| Euclid, Thomas Tate - 1849 - 108 pages
...the parallelogram ABCD is equal to EFGH. Wherefore parallelograms, &c. PHOP. XXXVII. THEOR. Triangles **upon the same base, 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 : The EADF triangle... | |
| American Association for the Advancement of Science - Science - 1899
...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 not show that the parallelograms can be divided into pairs of pieces admitting of superposition... | |
| Cambridge Philosophical Society - Science - 1849
...understood, and the proof being gone through, the truth of the proposition must be assented to. That **parallelograms upon the same base and between the same parallels are equal;** — that angles in the same segment are equal ; — these are propositions which we learn to be true... | |
| Her MAjesty' Inspectors of schools - 1850
...MENSURATION, AND TRIGONOMETRY. (Not more than one Question to be answered in each Section.) Section 1. 2. **Parallelograms upon the same base, and between the same parallels, are equal.** 1. When two straight lines intersect, the opposite anples are equal. . 3. J n an obtuse angled triangle,... | |
| ...advantages the towns possess in being situated as they are. EUCLID AND MECHANICS. First Year Student*. 1. **Parallelograms upon the same base and between the same parallels are equal to one another,** 2. If a straight line be divided into any two parts, the squares of the whol« line, and of one of... | |
| Euclides - 1852
...and the Proposition should be proved from it.] AEDH XXXV. 1. BOOK I. PROP. XXXVII. THEOR. Triangles **upon the same base, and between the same parallels, are equal to one another. Let the** triangles ABC, DEC be upon'the same base BC, and between the same parallels AD, BC : E The triangle... | |
| Euclides - 1852
...equal, the parallelogram is divided into two equal parts by the diagonal в c. WWD PBOP. XXXV. THEOB. **Parallelograms upon the same base and between the same parallels, are equal.** Let the parallelograms ABCDandEBCF, be on the same base в c, and between the same parallels AF and... | |
| Royal Military Academy, Woolwich - Mathematics - 1853
...is equal (1 Ax.) to EFGH. "Wherefore parallelograms, etc. QED PROPOSITION XXXVII. THEOR. Triangles **upon the same base, 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 : the triangle ABC... | |
| Euclides - 1853
...parallelogram ABCD is equal to EFGH. Wherefore, parallelograms, &c. QED PROP. XXXVII. THEOREM. Triangles **upon the same base 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. The triangle ABC... | |
| Euclides - Geometry - 1853 - 147 pages
...equal to efgh. Wherefore parallelograms, &c. QED PROPOSITION XXXVII. — THEOREM. Triangles upon tlie **same base, and between the same parallels, are equal to one another. LET 'the** triangles abС, dbС, be upon the same base bС and between the same parallels ad, bc The triangle... | |
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