 | John Playfair - Mathematics - 1806 - 320 pages
...the base. Book VI. PROP. I. THEOR. TRIANGLES of the same altitude are to one another as their bases ; and parallelograms of the same altitude are to one another as their bases. Let the triangles ABC, ACD and the parallelograms EC, CF, have the same altitude ; as the base BC is to... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...Wherefore, solid parallelepipeds, &c. QED . CoR. From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the prisms, the bases of which are the triangles AEM, CFG, and NBO, PDQ the triangles opposite to them,... | |
 | Euclides - 1816 - 588 pages
...Wherefore solid parallelepipeds, &c. QED COR. From this it is manifest, that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the prisms, the bases of which are the triangles AEM, CFG, and NBO, PDQ the triangles opposite to them,... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...parallelepipeds, &c. Q, ED COR. 1. From this it is manifest, that prisms upon triangular bases, and of the same altitude, are to one another as their bases. Let the prisms BNM, DPG, the bases of which are the triangles AEM, CFG, have the same altitude ; complete... | |
 | Euclides - 1821 - 294 pages
...A contained in-its consequent; .-. the As are to one another as their bases, (Def. 5. 5.). PART 2. Parallelograms of the same altitude, are to one another as their bases. Let their diagonals be drawn ; then since the As which are the halves of these parallelograms (34. 1.),... | |
 | Peter Nicholson - Architecture - 1823 - 210 pages
...2. — Triangles which have equal bases and equal altitudes are equal. THEOREM 50. 143. Rectangles, of the same altitude, are to one another as their bases. Let ABCD, AEFD, be two rectangles, which have a com- qp _c mon altitude AD ; they are to one another as... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...Wherefore solid parallelopipeds, &c. QED COR. From this it is manifest, that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the prisms, the bases of which are the triangles AEM, CFG, and NBO, ;PDQ the triangles opposite to... | |
 | Euclides - 1826 - 226 pages
...drawn from the vertex to the oase. PROPOSITION I. THEOREM. Triangles, and parallelograms, which have the same altitude, are to one another as their bases. Let there be the triangles ABC, ACD, also the parallelograms EC, CF, which have the same altitude, viz. the perpendicular... | |
 | Euclid - 1826 - 234 pages
...drawn from the vertex to the base. PROPOSITION I. THEOREM. Triangles, and parallelograms, which have the same altitude, are to one another as their bases. Let there be the triangles ABC, ACD, also the parallelograms EC, CF, which have the same altitude, viz. the perpendicular... | |
 | George Lees - 1826 - 276 pages
...Alg. be ; and hencec, that the A ABC : A ACD : : BC : CD. — Wherefore triangles, &c. QED Cor. 1. Parallelograms of the same altitude are to one another as their bases. .. .•/ -% OF GKOMKTKY. Book IV. PROP. II. THEOREM. If a straight line DE be drawn parallel to one... | |
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Triangles and parallelograms of the same altitude are to one another as their bases. 
