 | Euclides - 1871 - 136 pages
...may be shewn that AB is not less than AC ; .: AB=AC. QED NOTE XIII. Euclid-s Prop. VII. of Book I. 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 qf the base equal to one another, and their... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...&c.) Cor. It follows from this that all the sides of an equi-angular A are equal. PROPOSITION VII. Upon the same base, and on the same side of it, there...triangles having their sides which are terminated in the one extremity of the base equal to one another, and likewise those that are terminated in the other... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...may be shewn that AB is not less than AC; .: AB = AC. QED NOTE XIII. Euclid's Prop. VII. of Book I. 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 their... | |
 | Lewis Sergeant - 1873 - 182 pages
...Hence it follows that an equiangular triangle is also equilateral. Proposition 13. — Theorem. On the same base, and on the same side of it, there cannot be two triangles having tlie sides terminated by one extremity of the base equal, and also the sides terminated by the other... | |
 | Henry Major - Student teachers - 1873 - 588 pages
...triangle DBC is equal to the triangle ACB, the less to the greater } which is absurd. Therefore ATE is not unequal to AC, that is, it is equal to it. COROLLARY. — Hence every equiangular triangle is also equilateral. VII. — Upon the same hase, and... | |
 | Edward Atkins - 1874 - 428 pages
...triangle DBC is equal to the triangle ACB (I. 4), the less to the greater, * which is absurd. Therefore AB is not unequal to AC, that is, it is equal to it. Wherefore, if two angles, &c. QED * COROLLARY. — Hence every equiangular triangle is also equilateral. PmpBtioi 7.— ! fjiwii «i?... | |
 | Edward Atkins - 1874 - 426 pages
...equal to the triangle ACB (I. 4), the less to the greater, B - . -,-ii which is absurd. Therefore AB is not unequal to AC, that is, it is equal to it. Wherefore, if two angles, <fec. QED * COROLLARY. — Hence every equiangular triangle is also equilateral. Proposition 7. —... | |
 | Henry Evers - 1874 - 216 pages
...geometric figure that cannot alter its form without altering the length of its sides. It is Euclid I., 7. " Upon the same base, and on the same side of it, there cannot be two triangles which have their two sides terminated in one extremity on the base equal, and likewise those terminated... | |
 | Euclides - 1874 - 342 pages
...angles, &c. QED Cor. Hence an equiangular triangle is also equilateral. PROPOSITION 7. — 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... | |
 | Euclides - 1874 - 120 pages
...equal to the triangle ACB, [I. 4.] the less to the greater ; which is absurd. [Ax. 9.] Therefore AB is not unequal to AC, that is, it is. equal to it. Therefore, if two angles, &c. QEB Corollary. Hence every equiangular triangle is also equilateral.... | |
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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... 
