 | Robert Potts - 1868 - 434 sider
...wherefore the angle BDC is both equal to, and greater than the angle B CD; which is impossible. Thirdly. The case in which the vertex of one triangle is upon...Therefore, upon the same base and on the same side of it, &c. QED PROPOSITION VIII. THEOREM. If two triangles have two sides of the one equal to two sides of... | |
 | Euclides - 1871 - 136 sider
...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...their sides which are terminated in one extremity qf the base equal to one another, and their sides which are terminated in the other extremity of the... | |
 | Henry William Watson - 1871 - 320 sider
...equal to AC, and EB + ED is equal to DB, therefore AC + DB is greater than AB + DC. PROPOSITION 4. Upon the same base and on the same side of it there cannot be two triangles having the two sides terminated in one extremity of the base equal to each other, and at the same time... | |
 | Euclid, Charles Peter Mason - 1872 - 216 sider
...&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 cannot be two triangles having their sides which are terminated in the one extremity of the base equal to one another, and... | |
 | Henry Major - 1873 - 588 sider
...BDC is equal to BCD ; but BDC has been proved to be greater than the sameBCD, which is impossible. The case in which the vertex of one triangle is upon a side of the other, needs no demonstration. VIH. — If two triangles have two sides of the one equaf to two sides of the other, each to each,... | |
 | Lewis Sergeant - 1873 - 182 sider
...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... | |
 | Euclides - 1874 - 342 sider
...wherefore the angle BDC is both equal to, and greater than the angle BCD, which is impossible. Thirdly. The case in which the vertex of one triangle is upon...Therefore, upon the same base, and on the same side of it, &c. QED PROPOSITION 8.— Theorem. If two triangles have two sides of the one equal to two sides of... | |
 | Henry Evers - 1874 - 216 sider
...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 - 120 sider
...aho bisects the angle A and OA, BO and CO are all equal to one another. PROPOSITION 7. THEOREM. On the same base, and on the same side of it, there cannot be two triangles which have their sides which are terminated in one extremity of the base, equal to one another, and... | |
 | Robert Potts - 1876 - 446 sider
...•wherefore the angle BDC is both equal to, and greater than the angle BCD;- which is impossible. Thirdly. The case in which the vertex of one triangle is upon...Therefore, upon the same base and on the same side of it, &c. QBD PSOPOSITION VIIL THEOREM. If two triangles have two tides of the one equal to two tides of... | |
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Therefore, 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 extretnity equal... 
