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" From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the... "
A Text-book of Euclid's Elements for the Use of Schools - الصفحة 326
بواسطة Euclid - 1904 - عدد الصفحات: 456
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - عدد الصفحات: 540
...part of the cylinder. Wherefore, " every cone" &c. QED 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,...

Solid and Spherical Geometry and Conic Sections: Being a Treatise on the ...

A. Bell - 1837 - عدد الصفحات: 180
...the solid AB to the solid CD. Con. 1. — From this it is manifest that prisms upon triangular bases, 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...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - عدد الصفحات: 410
...to the solid CD. Wherefore parallelepipeds, &c. Cor. From this it is manifest that triangular prisms 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,...

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

Euclides - 1841 - عدد الصفحات: 378
...the third part of the cylinder. Wherefore every cone, &c. QED PROP. XI. THEOR. 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 diameters of their...

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

John Playfair - 1842 - عدد الصفحات: 332
...solid AB to the solid CD. 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 arc the triangles AEM, CFG, have the same altitude : complete...

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - عدد الصفحات: 546
...third part of the cylinder. Wherefore, every cone, &c. QKD PROPOSITION XI. THEOREM. 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,...

The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - عدد الصفحات: 382
...is the third part of the cylinder. A cone, therefore, &c. PROP. XI. THEOB. — 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,...

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

Euclid, John Playfair - 1846 - عدد الصفحات: 334
...solid AB to the solid CD. 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...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - عدد الصفحات: 292
...line drawn from its vertex perpendicular to the base. PROP. I. THEOR. Triangles 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, viz. the perpendicular...

Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - 1854 - عدد الصفحات: 534
...triangles СШя, ОАя, are similar, .-. OD : Oa :: Oa : OA ; that is, OD : OM : : OM : OA ; and since triangles of the same altitude are to one another as their bases, and that the altitude eD is the same for the triangles ODa, OMff, ОЛгг, it follows, from the proportion...




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