 | Euclides - 1853 - 176 pagina’s
...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... | |
 | William Somerville Orr - 1854 - 534 pagina’s
...rectangles of their containing sides (AB-BC and DE'EF). Draw AG, DH, perpendiculars to BC, EF. Then because parallelograms on the same base and between the same parallels are equal, AC=AG'BC, and DF=DH-EF. Also the rectangles AG-BC, AB-BC having the same altitude BC, are to each other... | |
 | Thomas Lund - 1854 - 520 pagina’s
...ratio (170), and join DH. Then DHG is the triangle required. For BDC, BDF, being triangles upon the same base and between the same parallels, are equal to one another (41). Also A.ADE — &ADG; .'.adding to these equals the AABD, it is evident that ADGF = the polygon... | |
 | Great Britain. Committee on Education - 1855 - 976 pagina’s
...also their other angles equal, each to each, namely, those to which the equal sides are opposite, 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. In any triangle, if the square of one of the sides is equal to the squares of the two other sides,... | |
 | Euclides - 1855 - 270 pagina’s
...reduce it, by degrees, to an equivalent triangle. PROP. XXXVIII. THEOREM. Triangles upon equal bases, and between the same parallels, are equal to one another. Let the triangles ABС, DEF, he upon equal bases B С, EF, and between the same parallels BF, 'A D. The triangle... | |
 | Robert Potts - 1855 - 1050 pagina’s
...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.... | |
 | Euclides - 1856 - 168 pagina’s
...parallelogram EHGF ; wherefore EHGF is also equal to ABC D. XXXIX.— EUCLID I. 37. Triangles upon the same base and between the same parallels are equal to one another. Let the triangles ABC, DBC (Fig. 31) be upon the same base BC, and between the same parallels AD, BC ; the... | |
 | Cambridge univ, exam. papers - 1856 - 252 pagina’s
...two equal and parallel right lines towards the same parts, are also themselves equal and parallel. 6. Parallelograms on the same base and between the same parallels, are .equal to each other. 7. If a right line be divided into any two parts, the square of the whole line is equal... | |
 | Cambridge univ, exam. papers - 1856 - 200 pagina’s
...two interior angles upon the same side together equal to two right angles. 6. Parallelograms upon the same base, and between the same parallels, are equal to one another. 7. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal... | |
 | War office - 1858 - 578 pagina’s
...simple interest ? Euclid 1. The greater side of every triangle is opposite to the greater angle. 2. Parallelograms on the same base and between the same parallels are equal to one another. VOLUNTARY PORTION. (1 .) "When are two magnitudes said to be equimultiples of two other magnitudes.... | |
| |
Triangles upon the same base, and between the same parallels, are equal to one another. 
