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" Similar triangles are to one another in the duplicate ratio of their homologous sides. "
Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ... - Page 95
by John Mason Good - 1813
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 317 pages
...the same has already been proved of 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, a third proportional M be taken, AB has (def....
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A course of practical geometry for mechanics

William Pease - Geometry - 1843 - 68 pages
...similar polygon, equal to the sum of the given polygons. For, " universally, similar'rectilineal figures are to one another in the duplicate ratio of their homologous sides." Duplicate ratio is the ratio of the square of one quantity to the square of another. EXAMPLES. 1. Make...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844
...and u the distance of A" from K. FRIDAY, Jan. 5. 9. ..ll£ SENIOR MODERATOR AND JUNIOR EXAMINER. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. Every solid angle is contained by plane angles which are together less than four right angles. 3....
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Report to the Trustees of the Dick Bequest for the Benefit of the ..., Volume 2

Church schools - 1844
...that their common chord will be bisected at right angles by a straight line joining their centres. 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. 5. About the centre of a given circle describe another circle, equal in area to half the former. TRIGONOMETRY...
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845
...are the doubles of equiangular triangles. PROPOSITION LXXI THEOREM. Similar polygons ABODE, FGHIK, may be divided „ into the same number of similar triangles, having the same ratio that the polygons have ; and the polygons are to one another as the squares of their corresponding...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...given straight line similar to one given, and so on. Which was to be done. PROPOSITION 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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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...easiest methods, however, of performing this and many other problems, the student 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 angles B and E equal, and AB : BC : : DE : EF, so that...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION XIX. THEOREM. 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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Commentaries on the Principia of sir Isaac Newton respecting his theory ...

Joseph Denison - 1846
...ultimately become similar, and consequently the approximating sides homologous, and (6 Euclid 19) because similar triangles are to one another in the duplicate ratio of their homologous sides; the evanescent triangles are in the duplicate ratio of the homologous sides; and this seems the proper...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...similar, and similarly situated, to a given rectilineal figure of six sides ; &c. QEF PROP. XIX. THEOB. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles, having the angle at B equal to the angle at E, and let AB be to...
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