 | 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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Parallelograms upon the same base and between the same parallels, are equal to one another. 
