 | Joseph Denison - Mechanics - 1841 - 210 pages
...lines are to each other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) similar triangles are to one another in the duplicate ratio of their homologous sides, therefore, (5 Euclid, 11.) the simi-lar triangles are to one another as the squares of their homologous... | |
 | Joseph Denison - Mechanics - 1841 - 210 pages
...lines are to each other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) similar triangles are to one another in the duplicate ratio of their homologous sides, therefore, (5 Euclid, 11.) the similar triangles are to one another as the squares of their homologous... | |
 | Euclides - Geometry - 1841 - 378 pages
...sides, and it has already been proved* in 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 * 11. 6. sides, a third* proportional M be taken, AB... | |
 | Euclides - 1842 - 316 pages
...proportionals, they are similar to one another ; and in the same manner a rectilineal figure of six or more sides may be described upon a given straight line similar to one given, and so on. QEF PROP. XIX. THEOR. SIMILAR triangles are to one another in the duplicate ratio of their homologous... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...proportionals, they are similar to one another ; and in the same manner a rectilineal figure of six, or more, sides may be described upon a given straight line similar to one given, and so on. PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of the homologous sides.... | |
 | William Pease - Geometry - 1843 - 80 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... | |
 | Church schools - 1844 - 456 pages
...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... | |
 | Education - 1844 - 688 pages
...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.... | |
 | Euclid - Geometry - 1845 - 218 pages
...proportionals, they are similar to one another : and in the same manner a rectilineal figure of six or more sides may be described upon a 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... | |
 | Euclides - 1845 - 546 pages
...angles proportionals, they are similar to one another. In the same manner a rectilineal figure of six sides may be 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... | |
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SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 
