 | Lewis Sergeant - 1873 - 182 pages
...21 41 21 228 2000 _1824 1~7G, <fcc. (See Arith., § 61.) * 3. Show that parallelograms and triangles upon the same base and between the same parallels are equal to one another. (10.) (This appears to mean that parallelograms on the same base and between the same parallels are... | |
 | Henry Major - Student teachers - 1873 - 588 pages
...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 AD both... | |
 | Philip Kelland - 1873 - 248 pages
...Ex. 1, Art. 7, DA=a-ß; and, changing all the signs, we get (20) for the corresponding lines, Ex. 4. Parallelograms upon the same base and between the same parallels are equal. It is necessary to remind the reader of what we have already stated, that examples such as this are... | |
 | Edward Atkins - 1874 - 426 pages
...parallelogram ABCD is equal to the parallelogram EFGH (Ax. 1). Proposition 37. — Theorem. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DEC be on the same base BC, and between the same parallels AD, BC ; The triangle ABC... | |
 | Euclides - 1874 - 120 pages
...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 : the triangle... | |
 | Braithwaite Arnett - 1874 - 130 pages
...to a given straight line of unlimited length from a given point without it. 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. If a straight line be bisected, and produced to any point, the rectangle contained by the whole... | |
 | Euclides - 1874 - 342 pages
...Therefore, parallelograms upon equal, &c. QE D. PROPOSITION 37.— Theorem. TriangUs upon the same oase and between the same parallels, are equal to one another. Let the triangles ABC, DBC be upon the same base BC, and between the same parallels AD, BC. D Then the triangle... | |
 | Edward Atkins - 1876 - 130 pages
...parallelogram EFGH (Ax. 1). Therefore, parallelograms, &c. QED Proposition 37. — Theorem. Triangles upon the same base, and between the same parallels, are equal to one another. Let the triangles ABC, DBC be on the same base BC, and between the same parallels AD, BC ; The triangle ABC... | |
 | Henry Major - 1876 - 784 pages
...side together equal to two right angles, the two straight lines shall be parallel to one another. 8. Parallelograms upon the same base, and between the same parallels, are equal to one another. Are the parallelograms equal in all respects ? 1. Simplify 1£ — | -j 1 — *-(*— §) >• , and... | |
 | William George Spencer - Geometry - 1876 - 118 pages
...triangles that shall be equal to each other, and yet not similar ? 137. Can you show that all triangles upon the same base and between the same parallels are equal to one another 'i 138. Can you place a circle, whose radius is 1J inch, so that its circumference may touch two points... | |
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PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... 
