 | John Playfair - 1806 - 320 σελίδες
...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, ACD and the parallelograms EC, CF, have the same altitude ; as the base BC is... | |
 | Euclides - 1821 - 294 σελίδες
...A contained 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.... | |
 | George Lees - 1826 - 276 σελίδες
...Alg. be ; and hencec, that the A ABC : A ACD : : BC : CD. — Wherefore triangles, &c. QED Cor. 1. Parallelograms of the same altitude are to one another as their bases. .. .•/ -% OF GKOMKTKY. Book IV. PROP. II. THEOREM. If a straight line DE be drawn parallel to one... | |
 | John Playfair - 1829 - 210 σελίδες
...the base. PROPOSITION I. THEOREM. 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. * — See Note. Let P and p denote two parallelograms, A and a their altitudes, B and o their bases;... | |
 | John Martin Frederick Wright - 1831 - 282 σελίδες
...straight line perpendicular to a plane from a given point without it. ST. JOHN'S COLLEGE, MAY 1830. 1. TRIANGLES and parallelograms of the same altitude are to one another as their bases. 2. If a solid angle be contained by three plane angles, any two of them are greater than the third.... | |
 | University of Cambridge - 1831 - 552 σελίδες
...principal planes of the paraboloid. SATURDAY MORNING .... 9 to 11. First, Second, Third and Fourth Classes. 1. TRIANGLES and parallelograms of the same altitude are to one another as their hases. 2. Planes to which the same straight line is perpendicular are parallel to one another. 3. Express... | |
 | Thomas Leybourn - 1835 - 682 σελίδες
...planes of the paraboloid. SATURDAY MORNING 9 o'clock to 11. First, Second, Third, and Fourth Classes. 1. Triangles and parallelograms of the same altitude are to one another as their bases. 2. Planes to which the same straight line is perpendicular are parallel to one another. 3. Express... | |
 | 1836 - 366 σελίδες
...taken in the circumference of a circle, the straight line which joins them falls within the circle. 26. Triangles and parallelograms of the same altitude are to one another as their bases. State Euclid's definition of proportion, and the algebraic definition, and shew that they coincide.... | |
 | John Playfair - 1836 - 148 σελίδες
...remainder that measures the preceding without a remainder, is the greatest common measure. PROP. II. THEOR. Parallelograms of the same altitude are to one another as their bases. 1> K C Let ABCD and AEFD, be two parallelograms which have the same altitude, they are to each other... | |
 | William Whewell - 1837 - 226 σελίδες
...angles respectively equal, and the sides about the equal angles respectively proportionals. *PROP. i. Triangles and parallelograms of the same altitude are to one another as their bases. *PROP. ii. If a straight line be drawn parallel to one of the sides of a triangle, it shall cut the... | |
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Triangles and parallelograms of the same altitude are to one another as their bases. 
