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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.
Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ... - Side 27
av A. Bell - 1837 - 164 sider
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## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

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...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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...
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## The Elements of Euclid; viz. the first six books, together with the eleventh ...

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...
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## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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,...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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...
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## The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

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.),...
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## The New Practical Builder and Workman's Companion, Containing a Full Display ...

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...
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## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

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...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

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...
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## Elements of Arithmetic, Algebra, and Geometry

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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