 | Euclides - 1865 - 80 pages
...the same thing are equal to one another; therefore the parallelograms ABCD and EBCF are equal. Cor. Triangles upon the same base and between the same parallels are equal to one another; for the triangle ABC is (40) half the parallelogram ABCD, and the triangle FCB is half the parallelogram... | |
 | William Harris Johnston - 1865 - 478 pages
...respects oblique parallelograms abo. By Euclid, Book I, Prop. 35, it is established that «parallelograms upon the same base and between the same parallels are equal to one another." Now, the perpendicular distance, D С, between the sides, DF and В С, of the oblique parallelogram... | |
 | Architecture - 1865 - 276 pages
...Given the vertical angle, and a side to construct the triangle. 3. Prop. 35. Theorem. Parallelograms upon the same base and between the same parallels are equal to one another. Shew this is equally true of triangles. 4. Prop. 44. — Problem. To a given straight line to apply... | |
 | Euclides - 1865 - 402 pages
...BC divides the parallelogram ACI>B into two equal parts. QED PROP. XXXV.— THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to each other. (References— Prop. I 4, 29, 34 ; ax. 1, 3, 6.) Let the parallelograms ABCD, EBCF, be... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...two equal parts. Wherefore, the opposite aides &c. QED PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the parallelograms A BCD, EBCF be on the same base BC, and between the sameparallels AF,BC: the... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...two equal parts. Wherefore, the opposite sides &c. QED PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the sameparallels AF, BC : the... | |
 | 1868 - 876 pages
...triangle be produced, the exterior nngle is greater than cither of the interior opposite angles 15 i 2. Triangles upon the same base, and between the same parallels, are equal to one another 15 3. In any right -angled triangle, the square \rhieh is described upon the side subtending the right... | |
 | Ellis A. Davidson - Mechanical drawing - 1869 - 140 pages
...not necessarily be of the same shape to be of equal area, and by Euclid* (Book I., prop, xxxvii.), " Triangles upon the same base, and between the same parallels, are equal." If, therefore, lines be drawn from ABCDE and F to G, five triangles will be formed, having the same... | |
 | E. M. Reynolds - Geometry - 1868 - 172 pages
...the parallelogram A CBF. Then ACBF = DBCE. But ABC is half of ACBF; therefore of DBCE. THEOREM IV. Triangles upon the same base and between the same parallels are equal. For each is half of any parallelogram on that base and between those parallels. COR. 1. Triangles upon... | |
 | Ellis A. Davidson - 1869 - 136 pages
...construct an Oblong equal to it in area. 33. What is meant by Parallel Lines ? 34. Show by a Drawing that " Triangles upon the same Base and between the same Parallels are equal." 35. Draw any Triangle, and another equal to six of the first added together. 36. Fill a Square with.... | |
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TRIANGLES upon the same base, and between the same parallels, are equal to one another. 
