 | Euclides - 1862 - 172 pages
...parallelogram E3CT. Therefore, parallelograms upon the same base, &c. QED PROP. XXXVI.— THEOREM. Parallelograms upon equal bases and between the same parallels are equal to one another. (References — Prop. i. 33, 34, 35; ax. 1.) Let ABCD, EFGH be parallelograms upon equal bases BC,... | |
 | Euclides - 1862 - 140 pages
...the triangle DBC. Conclusion. — Therefore, triangles, &c, QED PROPOSITION 38.— THEOREM. Triangles upon equal bases, and between the same parallels, are equal to one another. (References— Prop. I. 31, 34, 36; ax. 7.) Hypothesis. — Let the triangles ABC, DEF, be on equal... | |
 | Euclides - 1863 - 74 pages
...units, or uiiits of surface in the parallelogram. PROP. 36.— THEOR.— (A Corollary of the 35th). Parallelograms upon equal bases, and between the same parallels, are equal to one another. , CON.— Pst. 1.— DEM.— P. 34, Ax. 1, P. 33, Def. A, P. 35 Hyp. 1. Let the / — 7s ABCD, EFGH,... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...given point in a given straight line, make a rectilineal angle equal to a given rectilineal angle. 5. Parallelograms upon equal bases, and between the same parallels, are equal to one another. 6. Describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given... | |
 | Robert Potts - 1863 - 482 pages
...of an isosceles triangle be produced, the angles upon the other side of the base shall be equal. 9. Parallelograms upon equal bases and between the same parallels are equal to one another. A parallelogram has one side fixed, while the other sides move in such a manner that its area is- always... | |
 | Architecture - 1863 - 300 pages
...sides ; also by a line drawn perpendicular to one of the sides. 8. Proposition 38, Theorem ; Triangles upon equal bases and between the same parallels are equal to one another. 9. Divide an equilateral trianglo into four equal triangles. Book 2. 10. Proposition 7, Theorem ; It... | |
 | Euclides - 1864 - 262 pages
...the parallelogram-E.BCF. Therefore, parallelograms upon the same, &c. QED PROPOSITION XXXVI. THEOREM. Parallelograms upon equal bases and between the same parallels, are equal to one another. Let ABCD, EFGIfbe parallelograms upon equal bases BC, FG, and between the same parallels AH, BG. Then the parallelogram... | |
 | Woolwich roy. military acad - 1864 - 588 pages
...Find the present value of 1L due 12 years hence, when money bears 4^ per cent, compound interest. 9. Parallelograms upon equal bases and between the same parallels are equal to one another. other circle be described with centre C, chords of this latter which, produced if necessary, pa&s through... | |
 | Euclides - 1864 - 448 pages
...is equal to the triangle DBC. Wherefore, triangles, &c. QED PROPOSITION 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. Then the... | |
 | University of Cambridge - 1864 - 694 pages
...AB iť " sq. on AB," and for the rectangle contained by AB and CO, " the rect. AB, CD." 1. TRIANGLES upon equal bases and between the same parallels are equal to one another. If a quadrilateral figure have two sides parallel, and the parallel sides be bisected, the line joining... | |
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Triangles upon equal bases, and between the same parallels, are equal to one another. 
