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Similar triangles 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 ... - Seite 167
von Robert Simson - 1762 - 466 Seiten
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## The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 374 Seiten
...fides ; and it has already been proved in triangles. Therefore, univerfally fimilar rectilineal figures are to one another in the duplicate ratio of their homologous fides. CoR 2. And if to AB, FG, two of the homologous fides, hio-Def.5. a third proportional M be taken, AB...
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## Elements of Geometry;: Containing the First Six Books of Euclid, with a ...

John Playfair, Euclid - 1804 - 468 Seiten
...given flraight line fimilar to one given, »nd fo on. Which was to be done. PROP. XIX. THE OR. S IMILAR triangles are to one another in the duplicate ratio of their homologous fides. D 13. def-5. Let ABC, DEF be fimilar triangles, havfng the angle B equal to the angle E, and let AB...
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## The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804 - 530 Seiten
...fides, and it has already been proved in triangles. Therefore univerfally, fimilar rectilineal figures are to one another in the duplicate ratio of their homologous fides. CoR. 2. And if to AB, FG two of the homologous fides a h.io.Def.5. third proportional M be taken, AH...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 320 Seiten
...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...
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## Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Band 5

John Mason Good - 1813 - 722 Seiten
...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,...
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## The Eclectic review. vol. 1-New [8th], Band 1

1814 - 756 Seiten
...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....
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## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 588 Seiten
...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...
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## Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 Seiten
...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...
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## The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 Seiten
...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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## A Treatise on Practical Mensuration in Eight Parts ...

Anthony Nesbit - 1824 - 476 Seiten
...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...
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