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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
The figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 62
by Euclides - 1840
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...may be described upon a given 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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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1819 - 740 pages
...line to describe a rectilineal figure similar, and similarly situated to a given rectilineal figure. Prop. XIX. Theor. Similar triangles are to one another...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...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...may be described upon a given 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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1819 - 333 pages
...may he described upon a given straight line similar to one given, and so^ou. Which was to be done. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homOlogousjides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 pages
...*£-•& follows ex aquo, from the 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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...any triangle upon the first to a similar and similarly described triangle upon the second. PROP. T&. THEOR. 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...
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A treatise of practical mensuration

Anthony Nesbit - Measurement - 1824 - 434 pages
...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 - Mathematics - 1825 - 372 pages
...be described 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 Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 pages
...described similar and similarly situated to the given rectilineal figure CE. QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another 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 - 226 pages
...the angle ABG equal to that at CDF; hence the remaining angle. AG в is QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another 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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