 | Elias Loomis - Conic sections - 1858 - 256 pages
...triangle DBC is equal to the triangle ACB (Prop. VI.), the less to the greater, which is absurd. Hence AB is not unequal to AC, that is, it is equal to it. Therefore, if two angles, &c. Cor. Hence, every equiangular triangle is also equilateral. PROPOSITION... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...Find the cube of '07, and the square root of 63 to 4 decimal places. Obligatory Portion. EUCLID. 1. Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated on one extremity of the base, equal to one another, and... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...two angles, &c. QED COn. Hence an equiangular triangle is also equilateral. PROPOSITION VII. THEOREM. Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and... | |
 | Royal college of surgeons of England - 1860 - 332 pages
...circle, a rhombus. When are straight lines said to be parallel ? Write down the postu- l/ lates. 2. Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise... | |
 | Euclides - 1860 - 288 pages
...equal to AC. COR. — Hence every equiangular triangle is also equilateral. PROPOSITION VII. THEOREM. Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise... | |
 | Euclides - 1861 - 464 pages
...similar segments of a circle, is the same in principle with the 7th of Book I., which says, that, " on the same base and on the same side of it, there cannot be two triangles which have their sides terminated in one extremity of the base equal, and likewise those terminated... | |
 | Euclides - 1862 - 172 pages
...equal to the greater, which is absurd. Therefore AB is not unequal to AC, that l• AB IB equal to AC. Wherefore, if two angles, &c. QED Cor. Hence every...equiangular triangle is also equilateral. PROP. VII.^ THEOREM. Upon the same base and on the same side of it, there cannot be two triangles that have their... | |
 | Euclides - 1862 - 140 pages
...DBC is equal to the triangle ACB. (I. 4.) The less to the greater, B which is absurd. 6. Therefore AB is not unequal to AC, that is, it is equal to it. Conclusion. — Wherefore, if two angles, &c. QED* Corollary. — Hence every equiangular triangle... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. 7. Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and... | |
 | Euclides - 1864 - 448 pages
...two angles, &c. QED COB. Hence an equiangular triangle is also equilateral. PROPOSITION VII. THEOREM. Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremitg of the base, equal to one another, and... | |
| |
UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity... 
