| James Wharton - 1847
...and 6, the area = 9 . 6 = 54. By Euclid, Book I., Props. 35 and 36., it is seen that parallelograms **upon equal bases and between the same parallels are equal to one another,** which is, that the areas of all parallelograms are equal to that of a rectangular parallelogram with... | |
| Euclides - 1848
...XXXVII. THEOREM. Triangles upon the same base anti between the same parallels, are equal to one another. **PROP. XXXVIII. THEOREM. Triangles upon equal bases...between the same parallels, are equal to one another.** PROP. XXXIX. THEOREM. Equal triangles upon the same base and upon the same side of it, are between... | |
| J. Goodall, W. Hammond - 1848
...a circle, a sc alene triangle a rhomboid, and a trapezium. Section 2. 1. Prove that parallelograms **upon equal bases and between the same parallels are equal to one another.** 2. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal... | |
| Euclid, Thomas Tate - 1849 - 108 sider
...therefore the triangle ABC is equal to the triangle DBC. Wherefore triangles, &c. QED PROP. XXXVni. THEOR. **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 : The... | |
| Great Britain. Committee on Education - 1850
...• multiple, similar rectilineal figures, and duplicate ratio. 2. Prove Euc. I. 36. Parallelograms **upon equal bases, and between the same parallels, are equal to one another.** 3. Solve Euc. II. 11. To divide a given finite straight line into two parts, so that the rectangle... | |
| Harvey Goodwin - 1851 - 173 sider
...LEWIS HENSLEY, MA, Trinity College. JOHN SYKES, MA, Pembroke College. TUESDAY. Dec. 31. 9. ..12. 1. **TRIANGLES upon equal bases and between the same parallels are equal to one another.** Let ABC, ABD be two equal triangles upon the same base AB and on opposite sides of it ; join CD meeting... | |
| FRANCIS J. JAMESON - 1851
...between the same parallels,* are equal to one another. Hence AECD - ABCE - ABEA = AAED. 1851. (A]. **Triangles upon equal bases and between the same parallels are equal to one another,** (i. 38.) (E). Let ABC, ABD be two equal triangles upon the same base AB, and on opposite sides of it... | |
| 1867
...the vertices of all equal triangles ou the same base and on the same lide of it. 3. Parallelograms **upon equal bases, and between the same parallels, are equal to one another.** Trisect a parallelogram by lines drawn from a givtu point in one of its sides. SECTION IV. 1. Eqnal... | |
| Ralph Smyth, Sir Henry Edward Landor Thuillier - 1851 - 718 sider
...proved that ABCD being a parallelogram, AB = CD and AD =BC. THEO. XII. All parallelograms on the same or **equal bases and between the same parallels are equal to one another,** that is if BD — GH, and the lines BH and AF are parallel, then the paralellogram ABD C = BDFE = EFGH.... | |
| Euclides - 1852
...triangle ABC is equal to the triangle DEC. Wherefore triangles, &c. QED OF EUCLID. PROP. XXXVIII. THEOR. **Triangles upon equal bases, and between the same parallels, are equal to one another.** Let the triangles ABC, DEF be upon equal bases EC, EF, and between the same parallels BF, AD: The triangle... | |
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