 | Euclides - 1871 - 136 pages
...straight lines, and the lines AD, BC intersect in E, then the triangles AEC, BED are equal. Triangles upon equal bases, and between the same parallels, are equal to one another. Let AS ABC, DEF be on equal bases, BC, EF and between the same IIs BF, AD. Then must A ABC= A DEF.... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...ABC is equal to the area of the triangle DBC (Bk. IV. Prop. i, Cor.). PROPOSITION 7. Triangles upon equal bases and between the same parallels are equal to one another in area. Let ABC and DEF be two triangles upon the equal bases BC and EF, and between the same parallels... | |
 | Hugo Reid - Mathematics - 1872 - 148 pages
...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 - Geometry - 1872 - 376 pages
...reason thus : Each of the O« 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 - Geometry - 1873 - 192 pages
...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 - Student teachers - 1873 - 588 pages
...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... | |
 | Edward Atkins - 1874 - 428 pages
...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... | |
 | Braithwaite Arnett - 1874 - 130 pages
...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... | |
 | Euclides - 1874 - 342 pages
...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... | |
 | Euclides - 1874 - 120 pages
...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 :... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
