| Edward Riddle - 1824 - 551 pagina’s
...FI) E and ABC are equal, (Cor. Theo. 32.) QED THEOREM XXXVI. If two equal triangles as ABC, AD B, be **on the same base AB, and on the same side of it,** the line DC which joins their vertices, is parallel to the base A B. For if D С is not parallel to... | |
| Euclides - 1840
...B and C are equal. COR. — Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. **On the same base (AB), and on the same side of it,** there cannot be two triangles having their conterminous sides (AC and AD, BC and BD) at both extremities... | |
| Euclides - 1841 - 351 pagina’s
...likewise those which are terminated in the other extremity, equal to one another. If it be possible, upon **the same base AB, and on the same side of it, let** ACB, ADB be two triangles, which have their sides CA, DA terminated in A, one extremity of the base,... | |
| Euclides - 1845
...draw EG perpendicular to DB and meeting DC produced in G. Then CEG is an equilateral triangle. 69. **On the same base AB, and on the same side of it, let...angle ABD not a right angle ; then the triangle ABC** may be shewn to oe greater than the triangle ABD whether the angle ABD be acute or obtuse. 70. Let... | |
| Euclid, Robert Potts - 1847 - 478 pagina’s
...draw EG perpendicular to DB and meeting DC produced in G. Then CEG is an equilateral triangle. 69. **On the same base AB, and on the same side of it, let...angle ABD not a right angle; then the triangle ABC** may be shewn to oe greater than the triangle ABD whether the angle ABD be acute or obtuse. 70. Let... | |
| Euclides - 1852
...those sides which terminate in the other end of the base are not equal. Let the triangles ACB and ADB, **on the same base AB, and on the same side of it,** have the sides AC and AD equal; then the sides вc and BD are not equal. CASE 1. When the vertex of... | |
| Euclides - 1853
...BD by hyp8 : which is impossible. Hence in every case it has been shewn impossible for there to be **on the same base AB, and on the same side of it,** two triangles ACB, ADB, having their sides AC, AD terminated in one extremity A of the base equal,... | |
| Robert Potts - 1860 - 361 pagina’s
...ways, and the figure may be transformed into a triangle, by two constructions similar to that employetl **for a figure of four sides. If the figure consists...be a triangle whose vertical angle is A, and whose** base BC is bisected in D ; let any line EDG be drawn through D, meeting AC the greater side in G and... | |
| Euclides - 1864
...bisection of the base parallel to the two sides of the triangle. 108. This may be shewn ex absurdo. 1 09. **On the same base AB, and on the same side of it, let...constructed, having the side BD equal to BC, the angle ABC** aright angle, but the angle ABD not a right angle; then the triangle ABC is greater than ABD, whether... | |
| Euclid, Isaac Todhunter - 1867 - 400 pagina’s
...to one another, and likewise those which are terminated at the other extremity. If it be possible, **on the same base AB, and on the same side of it, let** there be two triangles ACB, £ B ADB, having their sides CA, DA, which are terminated at the extremity... | |
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