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" TRIANGLES upon the same base, and between the same parallels, are equal to one another. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Seite 45
von Euclides - 1838
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - 1872
...ABCD and EFGH, being each equal to the parallelogram ABGH, Are equal to each other. PBOPOSITION XXXVU. Triangles upon the same base and between the same parallels are equal to each other. For the construction in this proposition we must be ableto draw a straight line from a...
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First book of mathematics

Hugo Reid - 1872 - 124 Seiten
...produced. 142. If ote. — This illustrates the important geometrical truth, that — Parallelograms on the same base and between the same parallels are equal to one another; that is, equal in area. Fic.34 AEFD and ABCD are on the same base AD and between the same parallels...
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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873
...decimals. (10.) 21 41 21 228 2000 _1824 1~7G, <fcc. (See Arith., § 61.) * 3. Show that parallelograms and triangles upon the same base and between the same parallels are equal to one another. (10.) (This appears to mean that parallelograms on the same base and between the same parallels are...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873
...and DEC is the half of DBCF ; therefore ABC is equal to DEC. XXXVIII. — 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. Produce AD both ways to the...
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Pure mathematics, Band 1

Edward Atkins - 1874
...same base, and between the same parallels, are equal to one anot/ier. Let the triangles ABC, DBC be on the same base BC, and between the same parallels AD, BC ; The triangle ABC shall be equal to the triangle DBC. CONSTRUCTION. — Produce AD both ways, to the points E, F. Through B draw BE...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...divides the parallelogram ACDB into two equal parts. ~ QED PROPOSITION 35. — Theorem. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be upon the same base BC, and between the same parallels AF, BC. Then the...
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Pure mathematics, Band 1

Edward Atkins - 1874
...two equal parts. Therefore, the opposite sides, <fec. QED Proposition 35. — Theorem. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms A BCD, EBCF be on the same base BC, and between the same parallels AF, BC; The parallelogram...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874
...The diagonals of a parallelogram bisect each other. PROPOSITION 35. THEOREM. Parallelograms on the same base, and between the same parallels, are equal to one another. .. Let the parallelograms ABCD, EBCFbe on the '• same base BC, and between the same parallels AF, BC: the parallelogram...
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Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874
...to a given straight line of unlimited length from a given point without it. 2. Parallelograms on the same base and between the same parallels are equal to one another. 3. If a straight line be bisected, and produced to any point, the rectangle contained by the whole...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 Seiten
...two equal parts. Therefore, the opposite sides, &c. QED Proposition 35. — Theorem. Parallelograms upon the same base, and between the same parallels, are equal to one another. Let the parallelograms ABCD, EBCF be on the same base BC, and between the same parallels AF, BC; The parallelogram...
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