 | Euclid, James Thomson - 1837 - 410 sider
...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 similar triangles, having the angles B and E equal, and AB : BC : : DE : EF, so that... | |
 | Andrew Bell - 1837 - 290 sider
...a given straight line similar to one given ; and so on. PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF, he similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
 | Robert Simson - 1838 - 434 sider
...duplicate ratio of that which AB has to the homologous side FG. Wherefore, similar polygons, &c. Q. ED COR. 1. In like manner, it may be proved, that similar...2. And if to AB, FG, two of the homologous sides, a third proportional M be taken AB has (10. def. 5,) to M the duplicate ratio of that which AB has to... | |
 | Euclides - 1838 - 264 sider
...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 - 192 sider
...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,... | |
 | London city mission - 1840 - 620 sider
...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,... | |
 | Joseph Denison - 1840 - 96 sider
...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... | |
 | Euclides - 1840 - 82 sider
...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 - 1841 - 210 sider
...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 - 1841 - 378 sider
...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... | |
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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
