| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...first to a similar and similarly described rectilineal figure on the second. PROPOSITION 21. THEOREM. **Rectilineal figures which are similar to the same rectilineal figure, are also similar to** each other. Let each of the rectilineal figures A and B be similar to the rectilineal figure C: the... | |
| Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...about their equal angles are proportional, and the parallelograms are therefore similar to one another. **For the same reason the parallelogram ABCD is similar to the parallelogram FHCK.** Therefore each of the parallelograms EG and HK is similar to BD ; therefore the parallelogram EG is... | |
| Robert Potts - 1868 - 434 pages
...about the equal angles are proportionals ; and they are therefore similar to one another; (VI. def. 1.) **for the same reason, the parallelogram ABCD is similar to the parallelogram** FUCK: wherefore each of the parallelograms GE, Kffis similar to DB: but rectilineal figures which are... | |
| Euclides - 1874 - 342 pages
...the > equal angles are proportionals ; and they are therefore similar to one another (VI. Def. 1). **For the same reason, the parallelogram ABCD is similar to the parallelogram FHCK; wherefore** 6. Each of the parallelograms GE, KH is similar to DB ; but rectilineal figures which are similar to... | |
| Euclid - 1876 - 240 pages
...about the equal angles are proportionals ; and they are therefore similar to one another («) ; and **for the same reason, the parallelogram ABCD is similar...rectilineal figure are also similar to one another** (/) ; therefore the parallelogram, GE is similar to KH. PROPOSITION XXV. PROBLEM. To construct a rectilineal... | |
| Robert Potts - Geometry - 1876 - 446 pages
...about the equal angles are proportionals ; and they are therefore similar to one another; (vi. def. 1.) **for the same reason, the parallelogram ABCD is similar...rectilineal figure, are also similar to one another:** (vi. 21.) therefore the parallelogram GE is similar to KH. Wherefore, parallelograms, &c. QED PROPOSITION... | |
| James Hamblin Smith - Euclid's Elements - 1879 - 378 pages
...shall be to a given triangle in a given ratio. PROPOSITION XX. THEOREM. (EucL vi. 21.) Rectilinear **figures, which are similar to the same rectilineal figure, are also similar to** each other. B Let each of the rectilinear figures A and B be similar to the rectilinear figure C. Then... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...first to a similar and similarly described rectilineal figure on the second. PROPOSITION 21. THEOREM. **Rectilineal figures which are similar to the same rectilineal figure, are also similar to** each other. Let each of tho rectilineal figures A and B bo similar to the rectilineal figure C: the... | |
| Education, Higher - 1884 - 538 pages
...equiangular to one another, and shall have these angles equal which are opposite to the homologous sides. 15. **Rectilineal figures which are similar to the same rectilineal figure, are also similar to** each other. 16. From the same point in a given plane, there cannot be two straight lines at right angles... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...about their equal angles are proportional, and the parallelograms are therefore similar to one another. **For the same reason the parallelogram ABCD is similar to the parallelogram FHCK.** Therefore each of the parallelograms EG and HK is similar to BD ; therefore theparallelogram EG is... | |
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