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" SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Side 165
av Euclides - 1814
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid, Edmund Stone - 1765 - 464 sider
...all equilateral and equiangular figures are alike deferred upon any right lines. PROP. XIX. THE OR, Similar triangles are to one another in the duplicate ratio of their homologous fides. Let the trianges A B. c, DEF be fimilar, having the angle B equal to the angled ; and let AB...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 sider
...a given ftraight line li« milar to one given, and- fo on. Which was to be done. PROP. XIX. THEO R. SIMILAR triangles are to one another in the duplicate ratio of their homologous ftdes. Let ABC, DEF be fimilar triangles having the angle B equal to the angle E, and let AB be to...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 sider
...upon a given ftraight line ;.milar to one given, and fo ou. Which was to be doue. PROP. XIX. THEO R. SIMILAR triangles are to one another in the duplicate ratio of their homologous fides. Let ABC, DEF be fimilar triangles, having the angle B equal to the angle E, and let AB he to...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - 1795 - 400 sider
...given ftraight line fimilar tct one given, and fo on. Which was to be done. S PROP. XIX. THEO R. IMILAR triangles are to one another in the duplicate ratio of their homologous fides. Let ABC, DEF be fimilar triangles, having the nngle B equal to the angle E, and let AB be to...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 sider
...fimilar to CDKFE : and fo on. Which was to be done. PROP. BooK V|. PROP. XIX. THEOR. V>rv-vJ IMILAR triangles are to one another in the duplicate ratio of their homologous fides. Let ABC, DEF be fimilar triangles, having the angle B equal to the angle E, and let AB be to...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 sider
...therefore they are similar to each other. In the same manner a rectilineal figure of six, or more, sides may be described upon a given straight line similar to one given. Which was to be done. PROP. XIX. THEOR. SIMILAR triangles are to one another in the duplicate ratio...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volum 5

John Mason Good - 1813
...rectilineal figure similar, and similarly situated to a given rectilineal figure. Prop. XIX. Tbeor. 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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The Eclectic review. vol. 1-New [8th], Volum 1

1814
...though he should have met it before. The demonstration of the 19tb Prop, of Euclid's 6th book, ie " Similar triangles are to one another in the duplicate ratio of their homologous sides," requires the previous or the syn hro nous establishment of Props, vi. 11, v. 16, v. 11, vi. 15., and...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...sides, and it has already been proved in triangles. 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, k 10 Def. 5. a third proportional M be taken,...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 sider
...a rectilineal figure of six, or more, sides may be described upon a given straight line similar Co one given, and so on. Which was to be done. ^ PROP....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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