| 1857 - 488 pages
...PR be drawn to the extremities of the chord QR, which ii parallel to A It, then shall 6. Triangles **upon equal bases, and between the same parallels are equal to one another.** 7. Let ABC, AB D be two equal triangles on the same base AS, and on opposite sides of it; join CD,... | |
| Euclides - 1858 - 248 pages
...altitude, we obtain the square units, or units of surface, in the parallelogram. PROP. 36. — THEOR. **Parallelograms upon equal bases, and between the same parallels, are equal to one another.** CONSTRUCTION. — Pst. 1. A st. line may be drawn from any one point to any other point. DEMONSTRATION.... | |
| Euclides - 1868 - 88 pages
...Sul. DKM. 10 11 SCHoL. Ax. 2. 3. P. 34. P. 29. P. 4. Sub. Ax. 3. Recap. USE. Puor. XXXVI. THF.oII. **Parallelograms upon equal bases, and between the same parallels, are equal to one** anoti Coy. P*t. 1. DEM. P. 31. Ax. 1. P. 33. Def. AP 35. 60 PROP. XXXVI. UsE. Exp. 1 Hyp. 1. „ 2.... | |
| War office - 1858 - 578 pages
...in Euclid's First Book, in the proof of which, the property, printed above in italics, is used. 2. **Parallelograms upon equal bases and between the same parallels are equal to** each other. Show that the straight lines joining the points of bisection of the opposite sides of a... | |
| Sandhurst roy. military coll - 1859 - 672 pages
...bisect a given rectilineal angle, that is, to divide it into two equal angles. 2. Parallelograms on **equal bases, and between the same parallels, are equal to one another.** 3. In obtuse-angled triangles if a perpendicular be drawn from either of the acute angles to the opposite... | |
| Royal college of surgeons of England - 1860 - 336 pages
...angles ; and the three interior angles of every triangle are together equal to two right angles. 5. **Parallelograms upon equal bases and between the same parallels are equal to one another.** 6. If a straight line be divided into any two parts, the squares on the whole line and one of the parts... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...equal to the triangle DBC. Wherefore, triangles, &c. QED PROPOSITION XXXViII. THEOREM. T•iangles **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... | |
| Euclides - 1860 - 288 pages
...is (Ax. 3), the parallelogram ABCD is equal to the parallelogram EBCF. PROPOSITION XXXVI. THEOREM. **Parallelograms upon equal bases, and between the same -parallels, are equal to one another.** Givtn two parallelograms ABCD and EFGH upon equal bases BC and FG, and between the same parallels AH... | |
| Euclides - 1861 - 464 pages
...produced in a st. L. 3, I. From the gr. of two st. Ls. to cut off a pt. = the less. DEM. 38, 1. Triangles **upon equal bases and between the same parallels are equal to one another.** 1, V. Def. 5, V. The 1st of four Ms is said to have the same ratio to the 2nd which the 3rd has to... | |
| War office - 1861 - 714 pages
...why the product is not the square root of the product of 8 and •0002. EUCLID 1. Parallelograms on **equal bases and between the same parallels are equal to one another.** 2. If the square described on one of the sides of a triangle be equal to the squares described on the... | |
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