| Euclid - 1837 - 410 páginas
...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 - 240 páginas
...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 páginas
...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 páginas
...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 - 194 páginas
...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 páginas
...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 páginas
...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 páginas
...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 páginas
...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 páginas
...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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