 | Euclides - 1852 - 152 pages
...equal to the triangle DEC. Wherefore triangles, &c. QED OF EUCLID. PROP. XXXVIII. THEOR. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABC, DEF be upon equal bases EC, EF, and between the same parallels BF, AD: The triangle... | |
 | Euclides - 1853 - 146 pages
...ABC is equal to the triangle DBC. Wherefore, triangles, &c. QED PROP. XXXVIII. — 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. The triangle... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...the parallelogram DBCF, because the diameter DC bisects it : PROPOSITION XXXVIII. THEOR. 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 : the triangle... | |
 | Euclides - Geometry - 1853 - 176 pages
...parallelogram eb С f Therefore parallelograms upon the same base, &c. QED PROPOSITION XXXVI. — THEOREM. Parallelograms upon equal bases, and between the same parallels, are equal to one anotJier. a de ЬЕТ abСd, efgh, be parallelograms upon equal bases bС, fg, and between the same... | |
 | Thomas Lund - Geometry - 1854 - 520 pages
...parallelograms as the unit is contained in AB, and BEFC into as many as the unit is contained in BE. Then since parallelograms upon equal bases and between the same parallels are equal to one another (41 Cor. 1), the smaller parallelograms which make up ABCD, and BEFC, are all equal. Therefore the... | |
 | John Playfair - Euclid's Elements - 1855 - 340 pages
...equal (3. Ax.) that is, the parallelogram ABCD is equal to the parallelogram EBCF. PROP. XXXVI. THEOR. Parallelograms upon equal bases, and between the same...the same parallels AH, . BG ; the parallelogram ABCD -A- 1> is equal to EFGH. Join BE, CH ; and because BC is equal to FG, and FG to (34.1.) EH, BC is equal... | |
 | Euclides - 1855 - 270 pages
...upon the same base and on the same side of it, are between the same parallels. PROP. XXXVL THEOREM. Parallelograms upon equal bases and between the same parallels, are equal to one another. Let AC, EG be parallelograms upon equal bases BC, FG, and between the same parallels AH, BG. The parallelogram... | |
 | Cambridge univ, exam. papers - 1856 - 200 pages
...lines, make the alternate angles equal to each other, these two straight lines shall be parallel. 4. Parallelograms upon equal bases, and between the same parallels, are equal to one another. 6. If a straight line be divided into any two parts, the rectangle contained by the whole and one of... | |
 | Euclides - 1856 - 168 pages
...parallelogram DBCF (Prop. 37) ; wherefore the triangle ABC is equal to the triangle DEC. XL. Triangles upon equal bases and between the same parallels are equal to one another. Let the triangles ABC, DEF (Fig. 32) be upon equal bases BC, EF, and between the same parallels BF, A D.... | |
 | 1857 - 486 pages
...PR be drawn to the extremities of the chord QR, which ii parallel to A It, then shall 6. Triangles upon equal bases, and between the same parallels are equal to one another. 7. Let ABC, AB D be two equal triangles on the same base AS, and on opposite sides of it; join CD,... | |
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Parallelograms upon equal bases, and between the same parallels, are equal to one another. 
