 | 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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Triangles upon equal bases, and between the same parallels, are equal to one another. 
