 | W. PEASE - 1846 - 86 pages
...form the isosceles triangle required. The reason of this is (Prob. XXXVII. Bk. I. Euclid,) because triangles upon the same base, and between the same parallels, are equal to one another : ie the triangles ACB and AE B, being upon the base, AB, to which the line EC is parallel, therefore... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...•=• parts. Wherefore the opposite sides and angles, &c. PROP. XXXIV. THEOR. 3s. lEu. Parallelograms upon the same base, and between the same parallels, are equal to one another. PROP. XXXIV. FADE F \ . If the sides AD, DF, of the 1=1™ ABCD, DBCF, opp. to BC the base, be terminated... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...two = parts. Wherefore the opposite sides and angles, &c. PROP. XXXIV. THEOR. 35. lEu. Parallelograms upon the same base, and be-tween the same parallels, are equal to one another. FA DEFAEDF \ . If the sides AD, DF, of the / — 7"" ABCD, DBCF, opp. to RC the base, be terminated... | |
 | Euclides - 1846 - 292 pages
...to the triangle DBC. Wherefore, Triangles %c. QED 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 BC, EF, and between the same parallels BF, AD : the triangle ABC shall be equal... | |
 | London univ - 1846 - 326 pages
...exterior angles of any rectilineal figure are together equal to four right angles. 6. Parallelograms upon the same base and between the same parallels are equal to one another. 7. Show that the complements of the parallelograms which are about the diameter of any .parallelogram... | |
 | Anthony Nesbit - Plane trigonometry - 1847 - 492 pages
...parallelogram ABCD, is equal to the parallelogram DBCE. (Euc. I. 35. Simp. II. 2. Em. HI. 6.) THEOREM VL Let the triangles ABC, DBC be upon the same base BC,...parallels AD, BC ; the triangle ABC is equal to the triangle DBC. (Euc. I. 37. Simp. II. 2. Em. II. 10.) THEOREM VH. Let ABC be a right-angled triangle,... | |
 | Euclides - 1847 - 128 pages
...KLNC (Ax.2) = Dm BMNC. Wherefore the sum of the areas &c. — QED PEOP. XXXVII. THEOR. GEN. ENUN. — Triangles upon the same base, and between the same parallels, are equal to one another. PART. ENUN. — Let the A ABC, DBC be upon the same base BC, and between the same || s AD, BC ; then... | |
 | Thomas Gaskin - Geometry, Analytic - 1847 - 301 pages
...CAMBRIDGE, Nov. 1847. GEOMETRICAL PROBLEMS. ST JOHN'S COLLEGE. DEC. 1830. (No. I.) 1. PARALLELOGRAMS upon the same base and between the same parallels are equal to one another. 2. Of unequal magnitudes,, the greater has a greater ratio to the same than the less. 3. If the diameter... | |
 | Great Britain. Committee on Education - 1848 - 606 pages
...point out how the construction fails when that condition is not fulfilled. 2. Prove that parallelograms upon the same base and between the same parallels are equal to one another. Shew hence that the area of a parallelogram is properly measured by the product of the numbers that... | |
 | Euclides - 1848 - 52 pages
...diameter bisects them, that is, divides them into two equal parts. PROP. XXXV. THEOREM. Parallelograms upon the same base, and between the same parallels, are equal to one another. PROP. XXXVI. THEOREM. PROP. XXXVII. THEOREM. Triangles upon the same base anti between the same parallels,... | |
| |
Parallelograms upon the same base and between the same parallels, are equal to one another. 
