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" Equal triangles on the same base, and on the same side of it, are between the same parallels. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 47
by Euclid, Rev. John Allen - 1822 - 494 pages
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 355 pages
...line joining their vertices bisects the base at right angles. Ex. 841. Two triangles ABC, DCB stand on the same base BC and on the same side of it; prove that AD is parallel to BC if AB = DC and AC = DB. Ex. 842. In the diagonal AC of a parallelogram...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 456 pages
...and on the same side of it. are between the same parallels. Let the triangles ABC, DBC which stand on the same base BC, and on the same side of it be equal in area. Then shall the triangles ABC, DBC be between the same parallels; that is, if AD be...
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Syllabus of Plane' Geometry: (corresponding to Euclid, Book I-VI) : Prepared ...

Cora Lenore Williams - Geometry - 1905 - 42 pages
...altitudes. Theor. N. Equal triangles on the same base, or on equal bases in the same straight line, and on the same side of it, are between the same parallels. Prop. 88. A trapezoid is equal to a rectangle whose base is half the sum of the two parallel sides,...
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Annual Report - Dept. of Education

Saskatchewan. Department of Education - Education - 1906
...triangle be bisected the bisector is parallel to the base. 3 (a) Equal triangles on the same base, and on the same side of -it, are between the same parallels. — I. 39. (6) In what sense are these triangles equal ? (c) Prove that the straight line joining the...
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Introduction and books 1,2

Euclid - Mathematics, Greek - 1908
...base and on the same side are also in the same parallels. Let ABC, DEC be equal triangles which are on the same base BC and on the same side of it ; s [I say that they are also in the same parallels.] And [For] let AD be joined ; I say that AD is...
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Intermediate Geometry: Being Sections V and VI of "geometry, Theoretical and ...

Walter Percy Workman - Geometry - 1908
...equal in area (Euc. /. 38) 188 Ar.Sc. — Equal triangles on equal bases in the same straight line, and on the same side of it, are between the same parallels (Euc. I. 40) 188 Loci. L.6. — The locus of the vertex of a triangle of given area and standing upon...
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A School Geometry, Parts 1-4

Henry Sinclair Hall - 1908
...an arc of a circle, of which the given base is the chord. Let BAC, BDC be two equal angles standing on the same base BC, and on the same side of it. It is required to prove that A and D lie on an arc of a circle having BC as its chord. Let ABC be the...
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Education in Scotland

Great Britain. Scottish Education Dept - 1896
...sides, what conclusion is to be drawn respecting the other angles ? 2. Equal triangles on the same base and on the same side of it are between the same parallels. ABC is a fixed triangle; find the locus of a point P which moves so that the sum of the triangles PAB,...
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mathematical problem papers

...10. Five rods in the same plane are smoothly jointed together in the form of two triangles ABC, DBG on the same base BC, and on the same side of it, AD being parallel to BG. The middle points of AC and BD are joined by a string at tension T. Shew that...
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Report of Her Majesty's Civil Service Commissioners: Together ..., Volumes 15-16

1870
...to make a rectilineal angle equal to a given rectilineal angle. 2. Equal triangles on the same base and on the same side of it, are between the same parallels. 3. Define a square. To describe a square that shall be equal to a given rectilineal figure. 4. To bisect...
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