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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory, and N ... - Seite 30
von John Mason Good - 1819
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 Seiten
...given ftraight line fimilar to one given, and fo on. Which was to tx? done. PROP. XIX. THE OR. xiiLAR 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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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid, Edmund Stone - 1765 - 464 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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 Seiten
...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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 Seiten
...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 Seiten
...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 of their homologous sides. Let ABC, DEF be two similar triangles, having the angle B equal to the angle E ; and let AB be to BC,...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...third, so is any triangle upon the first to a similar and similarly described triangle upon the second. PROP. XX. THEOR. SIMILAR polygons may be divided into...triangles, having the same ratio to one another that thepolygons have; and the polygons have to one another the duplicate ratio of that which their homologous...
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The Eclectic review. vol. 1-New [8th], Band 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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