 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...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 AB,... | |
 | Euclides - 1840 - 192 pages
...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 - 1845 - 546 pages
...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 two triangles ABC, ABD be constructed, having the side BD equal to BC, the angle ABC a right angle,... | |
 | Euclid, Robert Potts - Euclid's Elements - 1847 - 118 pages
...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 two triangles ABC, ABD be constructed, having the side BD equal to BC, the angle ABC a right angle,... | |
 | Euclides - 1852 - 48 pages
...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 - Geometry - 1853 - 334 pages
...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,... | |
 | Euclides - 1864 - 262 pages
...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 two triangles ABC, ABD be constructed, having the side BD equal to BC, the angle ABC aright angle,... | |
 | Euclides - 1864 - 448 pages
...bisection of the base parallel to the two sides of the triangle. 108. This may be shewn ex absurdo. 109. On the same base AB, and on the same side of it, let two triangles ABC, ABD be constructed, having the side BD equal to BC, the angle ABC a right angle,... | |
 | Robert Potts - 1865 - 528 pages
...AECG the equivalent rectangle. Then AC is greater than EA, &c. 17. This may be shewn by Euc. I 20. 18. On the same base AB, and on the same side of it, let two triangles ABC, ABD be constructed, having the side BD equal to BC, the angle ABC a right angle,... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...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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ABC and ABD are two triangles on the same base AB, and on the same side of it, the vertex of each triangle being without the other. If AC equals AD, show that BC cannot equal BD (§ 154). 
