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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... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 308
by Euclid - 1892 - 518 pages
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...figure is the straight line drawn from its vertex perpendicular to 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,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

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

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

Euclides - 1821 - 294 pages
...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 - Architecture - 1823 - 210 pages
...150. COROLLARY. — Two triangles of the same base are to one another as their altitudes ; and two triangles, of the same altitude, are to one another as their bases. THEOREM 54. 151. The area of every trapezoid, ABCD, is equal to the product of half the sum of its...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

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...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826 - 276 pages
...figure is the 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....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 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 them,...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...parallelograms or triangles be equal, the proportion becomes P : p : : B : b, that is, parallelograms or triangles of the same altitude are to one another as their bases, which is the proposition. CoR. If the bases be equal, then P : p : : A : a, that is, parallelograms...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...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,...
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