 | Euclid, Thomas Tate - 1849 - 120 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 - 648 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 not show that the parallelograms can be divided into pairs of pieces admitting of superposition... | |
 | Cambridge Philosophical Society - Science - 1849 - 764 pages
...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 - 912 pages
...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,... | |
 | 582 pages
...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 - 152 pages
...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 - 48 pages
...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 - 400 pages
...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 - 146 pages
...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 - 176 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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PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... 
