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Therefore, universally, similar rectilineal figures 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 ... - Página 180
por Robert Simson - 1806 - 518 páginas
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## Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid - 1765 - 464 páginas
...homologous fides. This has been a4fe proved of triangles, therefore univerfally fimilar right lined figures are to one another in the duplicate ratio of their homologous fides. Euclid's Elements. Book Vf. Corollary. 2. And if a third proportional x be found to AB, FG :...
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## Instructions Given in the Drawing School Established by the Dublin Society ...

Joseph Fenn - 1769
...the Jame truth bas already been proved in triangles (P 19), it is tvident universally, that fimüar rectilineal figures are to one another in the duplicate ratio of their homologous fides. Wherefore, if te AB, FG two of I be homologous fides a third proportional X be taken ; becaufe...
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## The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 páginas
...their homologous 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.dcf.i. a third proportional M be...
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## The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 550 páginas
...their homologous fides, and it has atready 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 betaken,...
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## Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - 1795 - 444 páginas
...homologous fides, and it has already been proved in triangles. Therefore, univerfaUy fimilar reftilineal 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, h 1 1. def. 5. a third proportional M...
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## The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 páginas
...their homologous 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,...
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## The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...their homologous- 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,...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 páginas
...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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## Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volumen5

John Mason Good - 1813 - 722 páginas
...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], Volumen1

1814 - 756 páginas
...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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