 | Robert Potts - 1855 - 1050 pages
...times as great ? 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.... | |
 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...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 - 1856 - 168 pages
...BCD; therefore, the diameter BC divides the parallelogram into two equal parts. XXXVII. Parallelograms upon the same base and between the same parallels are equal to one another. Let the parallelograms ABCD, EBCF (Fig. 29) be upon the same base BC, and between the same parallels AF, BC... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...College. WILLIAM HENRY BESAHT, MA St John's College. TUESDAY, January 6, 1857. 9... 12. 1. PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another. ABC is an isosceles triangle, of which A is the vertex : AB, AC, are bisected in D and E respectively... | |
 | William Pease - 1856 - 108 pages
...to meet these perpendiculars, and the required rectangle will be formed. REASON : " Parallelograms, upon the same base, and between the same parallels," are equal to each other. (Euclid, Book I. Prop. 35.) PROBLEM LXX. To make a rectangle, one of its sides being given,... | |
 | Euclides - 1858 - 248 pages
...extensive use in the construction and measurement of Geometrical Figures. \ TO \ i / PROP. 37. — THEOR. Triangles upon the same base and between the same parallels are equal to one another. CONSTRUCTION. — Pst. 2. A st. line may be produced in a st. line. P. 31. Through a given point to... | |
 | War office - 1858 - 578 pages
...If the words printed above in italics be omitted, would the proposition as then stated be true ? 2. Triangles upon the same base, and between the same parallels, are equal to one another. Divide a given triangle into four equal parts. 3. "What is a rectangle ? If a straight line be divided... | |
 | Euclides - 1868 - 88 pages
...HC 4 P. 33. 5 Def. A. 6 D. 5. H. 7 P. 35. 8 P. 85. 9 Ax. 1. 10 Becap. • PilOP. XXXVII. Тикоа. Triangles upon the same base and between the same parallels are equal to one ano CON. Pst. 2. P. 31. Def. A. DEM. P. 35. 34. Ax. 7. SCHOL. PIIOP. XXXVIII. TIIEOU. Triangles upon... | |
 | Sandhurst roy. military coll - 1859 - 672 pages
...shall be greater than the base of the other. 2. Define a parallelogram ; prove that parallelograms upon the same base and between the same parallels are equal to one another. 3. If a straight line be divided into any two parts, the squares of the whole line and of one of the... | |
 | Robert Potts - Geometry, Plane - 1860 - 380 pages
...-BCdivides the parallelogram A CDB into two equal parts. QED PROPOSITION XXXV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms AB CD, EBCF be upon the same base 2? C, and between the same parallels AF, BC. Then... | |
| |
Parallelograms upon the same base and between the same parallels, are equal to one another. 
