 | Peter Fleming - Surveying - 1815 - 250 pages
...lined triangle, the greater angle is opposite the greater side, ...... 8. Parallelograms standing upon the same base, or on equal bases, and between the same parallels, are equivalent, 9. A triangle is the half of a parallelogram, when they stand upon the same base, and are... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...equal bases, and between the same parallels are equal, if therefore a triangle and a parallelogram be on the same base, or on equal bases, and -between, the same parallels, the parallelogram will be double the triangle. THEOREM XXXIV. If PÍ С , one of the sides of any trapezoid... | |
 | John Playfair - Geometry - 1829 - 210 pages
...following principle, which is so obvious that it may be admitted as an axiom. If any two solids standing on the same base, or on equal bases, and between the same parallels, be cut by numerous planes in directions parallel to their bases, and if all the sections at equal altitudes... | |
 | Abraham Crocker - 1841 - 486 pages
...El, and DI, and CEID will be the rhomboides. W For Practice. Note. Parallelograms constituted upon the same base (or on equal bases), and between the same parallels, are equal to one another. — EUCLID, I. 35. and 36. In every quadrilateral (or four-sided) figure, the four... | |
 | Horace Grant - 1852 - 112 pages
...A PARALLELOGRAM DHAWN EQUAL TO A GIVEN TRIAKGLE. A parallelogram has double the area of a triangle on the same base (or on equal bases), and between the same parallels (or of the same altitude). Bisect the base of the triangle by any line, and draw a line through the... | |
 | Alexander Bain - Logic - 1870 - 478 pages
...a repetition of the same apposite union of truths possessed, one might also infer that ' Triangles on the same base, or on equal bases, and between the same parallels, are equal.' By farther combinations, the reasoner might go on to deduce or infer the 47th, and so forth. All which... | |
 | Walter Smith - Geometrical drawing - 1872 - 72 pages
...between the same parallels, having the same altitude, are equal to one another in area. AXIOM II. — Parallelograms on the same base, or on equal bases, and between the same parallels, are equal in area. Thus the parallelograms ABCD, ABCE, ABEF, being between the same parallels 1 2, 3 4 and on... | |
 | William Alexander Willock - Circle - 1875 - 196 pages
...area. This follows immediately from the last three theorems. Triangles (last Theor.) are the halves of parallelograms on the same base or on equal bases and between the same parallels ; which parallelograms are (Theors. 6 and 7) proved equal. And therefore their halves, the triangles,... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry - 1899 - 400 pages
...can have three distinct altitudes, viz. a1, a2, a 3 , in the figure. b, PROPOSITION I. 145. Theorem. Parallelograms on the same base or on equal bases and between the same parallels are equal. D D CD' C' D CD' C'D D' C C' ABARAB FIG. 1. FIG. 2. Fio. 3. Given [U ABCD, ABC'D', on the same base... | |
 | Wooster Woodruff Beman, David Eugene Smith - Geometry, Modern - 1899 - 272 pages
...have three distinct altitudes, viz. <ii, a3, a 3 , in the figure. b b, PROPOSITION I. 145. Theorem. Parallelograms on the same base or on equal bases and between the same parallels are equal. p__D C--tf C' D CD' C'D P' C C' X?\7\7V/V ABABAB Fio. 1. FIG. 2. FIG. 3. Given U] ABCD, ABC'D', on... | |
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Parallelograms on the same base, or on equal bases, and between the same parallels, are equal. 
