 | Isaac Hammond Morris - Geometry, Plane - 1890 - 440 pages
...enclosed by its boundary, or perimeter. It depends upon both the shape and the perimeter of the figure. 2. Parallelograms upon the same base, and between the same parallels, are equal. (Eue. i. 35.) ABСD = ABDE. (Fig. 1.) PGHJ = PGKL. (Fig. 2.) 8. Parallelograms upon equal bases, and... | |
 | Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...the diameter bisects the parallelogram, ie divides it into two equal parts. 35. Parallelograms on the same base and between the same parallels are equal to one another. 36. Parallelograms on equal bases and between the same parallels are equal to one another. 37. Triangles... | |
 | Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 188 pages
...same base and between the same parallels are equal in area. Let ABCD, EBCF represent parallelograms, upon the same base BC, and between the same parallels AF, BC ; it is required to prove that the area of ABCD is equal to the area of EBCF. The sides AD, EF of the... | |
 | Augustus De Morgan - Mathematics - 1898 - 316 pages
...BGHA and BPKD are four-sided figures, etc. (Construction.) . -. BGHA and BPKD are parallelograms. IX. Parallelograms upon the same base and between the same parallels are equal. (Proved.) EBAF and BGHA, are parallelograms, etc. (Construction.) .•. EBAF and BGHA are equal. X.... | |
 | American Association for the Advancement of Science - American periodicals - 1899 - 646 pages
...part a strict treatment of equivalence. Even Euclid, in proving his I. 35, " Parallelograms on the same base, and between the same parallels, are equal to one another," does not show that the parallelograms can be divided into pairs of pieces admitting of superposition... | |
 | Seymour Eaton - 1899 - 362 pages
...find the area of a parallelogram. Let DABC be the parallelogram. Then it is proven in geometry that parallelograms upon the same base and between the same parallels are equal ; therefore the parallelogram DABC is equal to the parallelogram or rectangle FABE. Hence the area... | |
 | American Association for the Advancement of Science - Science - 1899 - 650 pages
...third part a strict treatment of equivalence. Even Euclid, in proving his I. 35, "Parallelograms on the same base, and between the same parallels, are equal to one another," does notshowthat the parallelograms can be divided into pairs of pieces admitting of superposition... | |
 | Thomas Franklin Holgate - Geometry - 1901 - 462 pages
...same side of the line shall be a minimum. § 334. 2. 4. THEOREMS ON THE AREAS OF PARALLELOGRAMS. (1) Parallelograms upon the same base and between the same parallels are equal in area. § 292. (2) Parallelograms upon equal bases and between the same parallels are equal in area.... | |
 | Eldred John Brooksmith - Mathematics - 1901 - 368 pages
...are equal in every respect. 3. Define parallel straight lines ; and show that parallelograms on the same base and between the same parallels are equal to one another. 4. Enunciate the proposition which is represented in algebraical symbols by and give the construction... | |
 | 1902 - 482 pages
...line makes with another upon the same side of it are together equal to two right angles. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. 3. Prove that if one side of a triangle be produced, the exterior angle is greater than either of the... | |
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PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... 
