 | John Playfair - 1806 - 320 σελίδες
...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,... | |
 | Robert Simson - 1806 - 546 σελίδες
...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,... | |
 | Euclides - 1816 - 588 σελίδες
...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,... | |
 | John Playfair - 1819 - 350 σελίδες
...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... | |
 | Euclides - 1821 - 294 σελίδες
...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 - 210 σελίδες
...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... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...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... | |
 | George Lees - 1826 - 276 σελίδες
...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.... | |
 | Robert Simson - 1827 - 546 σελίδες
...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,... | |
 | John Playfair - 1829 - 210 σελίδες
...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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From this it is manifest that prisms upon triangular bases, of the same altitude, are to one another as their bases. Let the... 
