| Hugo Reid - 1872 - 124 pāgines
...ote. — This illustrates the important geometrical truth, that — Parallelograms on the same base **and between the same parallels are equal to one another; that is,** equal in area. Fic.34 AEFD and ABCD are on the same base AD and between the same parallels AD and EC.... | |
| Euclides, James Hamblin Smith - 1872 - 349 pāgines
...reason thus : Each of the OĢ is double of &BDC; 1.34. QED PROPOSITION XXXVI. THEOREM. Parallelograms on **equal bases, and between the same parallels, are equal to one another.** A. J) M !_-. JT Let the Os A BCD, EFGH be on equal bases BC, FG, and between the same II s AH, BG.... | |
| Henry Angel - 1873 - 182 pāgines
...problems of this chapter. b. Parallelograms (squares, rectangles, and rhomboid figures) or triangles upon **the same or equal bases, and between the same parallels, are equal** in area (Eviclid, Tk. I., Defs. 35-38). a. The squares on the base and perpendicular of a right-angled... | |
| Henry Major - 1873
...bisects it ; and DEC is the half of DBCF ; therefore ABC is equal to DEC. XXXVIII. — Triangles upon **equal bases, and between the same parallels, are equal to one another.** Let the triangles ABC, DEF, be upon equal bases BC, EF, and between the same parallels BF, AD. Produce... | |
| 1874
...to the triangle DBC. Therefore, triangles, &c. Q. E, D. Proposition 38. — Theorem, Triangles upon **equal bases, and between the same parallels, are equal to one another.** Let the triangles ABC, DEF, be on equal bases BC, EF, and between the same parallels BF, AD. The triangle... | |
| 1874
...consecutive angles of a quadrilateral is half the sum of the two remaining angles. 2. Parallelograms -on **equal bases, and between the same parallels, are equal to one another.** 3. Divide a given straight line into two parts, so that the rectangle contained by the whole and one... | |
| James Martin (of the Wedgwood inst, Burslem) - 1874
...equal to the triangle DBC. Wherefore, triangles, &c. QED PROPOSITION 38. — Theorem. Triangles upon **equal bases and between the same parallels, are equal to one another.** Let the triangles ABC, DEF be upon' equal bases BC, EF, and between the same parallels BF, AD. Then... | |
| Charles Mansford - 1874
...CB ; shew that the triangle AOD is equal to the triangle BOC. PROPOSITION 38. THEOREM. Triangles on **equal bases, and between the same parallels, are equal to one another.** . Let the triangles ABC, DEF be on equal bases 1 • BC EF and between the same parallels Bf, AD :... | |
| James Martin (of the Wedgwood inst, Burslem.) - 1876
...are equal, as ' ' the halves of equal things are equal." — Euc. I., Ax. 7. (D.) " Triangles upon **equal bases and between the same parallels are equal to one another"** (in area). — Euc. I.. 38. Ex. ABC, KEFNOTE. -It can be readily seen that A BC is a half of the parallelogram... | |
| Robert Potts - 1876 - 403 pāgines
...the three interior angles of every triangle are together equal to two right angles. 4. Triangles on **equal bases and between the same parallels are equal to one another.** 5. If the square described on one of the sides of a triangle be equal to the squares described on the... | |
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