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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 - Strona 326
autor: Euclid - 1904 - Liczba stron: 456
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - Liczba stron: 311
...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: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - Liczba stron: 518
...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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - Liczba stron: 528
...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 - 1819 - Liczba stron: 333
...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
...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 - Liczba stron: 596
...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 - 1825 - Liczba stron: 372
...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
...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 - 1827 - Liczba stron: 513
...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 - 1829 - Liczba stron: 186
...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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