| Thomas Lund - Geometry - 1854 - 522 pages
...FG is equal to that 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... | |
| John Playfair - Euclid's Elements - 1855 - 340 pages
...same EBCH : Therefore also the parallelogram ABCQ i* *qual to EFGH. PROP. XXXVII. THEOR. Trim gles **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 is equal to... | |
| Euclides - 1855 - 262 pages
...only which are at the vertices of any two of its opposite angles. PROP. XXXV. THEOREM. Parallelograms **upon the same base, and between the same parallels, are equal to one another. Let the** parallelograms AС, B Г be upon the same base B С, and and between the same parallels AF, BС. The... | |
| 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
...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,... | |
| 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 - 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... | |
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