 | 1864 - 370 pages
...Find the limits of a hyperbola when it is produced by an Irish member. IV. Similar figures upon the same base, and between the same parallels, are equal to one another. Apply this theorem to show the base similarity of certain persons who cut similar figures in Parliament.... | |
 | Euclides - 1864 - 448 pages
...(ax. 1.) Therefore, parallelograms upon equal, &c. QED PROPOSITION XXXVII. THEOREM. Triangles upon the same base and between the same parallels, are equal to one another. Let the triangles ABC, DBCbe upon the same base BC, and between the same parallels AD, BC. Then the... | |
 | Euclides - 1865 - 80 pages
...parallelogram ABCD is equal to the rectangle EBCF. PROPOSITION XLIV. THEOR. Parallelograms upon the same base and between the same parallels are equal to one another. Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF and BC,... | |
 | William Harris Johnston - 1865 - 478 pages
...oblique parallelograms abo. By Euclid, Book I, Prop. 35, it is established that «parallelograms upon the same base and between the same parallels are equal to one another." Now, the perpendicular distance, D С, between the sides, DF and В С, of the oblique parallelogram... | |
 | Robert Potts - 1865 - 528 pages
...1.) Therefore, parallelograms upon equal, &e. QE u. PROPOSITION XXXVII. THEOREM. Triangles upon the same base and between the same parallels, are equal to one another. Let the triangles ABC, DBC\lQ upon the same base BC, and between the same parallels AD, BC. Then the... | |
 | J. F. H. de Rheims - Geometrical drawing - 1865 - 336 pages
...and between the same parallels are equal to one another. Prop. 37. — Theorem. Triangles upon the same base and between the same parallels are equal to one another. Prop. 47. — Theorem. In any right angled trinngle, the square which is described upon the side subtending... | |
 | Architecture - 1865 - 276 pages
...vertical angle, and a side to construct the triangle. 3. Prop. 35. Theorem. Parallelograms upon the same base and between the same parallels are equal to one another. Shew this is equally true of triangles. 4. Prop. 44. — Problem. To a given straight line to apply... | |
 | Euclides - 1865 - 402 pages
...parallelogram EFGH. (ax. 1.) Wherefore, parallelograms, &c. QED PROP. XXXVII.— THEOREM. Triangles upon the same base, and between the same parallels, are equal to one another. (References — Prop. i. 31, 34, 35; ax. 7.) Let the triangles ABC, DBC, be on the same base BC, and... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...differences of identically equal magnitudes are equal, although they may not be identically equal. THEOR. I. Parallelograms on the same base and between the same parallels are equal. Let ABCD, EBCF be two parallelograms on the same base EC, and between the same parallels AF, BC : \*:... | |
 | Stewart W. and co - 1884 - 272 pages
...same EBCH ; therefore, also the parallelogram ABCJ) is equal to EFGH. JLX.XVJI. — Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles be ABC, DBC. Produce AD both ways to the points E, F, and through B draw BE parallel... | |
| |
Parallelograms on the same base, and between the same parallels, are equal to one another. 
