in the duplicate ratio of their homologous sides. QB p. 2. And if to AB, FG, we take a third proportional x ; AB has to xa duplicate ratio of that which...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...second. duplicate ratio of their homologous sides; and it has been already proved in triangles. Wherefore universally similar rectilineal figures are to one...in the duplicate ratio of their homologous sides. QEF Deduction. Any regular polygon inscribed in a circle, is a mean proportional between the inscribed...
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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 • of their homologous sides. Let ABC, DEF, be similar triangles, having the angle B equal to the angle E, and let AB : BC : : DE...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...to be done. • 12 Def. •11.6. * 16. 5. t Co1utr. • 11. 5. 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 angle B equal to the angle E, and let AB be to BC, as...
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