 | Robert Simson - 1806 - 546 sider
...third part of the cylinder, cone, fcc. QED Wherefore, every PROP. XL THEOR. See N. CONES and cylinders of the same altitude are to one another as their bases. Let the cones and cylinders, of which the bases are the circles ABCD, EFGH, and the axes KL, MN, and AC, EG... | |
 | John Playfair - 1806 - 320 sider
...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 the... | |
 | Euclides - 1814 - 560 sider
...solid GK to the solid AJi : Therefore as the base AE to the base CF, so is the solid AB to the CoR. From this it is manifest, that prisms upon triangular...same altitude, are to one another as their bases. solid CD. Wherefore solid parallelepipeds, &c. QED Let the prisms, the bases of which are the triangles... | |
 | Euclides - 1816 - 588 sider
...part of the cylinder. Wherefore every cone, &c. Q. E D. PROP. XI. THEOR. . See N. CONES and cylinders of the same altitude, are to one another as their bases. Let the cones and cylinders, of which the bases are the circles ABCD, EFGH, and the axes KL, MN, and AC, EG,... | |
 | John Playfair - 1819 - 350 sider
...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...complete the parallelograms AE, CF, and the solid parallelepipeds AB, CD, in the first of which let AN, and ID the other let CP be one of the insisting... | |
 | Euclides - 1821 - 294 sider
...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 - 1823 - 210 sider
...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 - 1825 - 1046 sider
...AE to the base CF, so is the solid AB to the solid CD. Wherefore solid parallelopipeds, &c. QED COR. From this it is manifest, that prisms upon triangular...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, have the... | |
 | Euclid, John Playfair - 1826 - 326 sider
...parallelopipeds, &e. QKt) COR. 1. From this it is manifest, that prisms upon triangular basesl and of the same altitude, are to one another as their bases. Let the prisms BNM, D?G,thebaSesof whieh are the triangles AEM, CFG* have the same altitude; eomplete the parallelograms... | |
 | George Lees - 1826 - 276 sider
...straight line drawn from its vertex perpendicular to its base. Book IV. PROP. I. THEOREM. Triangles of the same altitude are to one another as their bases. Let the triangles ABC, ACD, have the same altitude, viz. the perpendicular drawn from the point A to BD. Then... | |
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FC, as the solid HD to the solid DC. But the base HF is equal to the base AE, and the solid GK to the solid AB ; therefore, as the base AE to the base CF, so is the solid AB to the solid CD. 
