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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 28
by Euclides - 1821
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 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 - 800 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...in the duplicate ratio of their homologous sides. Prop. XX. Theor. Similar polygons may be divided into the same number of similar triangles, having...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 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 - Circle-squaring - 1819 - 350 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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A Treatise on Practical Mensuration in Eight Parts ...

Anthony Nesbit - Surveying - 1824 - 476 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 - 1046 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 - 234 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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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...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 - Trigonometry - 1827 - 546 pages
...similar to one given, and so on. Which was 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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