 | American Association for the Advancement of Science - 1899 - 648 σελίδες
...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... | |
 | Her MAjesty' Inspectors of schools - 1850 - 912 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | Euclides - 1853 - 146 σελίδες
...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... | |
 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...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 - 176 σελίδες
...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... | |
 | Thomas Lund - 1854 - 520 σελίδες
...the parallelogram ABCD shall be equal to the parallelogram EBCF. * EUCLID'S enunciation of this is ' Parallelograms upon the same base and between the same parallels are equal to one another'. By 4 base' is meant the side on which the parallelogram may be supposed to stand; and ' between the... | |
 | Robert Potts - 1855 - 1050 σελίδες
...? The line joining the bisections of two sides of a triangle is parallel to the base. 3. Triangles upon the same base, and between the same parallels are equal to one another. The lines joining the bisections of the sides of any quadrilateral figure, together constitute a parallelogram.... | |
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PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another... 
