| Robert Simson - 1806 - 518 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 - 311 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
...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 - 528 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 - 333 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
...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 - 596 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 - 372 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 - 320 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
...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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