 | Euclides - 1838 - 264 pagina’s
...proved that similar four-sided figures, or of any number of sides, are to one another as the squares of their homologous sides : and it has already been...universally, similar rectilineal figures are to one another as the squares of their homologous sides. COR. 2. And if to AB, FG, two of the homologous sides, ,,,... | |
 | Euclides - 1840 - 82 pagina’s
...similar to a given rectilineal figure, and similarly situated. PROP. XIX. THEOR. 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, each similar... | |
 | Joseph Denison - 1840 - 96 pagina’s
...that proposition the nineteenth proposition of the sixth book of Euclid, viz. that similar triangles are to one another in the duplicate ratio of their homologous sides becomes turned into the following one, viz. that similar triangles are to one another as the squares... | |
 | London city mission - 1840 - 620 pagina’s
...testimony would suit the determination of such a case. If I want to determine whether similar triangles are to one another in the duplicate ratio of their homologous sides; the proper evidence will be to examine, by the powers of the mind, into the proofs which are alleged,... | |
 | Euclides - 1840 - 192 pagina’s
...the given figure, and similarly situated (vi.Def.i). PROP. XIX. THEOR. Similar triangles (ABC, DEF) are to one another in the duplicate ratio of their homologous sides. Let A, D be equal angles, and AB, DE homologous sides of the similar triangles ABC, DEF ; and on AB,... | |
 | Euclides - 1841 - 378 pagina’s
...rectilineal figure of six, or any number of sides. 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 BC, as... | |
 | Joseph Denison - 1841 - 210 pagina’s
...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... | |
 | Joseph Denison - 1841 - 210 pagina’s
...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... | |
 | Euclides - 1842 - 316 pagina’s
...Wherefore similar polygons, &c. QED COR. 1. In like manner it may be proved that similar figures of four, or of any number of sides, are one to another in the...in the duplicate ratio of their homologous sides. NB Squares are similar figures, and therefore they are to one another in the duplicate ratio of their... | |
 | William Pease - 1843 - 80 pagina’s
...a 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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... rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
