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" Triangles upon equal bases, and between the same parallels, are equal to one another. "
The school Euclid: comprising the first four books, by A.K. Isbister - Side 43
av Euclides - 1862
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THE ELEMENTS OF DEDUCTIVE LOGIC

Thomas Fowler - 1887 - 365 sider
...which our deductive reasoning proceeds. The proposition proved in Euclid, Book i. Prop. 38, that ' Triangles upon equal bases, and between the same parallels, are equal to one another,' is derived from, or is the total result of, the previous deductions (i) that ' Parallelograms upon...
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Annual Report

Canada. Department of the Interior - 1888
...sides of the other, each to each, the triangles shall be eqnal in all respects. 2. Parallelograms on equal bases and between the same parallels are equal to one another. 3. If a straight line be divided into two equal, and also into two unequal parts, the squares on the...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - 1889
...angles. No straight line can be placed within a parallelogram greater than the greater diameter. 3. Triangles upon equal bases, and between the same parallels, are equal to one another. The line AD is drawn from the vertex of the isosceles triangle ABC perpendicular to the base, and is...
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Practical Plane Geometry: Giving the Simplest Modes of Constructing Figures ...

John Fry Heather - 1890 - 172 sider
...EQUIVALENT AND SIMILAR FIGURES. THEOREMS. 214. THEOR. 29. — Parallelograms and triangles upon the same or upon equal bases, and between the same parallels, are equal to one another. (Eu. I. 35 — 38.) 215. THEOR. 30. — If a parallelogram and a triangle be upon the same base and...
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The R.I.B.A. Kalendar [list of Members].

Royal Institute of British Architects - 1890
...rectilineal angle, ie, to divide it into two equal parts. (Euclid, Bk. 1, prop. 9). 11. Parallelograms upon equal bases and between the same parallels are equal to one another. (Euclid, Bk. 1, prop. 36).* Tuesday Afternoon: one hour and a half. GEOGEAPHY AND HISTORY. Hon. Examiner:...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...DBC is half of the ||gm DBCF, [I. 34. ... A ABC = ADBC. [Ax. 7. PROPOSITION 38. THEOREM. Triangles on equal bases and between the same parallels are equal to one another. Let ABC and DEF be As on equal bases, BC and EF, and between the same parallels BF and AD, then ABC...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 400 sider
...equal in area. Now A ABP = half a ABPX, and A ABQ = half a ABYQ ; /. A ABP = A ABQ. Proposition 38. THEOREM — Triangles upon equal bases, and between the same parallels, are equal in area. Let A» PAB, QCD be on equal bases AB, CD, and between the same ||" PQ, AD. Draw AX || to...
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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - 1891 - 79 sider
...Triangles on the same base and between the same parallels are equal to one another. 38. Triangles on equal bases and between the same parallels are equal to one another. 39. Equal triangles on the same base and on the same side of it are between the same parallels. 40....
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Pitman's Journal of Commercial Education, Volum 52

1893
...dates are chiefly produced, and where gold, coal, and tin are found. EUCLID (BOOKS I.-IV. )— (i) Triangles upon equal bases and between the same parallels are equal to one another. The base BC of the triangle ABC is bisected in D, and through B a line is drawn meeting AC in E and...
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Mining: A Journal Devoted to the Interests of Mines and Mining Students, Volum 2

1894
...EBCF be two parallelograms. Then ABCD is equal in area to EBCF. IX. Triangles upon the same base, or upon equal bases, and between the same parallels are equal to one another. Thus the triangle ABC, Fig. 25, is equal in area to the triangle DEF. X. A triangle is equivalent to...
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