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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 ... - Σελίδα 167
των Robert Simson - 1762 - 466 σελίδες
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## Euclid's Elements of Geometry: From the Latin Translation of Commandine. To ...

John Keill - 1723 - 444 σελίδες
...tie duplicate Proportion of their homologous Sides. 1" ET ABC, DEF, be fimilar Triangles, having -LJ the Angle B equal to the Angle E ; and let AB be to BC as DE is to EF, fo- that BC be the Side homologous to EF. I fay, the Triangle ABC, to the Triangle DEF, has...

## Euclid's Elements of Geometry,: From the Latin Translation of Commandine. To ...

Euclid, John Keill - 1733 - 444 σελίδες
...PROPOSITION XIX. THEOREM. Similar "Triangles are in the duplicate Ft ofortion of their homologous Sides. LET ABC, DEF, be fimilar Triangles, having the Angle...B equal to the Angle E ; and let AB be to BC as DE is to EF, fo that BC be the Side homologous to £ F. I fay, the Triangle ABC, to the Triangle DEF,...

## Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid - 1765 - 492 σελίδες
...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 : [by i0....

## Instructions Given in the Drawing School Established by the Dublin Society ...

Joseph Fenn - 1769 - 536 σελίδες
...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 А В...

## The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 534 σελίδες
...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...

## The Elements of Euclid,: In which the Propositions are Demonstrated in a New ...

Euclid - 1776 - 318 σελίδες
...Wherefore, &c? PROP. XIX. THEO R. O 1 MILAR triangles are to one another in the duplicate ratiQ. ^ of their homologous fides. Let ABC, DEF, be fimilar triangles having the angles at B and E equal ; and AB, to BC, as DE to EF, and BC the fide homologous to EF ; then the triangle^...

## The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 σελίδες
...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,...

## Euclid's Elements of Geometry: From the Latin Translation of Commandine, to ...

John Keill - 1782 - 476 σελίδες
...PROPOSITION XIX. THEOREM. Similar Triangles are in the duplicate Proportion of their homologous Sides. LET ABC, DEF, be fimilar Triangles" having the Angle...equal to the Angle E ; and let AB be to BC, as DE is to EF, fo that BC he the Side homologous to E F. I fay, the Triangle ABC, to the Triangle DEF, has...

## A Complete Treatise on Practical Mathematics: Including the Nature and Use ...

John McGregor (teacher of mathematics.) - 1792 - 532 σελίδες
...fide of each being rt Regular polygons of the like number of fides are fimilar, rind fimilar furfaces are to one another in the duplicate ratio of their homologous fides ; but the fides of the polygons in the foregoing table are each of them i ; therefore, as the fquare...

## Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - 1795 - 462 σελίδες
...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 be taken,...